United States

Department of 

Agriculture

Forest Service

Northern 

Research Station

General Technical

Report NRS-88

Methods and Equations for 

Estimating Aboveground 

Volume, Biomass, and 

Carbon for Trees in the 

U.S. Forest Inventory, 2010

Christopher W. Woodall

Linda S. Heath

Grant M. Domke

Michael C. Nichols

VOLUME

BIOMASS

&$5%21
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Manuscript received for publication 4 April 2011

Abstract

The U.S. Forest Service, Forest Inventory and Analysis (FIA) program uses numerous 

models and associated coefficients to estimate aboveground volume, biomass, and 

carbon for live and standing dead trees for most tree species in forests of the United 

States. The tree attribute models are coupled with FIA’s national inventory of sampled 

trees to produce estimates of tree growing-stock volume, biomass, and carbon, which are 

available in the Forest Inventory and Analysis database (FIADB; http://fi atools.fs.fed.us). To 

address an increasing need for accurate and easy-to-use documentation of relevant tree 

attribute models, needed individual tree gross volume, sound volume, biomass (including 

components), and carbon models for species in the United States are compiled and 

described in this publication with accompanying electronic fi les on a CD-ROM included with 

the publication. This report describes models currently in use as of 2010. These models are 

subject to change as the FIADB and associated tree attribute models are improved.

Cover and disk artwork courtesy of Suzy Stephens, U.S. Forest Service.

Printed on Recycled Paper
1

INTRODUCTION

Th e offi cial annual U.S. greenhouse gas (GHG) inventories contain forest 

carbon and other greenhouse gas estimates (e.g., see U.S. Environmental 

Protection Agency 2010) based on U.S. Forest Service’s, Forest Inventory and 

Analysis (FIA) program survey data, coupled with other basic models (Heath 

et al. 2010). Th e FIA program, through its regional units (Northern, Southern, 

Rocky Mountain, and Pacifi c Northwest; see USDA For Serv. 2011), is the 

primary provider of state-, regional-, and national-scale forest population 

estimates such as forest land area, and tree volume, growth, mortality, and 

removals. U.S. forest carbon inventories have used biomass estimates based on 

equations from Jenkins et al. (2003 and 2004), due to previous inconsistencies 

in tree biomass estimates between FIA regions (pre-2009). Estimates for a tree 

species in one region may have diff ered notably from estimates of the same 

species in another region. In 2009, FIA adopted a process for estimating tree 

biomass (Heath et al. 2009). Th is methodology is now consistently applied 

across the United States, with estimates reported in the publicly available 

Forest Inventory and Analysis database (FIADB; USDA For. Serv. 2010a).

With emerging carbon markets and growing interest in bioenergy at various 

scales across the United States, many individuals are interested not only in 

the models FIA uses for individual tree species, but also in adjusting models 

and associated coeffi cients for their own population estimates. Th e purpose of 

this report is to present in an accessible format the methodology and requisite 

equations for estimating attributes for most of the tree species in the United 

States. Until publication of this report, similar information had been only 

available for the southern (Oswalt and Conner 2011) and northern (Miles 

and Hill 2010) regions of the eastern United States. Th e volume and biomass 

attributes described in this paper and the conditions under which they are 

computed are described in the following tabulation. Carbon estimates follow 

directly from biomass estimates based on the assumption that biomass is 50 

percent carbon (Birdsey 1992).

Th e process of tree attribute estimation for all sample trees 5 inches in diameter 

and larger begins with the estimation of tree gross volume (VOLCFGRS) and 

tree sound volume (VOLCFSND). For the majority of tree species (nonwoodland trees where diameter is measured at 4.5 feet above ground; refer to 

REF_SPECIES.xlsx for woodland species designation) biomass and carbon 

by component (stump, bole and tops) are also estimated (Table 1). For all 

woodland trees (trees where diameter is measured at the root collar) biomass 

and carbon are estimated but are not broken down by component. For all 

sample trees between 1 to 4.9 inches in diameter only total biomass and 

carbon are estimated. Estimates of volume (VOLCFGRS and VOLCFSND) 

and breakdowns of total biomass and carbon into components are not made 

for trees < 5.0 inches in diameter. No estimates of volume, biomass, or carbon 

are made for sample trees where diameter is < 1.0 inch.

Th e Authors

CHRISTOPHER W. WOODALL 

is a research forester with the Forest 

Inventory and Analysis program of the 

U.S. Forest Service, St. Paul, MN.

LINDA S. HEATH is a research 

forester, U.S. Forest Service, Forest 

Inventory and Analysis, Durham, 

NH; currently on detail as Senior 

Forest Climate Change Specialist at 

the Global Environment Facility, 

Washington, DC.

GRANT M. DOMKE is a postdoctoral research forester with 

the Forest Inventory and Analysis 

program of the U.S. Forest Service, 

St. Paul, MN.

MICHAEL C. NICHOLS is a 

scientifi c programmer with the Forest 

Inventory and Analysis program of the 

U.S. Forest Service, Durham, NH.
2

Biomass for woodland species < 5.0 inches in diameter and saplings (non-woodland species 

between 1.0 to 4.9 inches in diameter) are estimated directly from the biomass equation in 

Jenkins et al. (2003 and 2004) using the observed diameter and a sapling adjustment factor. 

Biomass for woodland species ≥ 5.0 inches diameter is based on volume estimates for the entire 

aboveground portion of the sample tree with no component breakdown.

Volume, biomass, and carbon models for tropical trees (e.g., species in Puerto Rico or Hawaii) 

are not included in this report. Th is compilation does not necessarily refl ect the ideal system for 

estimating an array of tree attributes (e.g., volume and carbon) that are additive among 

individual tree components (i.e., scalable tree attributes from components to whole tree) and 

consistent across diverse forest conditions at a national scale (i.e., do not arbitrarily change at 

political boundaries). Rather, this system refl ects an eff ort to meld localized tree volume/

biomass information into a consistent, national approach. We suggest that future research focus 

on consistent national-scale individual tree volume/biomass/carbon equations that 

accommodate the diversity of tree habitats (e.g., woodlands or tropics) and conditions (e.g., 

sound or rotten).

Table 1.—Volume and biomass components estimated by FIA for live and standing dead trees

Non-woodland species:

Diameter is measured at 

4.5 feet above ground

Woodland species:

Diameter is measured at root 

collar

Less than 1.0 inches in diameter No estimates of volume or biomass

1.0 to 4.9 inches in diameter No estimate of volume

Sapling biomass =

Total aboveground biomass

Biomass of woodland species =

Total aboveground biomass

5.0 inches in diameter and larger Gross volume

Sound volume

(Stump wood biomass +

Stump bark biomass +

Bole wood biomass +

Bole bark biomass +

Top and branch biomass) =

Total aboveground biomass

Gross volume

Sound volume

Biomass of woodland species =

Total aboveground biomass
3

METHODS FOR BIOMASS ESTIMATION

Th e approach used for nationally consistent biomass estimation of non-sapling and nonwoodland trees in the FIADB is called the component ratio method (CRM; Heath et al. 

2009). CRM entails 1) measuring attributes of the tree in the fi eld; 2) applying those tree 

measurements to the applicable volume model to compute both gross cubic-foot volume 

(VOLCFGRS) and sound cubic-foot volume (VOLCFSND) of wood in the bole; 3) converting 

the sound cubic-foot volume (VOLCFSND) of wood in the bole to mass and estimating bark 

biomass using compiled sets of specifi c gravity (Miles and Smith 2009); 4) calculating the 

biomass of tops and limbs as a proportion of the bole based on component proportions from 

Jenkins et al. (2003); 5) calculating stump volume based on equations in Raile (1982) and 

converting to biomass, and 6) summing all aboveground components for a total aboveground 

biomass estimate.

Th e use of CRM requires the calculation of VOLCFSND. Because VOLCFSND is based on 

gross cubic-foot volume (VOLCFGRS) for many areas of the country, VOLCFGRS must also 

be calculated. It should be noted that FIA calculates many types of volumes of interest to a 

range of user groups including: total stem volumes (calculated for all trees ≥1.0-inch d.b.h.), 

cubic-foot volumes up to various top diameters (e.g., 4-, 6-, or 8-inch tops), and board-foot 

volumes using Scribner or International 1⁄4 inch volume rules (for defi nitions see Helms 1998). 

Th e CRM is based on VOLCFGRS and VOLCFSND; only those volume equations are 

compiled in this study (Appendix A).

Th e fi ve general steps for calculation of tree (d.b.h. ≥ 5.0 inches) oven-dry mass (lb) are: 

1) Obtain needed tree and plot or condition measurements using FIA protocols (e.g., tree 

diameter, rotten and missing cull, site index, height, basal area)

2) Calculate VOLCFGRS

3) Calculate VOLCFSND (i.e., subtract rotten or missing from VOLCFGRS)

4) Convert VOLCFSND to bole biomass

5) Calculate additional biomass components (e.g., tops and limbs, stump) that are 

summed for total biomass

Note that estimation procedures are diff erent for saplings (d.b.h. ≥ 1.0 inch and < 5.0 inches). 

Sapling biomass is based on biomass computed from Jenkins et al. (2004) using the observed 

diameter and an adjustment factor—computed as a national average ratio of the CRM total 

biomass divided by the Jenkins et al. (2003 and 2004) total biomass for all 5.0-inch trees, 

which is the size at which biomass based on volume begins (Heath et al. 2009). At this time 

estimation procedures are not diff erent for standing dead trees. Users of this documentation 

should consider adopting decay and structural reduction factors for standing dead trees such 

as those currently under development by FIA (Domke et al. in press). Such information could 

reduce any potential upward bias of estimating standing dead wood volume/biomass using live 

tree procedures.

Th e steps for biomass calculation are described for each component separately in the Biomass 

Calculations section of this report. We also provide example calculations for a live growing-
4

stock tree, a live rough cull tree, a standing dead tree, and a small diameter tree for comparison 

and reference. Th e text refers to appendices where volume equations are presented; coeffi cients 

for the equations and species-specifi c information can be found in the companion spreadsheets 

(volcfgrs_eqn_coefs.xlsx, volcfsnd_eqn_coefs.xlsx, and REF_SPECIES.xlsx) on the CD included 

in this report.

Tree Measurements

Field protocols for FIA are found in USDA For. Serv. (2010b). Th e diameter of most tree 

species is measured at d.b.h., except in the case of woodland tree species where it is measured 

at d.r.c. Species information, including species names, codes, diameter type, wood and bark 

specifi c gravity, bark percentage, sapling adjustment factors, Jenkins et al. (2004) biomass 

coeffi cients, and Raile (1982) stump volume coeffi cients can be found in the REF_SPECIES 

table in FIADB, the original publications cited in this document, or on the CD included with 

this report. Models may diff er by state or ecoregion within a state, thus location of the tree is 

important. See Figure 1 for defi nition of areas for model determination. Other information that 

may be needed includes site index, height, bole height, percent of cubic-foot volume rotten or 

missing, percent of sound dead cull as a percentage of merchantable bole, and number of stems 

(for trees measured at d.r.c.). For standing dead trees, a decay class is determined for each tree, 

but is not currently used in estimation procedures (USDA For. Serv. 2010b).

Gross Volume Estimation

Gross cubic-foot volume is defi ned as “the total volume inside bark of the central stem of a 

tree ≥5.0 inches d.b.h. from a 1-foot stump to a minimum 4-inch top diameter outside bark 

(d.o.b.), or to where the central stem breaks into limbs all of which are less than 4.0 inches 

d.o.b.” (Woudenberg et al. 2010). Gross volume includes rotten and missing parts and form 

cull. Rotten and missing cubic-foot cull volume is estimated to the nearest 1 percent in the fi eld. 

Th is estimate does not include any cull deduction above actual length so volume lost from a 

broken top is not included. Form cull is the percent of the cubic-foot volume that is cull due to 

form defect, and is only collected at some locations. Gross volume is set to null (not available) 

if d.b.h. is not available. Usually, if d.b.h. is < 5.0 inches, gross volume is set to null, with the 

possible exception of woodland tree species (i.e., d.r.c.) in Rocky Mountain and Southern States.

Th e form of the models to calculate VOLCFGRS are listed by FIA unit (i.e., Northern or 

Southern) and sub-unit model region (i.e., eastern MT or western MT; Fig. 1) in Appendices 

A and B (see CD for model coeffi cients), along with the reference for each model. Unless 

otherwise noted, the b values in these tables are regression parameter estimates and the x values 

are the observed attributes. Th e bold text indicates conditions that should be met regarding the 

observed attributes. Th e values for the coeffi cients are given in the VOLCFGRS spreadsheet 

provided on a CD in this report. To fi nd the appropriate model and coeffi cients for the tree 

species and location, use the following steps:

1) To calculate VOLCFGRS, locate the species-specifi c equation for the region of interest 

found in Tables 1-4 of Appendix A and Table 6 of Appendix B.

2) Find species-specifi c coeffi cients (denoted by the letter b, as in b1, b2, etc.) in the 

spreadsheet volcfgrs_eqn_coefs.xlsx.
5

3) In the volcfgrs_eqn_coefs spreadsheet, locate the regional confi g worksheet for the 

area of interest. Th ey are designated as follows: NCCS – North Central Central States; 

NCLS – North Central Lake States; NCPS – North Central Plains States; NE – 

Northeastern States; AZ_N_NM_N – northern Arizona and northern New Mexico; 

AZ_S_NM_S – southern Arizona and southern New Mexico; CO_E_WY_E – eastern 

Colorado and eastern Wyoming; CO_W_WY_W – western Colorado and western 

Wyoming; ID_MTW – Idaho and western Montana; MT_E – eastern Montana; 

NV – Nevada; UT_NE – northern and eastern Utah; UT_SW – southern and 

western Utah; S – Southern States; CA – California (except mixed conifer forest type); 

CA_MC – California mixed conifer forest type; OR_E – eastern Oregon; OR_WA – 

western Oregon; OR_JJ – Oregon (Jackson and Josephine Counties); WA_E – eastern 

Washington; WA_W – western Washington; and WA_CF – Washington (highelevation silver fi r region).

4) Find the row corresponding to the particular species; the sheet is ordered by species 

number (Column C). For a list of all species with common and scientifi c names, refer 

to the worksheet ref_species_reduced. Th e column COEF_TABLE contains the name 

Figure 1.—Delineated areas for identifi cation of gross cubic-foot growing stock volume models and coefficients from the 

spreadsheet fi le. Further description is given in U.S. Forest Service (2010b; Appendix c).
6

of the table which has the coeffi cients for this species. Th e column COEF_TBL_SP 

contains the species number you should look for in the table.

5) Insert the appropriate coeffi cients and the tree-specifi c variables into the equation from 

step 1 to estimate VOLCFGRS.

Sound Volume Estimation

Sound cubic-foot volume is the volume of sound wood in the central stem of a tree ≥ 5.0 

inches diameter from a 1-foot stump to a minimum 4-inch top d.o.b., or to where the central 

stem breaks into limbs, all of which are less than 4.0 inches d.o.b. Note that in some instances 

VOLCFSND may be 0 or null and the VOLCFGRS is > 0 in FIADB. In those cases, biomass is 

calculated using VOLCFGRS adjusted for the percentage sound. When both VOLCFSND and 

VOLCFGRS are 0 or null, biomass is calculated using net cubic-foot volume (VOLCFNET) 

adjusted for the percentage sound (Woudenberg et al. 2010).

Th e form of the models to calculate VOLCFSND from VOLCFGRS are listed by FIA 

region in Table 5 of Appendix A (see CD for model coeffi cients; see Appendix C for Alaska 

VOLCFSND algorithm), along with the reference for the model. Unless noted, the b values in 

these tables are regression parameter estimates and the x values are the observed attributes. Th e 

bold text indicates conditions that should be met regarding the observed attributes. To fi nd the 

appropriate model and coeffi cients for the tree species and location, use the following steps: 

1) To calculate VOLCFSND, locate the appropriate equation in Appendix A, Table 5 

(see Appendix C for Alaska VOLCFSND algorithm). Only a few of the equations use 

species-specifi c coeffi cients (denoted by the letter b, as in b1, b2, etc.). If the applicable 

volume equation you want to use contains these coeffi cients, they may be found in the 

Excel spreadsheet volcfsnd_eqn_coefs.xlsx

2) In the volcfsnd_eqn_coefs spreadsheet, locate the regional confi g worksheet for the 

area of interest. Th ey are designated as follows: NCCS – North Central Central States; 

NCLS – North Central Lake States; and NCPS – North Central Plains States. Th e 

column COEF_TABLE contains the name of the table containing the coeffi cients for 

this species. Th e column COEF_TBL_SP contains the species number you should look 

for in the table

3) Insert the appropriate coeffi cients (if present), the tree-specifi c variables and the 

VOLCFGRS (calculated in step 5 under Gross Volume Estimation) into the equation 

from step 1 in this section to estimate VOLCFSND.

Biomass Calculations

Biomass of bole

Biomass in the bole of a species is calculated by multiplying the VOLCFSND by weight of 1 

cubic foot of water (62.4 lb) to convert volume to mass, and then multiplying by the specifi c 

gravity of wood and bark, separately for the species listed in Miles and Smith (2009). For a 

complete list of specifi c gravities for all tre species in FIADB, please refer to REF_SPECIES.xlsx 

included in this publications’s CD-ROM. Th e specifi c gravities of bark and wood are diff erent. 
7

Th e bark component includes an additional term, bark as a proportion of wood volume, so the 

two components must be calculated separately and then summed.

Bole wood biomass:

 Bodw = Vgw * SGgw * W (eq. 1)

where

Bodw = oven-dry biomass (lb) of wood

Vgw = VOLCFSND of green wood in the central stem

SGgw = basic specifi c gravity of wood (oven-dry mass of green volume)

W = weight of ft3 of water (62.4 lb)

Bark biomass:

 Bodb = Vgw * BV% * SGgb * W (eq. 2)

where

Bodb = oven-dry biomass (lb) of bark

Vgw = VOLCFSND of green wood in the central stem

BV% = bark as a percentage of wood volume 

SGgb = basic specifi c gravity of bark (oven-dry mass of green volume)

W = weight of ft3 of water (62.4 lb)

Total bole (bole and bark) biomass (DRYBIO_BOLE):

 Bodt = Bodw + Bodb (eq. 3)

where

Bodw = oven-dry biomass (lb) of wood

Bodb = oven-dry biomass (lb) of bark

Bodt = total oven-dry bole biomass (lb) in wood and bark

Biomass of tree components

Biomass in the stumps and tops and limbs of trees ≥ 5.0 inches d.b.h. is estimated as a 

proportion of CRM bole biomass (eq. 3) using component ratios from Jenkins et al. (2004) and 

Raile (1982). All tree components derived from Jenkins et al. (2004) and Raile (1982) must be 

multiplied by an adjustment factor to estimate CRM biomass.

CRM adjustment factor:

CRMAdjFac = Bodt/MST (eq. 4)

where

CRMAdjFac = component ratio method adjustment factor for tree components derived from 

Jenkins et al. (2003) and Raile (1982)

Bodt = total oven-dry biomass (lb) (eq. 3)

MST = merchantable oven-dry bole biomass (lb) (Jenkins et al. 2004)

Biomass in the stump of a species is estimated using volume equations developed by Raile 

(1982), converting volume to mass by multiplying by the specifi c gravity of wood and bark 

(Miles and Smith 2009) and by 1 cubic foot of water (62.4 lb), and fi nally multiplying by the 

CRM adjustment factor (eq. 4).
8

Stump volume:

 Svosb or visb = ߨሺܾ݄݀ሻଶ

ͶሺͳͶͶሻ ൤൬ሺܣ െ ܤሻଶ݄ ൅ ͳͳܤሺܣെܤሻሺ݄൅ͳሻ െ ͵ͲǤʹͷ݄൅ͳܤଶ൰൨ ܾ

ܽ

 (eq. 5)

where

Svosb or visb = stump volume inside bark (visb) or outside bark (vosb) (ft3)

A = Coeffi cient (species parameter) from Table 2 in Raile (1982)

B = Coeffi cient (species parameter) from Tables 1 and 2 in Raile (1982)

h = height above ground (ft)

ln = natural logarithm

a = lower stump height (ft) – 0 ft in FIADB

b = upper stump height (ft) – 1 ft in FIADB

For stump volume estimates outside (vosb) the bark, A should be set to 1 and the species 

parameter (B) in Table 1 should be used. For stump volume estimates inside the bark (visb), 

Table 2 in Raile (1982) should be used for both coeffi cients.

Stump wood biomass:

 Sodsw = Svisb * SGgw * W (eq. 6)

where 

Sodsw = oven-dry biomass (lb) of stump wood

Svisb = stump volume inside the bark (eq. 5)

SGgb = basic specifi c gravity of wood (oven-dry mass of green volume)

W = weight of ft3of water (62.4 lb)

Stump bark biomass:

 Sodsb = (Svosb – Svisb)SGgb * W (eq. 7)

where 

Sodsb = oven-dry biomass (lb) of stump bark 

Svosb = volume (ft3) of stump outside the bark (eq. 5)

Svisb = volume (ft3) of stump inside the bark (eq. 5)

SGgb =basic specifi c gravity of bark (oven-dry mass of green volume)

W = weight of ft3 of water (62.4 lb)

Total stump (wood and bark) biomass (DRYBIO_STUMP):

 Sodt = (Sodsw + Sodsb)CRMAdjFac (eq. 8)

Where

Sodt = oven-dry stump biomass (lb) 

Bodw = oven-dry biomass (lb) of wood (eq. 6)

Bodb = oven-dry biomass (lb) of bark (eq. 7)

CRMAdjFac = component ratio method adjustment factor (eq. 4)

Th e tops and limbs component ratio is calculated by subtracting the total aboveground biomass 

estimate from Jenkins et al. (2004) from the aboveground biomass components for that species 

in Jenkins et al. (2004)—foliage, stem bark and wood, and stump (from Raile 1982)—and 

multiplying by the CRM adjustment factor (eq. 4).
9

Top and branch biomass:

Todt = (TAB – MST – STP – FOL)CRMAdjFac (eq. 9)

where

Todt = oven-dry biomass (lb) of top and branches 

TAB = total aboveground oven-dry biomass (lb) (Jenkins et al. 2004)

MST = merchantable stem oven-dry biomass (lb) (Jenkins et al. 2004)

STP = stump oven-dry biomass (lb) (Raile 1982)

FOL = foliage oven-dry biomass (lb) (Jenkins et al. 2004) 

CRMAdjFac = component ratio method adjustment factor (eq. 4)

Biomass of saplings

Biomass of saplings (trees < 5.0 inches d.b.h.) is based on estimates from Jenkins et al. (2004) 

on the observed diameter multiplied by a sapling adjustment factor. Th e adjustment factors 

currently used are computed as a national average ratio of the CRM total biomass divided by 

the total biomass from Jenkins et al. (2004) for all 5.0-inch trees, which is the size at which 

biomass-based volume begins. Each species group has an adjustment factor listed in Heath et al. 

(2009), and which can be found in the REF_SPECIES fi le on the CD.

Sapling biomass (DRYBIO_SAPLING):

 Sapodt = (TAB – FOL)Sapadj (eq. 10)

where

Sapodt = oven-dry sapling biomass (lb)

TAB = total aboveground oven-dry biomass (lb) (Jenkins et al. 2004)

FOL = foliage oven-dry biomass (lb) (Jenkins et al. 2004)

Sapadj = sapling adjustment factor (Heath et al. 2009)

Biomass of woodland species (DRYBIO_WDLD_SPP)

Woodland species are defi ned as those sample trees where diameter is measured at root collar 

(Woudenberg et al. 2010). Woodland species biomass for stems < 5.0 inches d.r.c. is estimated 

in the same way as sapling biomass is estimated. Woodland species ≥ 5.0 inches in diameter 

have a volume estimate from ground to tip, which is used to estimate total aboveground 

biomass in the same way bole biomass is calculated.

Biomass of standing dead trees

Standing dead biomass is computed in the same manner as live tree biomass. Standing dead 

trees, like live trees, can have rotten and missing cull which is deducted when converting 

VOLCFGRS to VOLCFSND. Future research into decay and structural reductions based on 

a tree’s decay class is suggested as a way to reduce potential overestimates of volume/biomass 

(Domke et al. in press).
10

EXAMPLES

We present example calculations for using the CRM to estimate aboveground biomass and 

carbon for 10.5-inch growing stock, rough cull, and standing dead quaking aspen trees and 

a 4.5-inch quaking aspen sapling in the North Central - Lake States (NCLS) region. Each 

example refl ects actual sample trees in the FIADB. Species information including specifi c 

gravity values for wood and bark, bark percentage estimates, sapling adjustment factors and 

biomass model coeffi cients are found in the publications cited in this report, FIADB in the 

REF_SPECIES table, or in the REF_SPECIES.xlsx workbook on CD. Each biomass equation 

used in the examples is referenced back to the original text description in this document 

where coeffi cients are described and the original citation is provided. Note that values in these 

examples may vary slightly from FIADB values due to rounding.

Example 1: Volume, biomass, and carbon calculations for a live growing-stock tree

Example tree information: live (STATUSCD = 1) growing stock (TREECLCD = 2) quaking 

aspen (SPCD = 746) that is 10.5 inches d.b.h.

1. Gross volume (VOLCFGRS)

V1 = top diameter outside bark = 4 inches

V2 = predicted bole length = b12 + b13

௕భలሺܾଵ଻ െ ௏భ

௫భ

ሻ௕భఴݔଷ

௕భవ ሺͳ െ݁ି௕భర௫భሻ௕భఱݔଶ = 4.5 

+ 6.4301(1 – e-0.23545*10.5)

1.338 * 660.4737(1.00001 – 4.5/10.5)0.73385 * 72.530.08228 = 

46.11 ft

x1 = d.b.h. = 10.5 inches

x2 = site index = 66 ft

x3 = basal area of live trees on plot/condition = 72.53 ft2

VOLCFGRS = (b0 + b1x1 + b2V1 + b3x1

2 + b4x12V2 + b5V22 + b6V2V12 + b7x12V23 + 

b8x1

2V22V1)b9(b10 + b11x1) / 100 = (0.0030086 + 0.0020355*10.5 + -0.0030018*4 

+ 0.000062381*10.52 + 0.000025705*10.52*46.11 + -0.000007009*46.112 + 

0.000036708*46.11*42 + 0.000000000814*10.52*46.113 + -0.0000000019*10.52*4

6.112*4)79(91.51 + 0.37*10.5) / 100 = 12.74 ft3

2. Sound volume (VOLCFSND)

VOLCFSND = VOLCFGRS(1 - ௕భ௕మ

ଵ଴଴ ) = 12.74(1- ହǤଶכ଴Ǥଵ

ଵ଴଴ ) =12.68 ft3

3. Bole biomass (DRYBIO_BOLE)

Bolewood biomass (eq. 1): Bodw = Vgw * SGgw * W = 12.68 * 0.35 * 62.40 = 276.89 lb

Bole bark biomass (eq. 2): Bodb = Vgw * BV% * SGgb * W = 12.68 * 0.144 * 0.5 * 62.4 

= 56.96 lb

Total bole biomass (eq. 3): Bodt = Bodw + Bodb = 276.89 + 56.96 = 333.85 lb

4. Component ratio method adjustment factor (CRMAdjFac)

CRM adjustment factor (eq.4): CRMAdjFac = ஻೚೏೟

ெௌ் = ଷଷଷǤ଼ହ

ସସସǤ଼଻ = 0.75

5. Stump volume and biomass (DRYBIO_STUMP)

Stump volume (eq. 5): Svosb = గ(ௗ௕௛)మ

ସ(ଵସସ) ቂቀ(ܣെܤ(ଶ݄ + 11ܤ)ܣെܤ(ln(݄ + 1) െ ଷ଴.ଶହ

௛ାଵ

ܾ ଶቁቃܤ

ܽ

 = 

గ(ଵ଴.ହ)మ

ସ(ଵସସ) ቂቀ(1 െ 0.09658)ଶ1 + 11 כ 0.09658)1 െ 0.09658)ln(1+1) െ ଷ଴.ଶହ

ଵାଵ 0.09658ଶቁ െ

ቀ(1 െ 0.09658)ଶ0 + 11 כ 0.09658)1 െ 0.09658)ln(0+1) െ ଷ଴.ଶହ

଴ାଵ 0.09658ଶቁቃ = 0.97565 ft3
11

Svisb = గ(ଵ଴.ହ)మ

ସ(ଵସସ) ቂቀ(0.91882 െ 0.08593)ଶ1 + 11 כ 0.08593)0.91882 െ 0.08593)ln(1+1) െ

ଷ଴.ଶହ

ଵାଵ 0.08593ଶቁ െ ቀ(0.91882 െ 0.08593)ଶ0 + 11 כ 0.08593)0.91882 െ 0.08593)ln(0+1) െ

ଷ଴.ଶହ

଴ାଵ 0.08593ଶቁቃ = 0.81243 ft3

Stump wood biomass (eq. 6): Sodsw = Svisb * SGgw * W = 0.81243 * 0.35 * 62.4 = 17.74 lb

Stump bark biomass (eq. 7): Sodsb = (Svosb – Svisb)SGgb * W = (0.97565 - 0.81243)0.5 *

62.4 = 5.09 lb

Total stump biomass (eq. 8): Sodt = (Sodsw + Sodsb)CRMAdjFac = (17.74 + 5.09)0.75 = 

17.14 lb

6. Top and branch biomass (DRYBIO_TOP)

Top and branch biomass (eq. 9): Todt = (TAB – MST – STP – FOL) CRMAdjFac = 

(612.75 – 444.87 – 22.84 – 12.90)0.75 = 99.17 lb

7. Total aboveground biomass (CRM)

Total aboveground biomass = Bodt + Sodt + Todt = 333.85 + 17.14 + 99.17 = 450.16 lb

8. Total aboveground carbon (CARBON_AB)

Total aboveground carbon = (Bodt + Sodt + Todt) * 0.5 = (333.85 + 17.14 + 99.17)0.5 = 

225.08 lb

Example 2: Volume, biomass, and carbon calculations for a live rough cull tree 

Example tree information: live (STATUSCD = 1) rough cull (TREECLCD = 3) quaking aspen 

(SPCD = 746) sample tree that is 10.5 inches d.b.h.

1. Gross volume (VOLCFGRS)

V1 = top diameter outside bark = 4 inches

V2 = predicted bole length = b12 + b13 (1 െ ݁ି௕భర௫భ)௕భఱݔଶ

௕భల(ܾଵ଻ െ ௏భ

௫భ

)௕భఴݔଷ

௕భవ = 4.5 

+ 6.4301(1 – e-0.23545*10.5)

1.338 * 730.4737(1.00001 – 4.5/10.5)0.73385 * 82.27.08228 = 

48.59 ft

x1 = d.b.h. = 10.5 inches

x2 = site index = 73 ft

x3 = basal area of live trees on plot/condition = 82.27 ft2

VOLCFGRS = (b0 + b1x1 + b2V1 + b3x1

2 + b4x12V2 + b5V22 + b6V2V12 + b7x12V23 + 

b8x1

2V22V1)b9(b10 + b11x1) / 100 = (0.0030086 + 0.0020355*10.5 + -0.0030018*4 

+ 0.000062381*10.52 + 0.000025705*10.52

*48.59 + -0.000007009*48.592 + 

0.000036708*48.59*42 + 0.000000000814*10.52

*48.593 + -0.0000000019*10.52*48.

592

*4)79(91.51 + 0.37*10.5) / 100 = 13.36 ft3

2. Sound volume (VOLCFSND)

VOLCFSND = VOLCFGRS(1 - ܾଵܾଶ

100 ) = 13.36(1- ଶଵ.଼כ଴.ଵହ

ଵ଴଴ ) = 12.92 ft3

3. Bole biomass (DRYBIO_BOLE)

Bolewood biomass (eq. 1): Bodw = Vgw * SGgw * W = 12.92 * 0.35 * 62.40 = 282.17 lb

Bole bark biomass (eq. 2): Bodb = Vgw * BV% * SGgb * W = 12.92 * 0.144 * 0.5 * 62.4 

= 58.05 lb
12

Total bole biomass (eq. 3): Bodt = Bodw + Bodb = 282.17 + 58.05 = 340.30 lb

4. Component ratio method adjustment factor (CRMAdjFac)

CRM adjustment factor (eq.4): CRMAdjFac = ஻೚೏೟

ெௌ் = ଷସ଴.ଷ଴ସସସ.଼଻

 = 0.76

5. Stump volume and biomass (DRYBIO_STUMP)

Stump volume (eq. 5): Svosb = గ(ௗ௕௛)మ

ସ(ଵସସ) ቂቀ(ܣെܤ(ଶ݄ + 11ܤ)ܣെܤ(ln(݄ + 1) െ ଷ଴.ଶହ

௛ାଵ ܤଶቁቃ ܾ

ܽ

= 

గ(ଵ଴.ହ)మ

ସ(ଵସସ) ቂቀ(1 െ 0.09658)ଶ1 + 11 כ 0.09658)1 െ 0.09658)ln(1+1) െ ଷ଴.ଶହ

ଵାଵ 0.09658ଶቁ െ ቀ(1 െ

0.09658)ଶ0 + 11 כ 0.09658)1 െ 0.09658)ln(0+1) െ ଷ଴.ଶହ

଴ାଵ 0.09658ଶቁቃ = 0.97565 ft3

Svisb = గ(ଵ଴.ହ)మ

ସ(ଵସସ) ቂቀ(0.91882 െ 0.08593)ଶ1 + 11 כ 0.08593)0.91882 െ 0.08593)ln(1+1) െ

ଷ଴.ଶହ

ଵାଵ 0.08593ଶቁ െ ቀ(0.91882 െ 0.08593)ଶ0 + 11 כ 0.08593)0.91882 െ 0.08593)ln(0+1) െ

ଷ଴.ଶହ

଴ାଵ 0.08593ଶቁቃ = 0.81243 ft3

Stump wood biomass (eq. 6): Sodsw = Svisb * SGgw * W = 0.81243 * 0.35 * 62.4 = 17.74 lb

Stump bark biomass (eq. 7): Sodsb = (Svosb – Svisb)SGgb * W = (0.97565 - 0.81243)0.5 *

62.4 = 5.09 lb

Total stump biomass (eq. 8): Sodt = (Sodsw + Sodsb)CRMAdjFac = (17.74 + 5.09)0.76 = 

17.47 lb

6. Top and branch biomass (DRYBIO_TOP)

Top and branch biomass (eq. 9): Todt = (TAB – MST – STP – FOL) CRMAdjFac = 

(612.75 – 444.87 – 22.84 – 12.90)0.76 = 101.09 lb

7. Total aboveground biomass (CRM)

Total aboveground biomass = Bodt + Sodt + Todt = 340.30 + 17.47 + 101.09 = 458.86 

lbs

8. Total aboveground carbon (CARBON_AB)

Total aboveground carbon = (Bodt + Sodt + Todt) * 0.5 = (340.30 + 17.47 + 101.09)0.5 

= 229.43 lb

Example 3: Volume, biomass, and carbon calculations for a standing dead tree

Example tree information: live (STATUSCD = 2) rough cull (TREECLCD = 4) quaking aspen 

(SPCD = 746) sample tree that is 10.5 inches d.b.h.

1. Gross volume (VOLCFGRS)

V1 = top diameter outside bark = 4 inches

V2 = predicted bole length = b12 + b13 (1 െ ݁ି௕భర௫భ)௕భఱݔଶ

௕భల(ܾଵ଻ െ ܸଵ

ଵݔ

)௕భఴݔଷ

௕భవ = 4.5 +

 6.4301(1 – e-0.23545*10.5)

1.338 * 730.4737(1.00001 – 4.5/10.5)0.73385 * 78.33.08228 = 

48.42 ft

x1 = d.b.h. = 10.5 inches

x2 = site index = 73 ft

x3 = basal area of live trees on plot/condition = 78.33 ft2

VOLCFGRS = (b0 + b1x1 + b2V1 + b3x1

2 + b4x12V2 + b5V22 + b6V2V12 + b7x12V23 + 

b8x1

2V22V1)b9(b10 + b11x1) / 100 = (0.0030086 + 0.0020355*10.5 + -0.0030018*4 
13

+ 0.000062381*10.52 + 0.000025705*10.52

*48.42 + -0.000007009*48.422 + 

0.000036708*48.42*42 + 0.000000000814*10.52

*48.423 + -0.0000000019*10.52*48.

422

*4)79(91.51 + 0.37*10.5) / 100 = 13.32 ft3

2. Sound volume (VOLCFSND)

VOLCFSND = VOLCFGRS(1 - ௕భ௕మ

ଵ଴଴ ) = 13.32(1- ଺ଵ.଼כ଴.଻ହ

ଵ଴଴

) = 7.14 ft3

3. Bole biomass (DRYBIO_BOLE)

Bolewood biomass (eq. 1): Bodw = Vgw * SGgw * W = 7.14 * 0.35 * 62.40 = 155.94 lbs

Bole bark biomass (eq. 2): Bodb = Vgw * BV% * SGgb * W = 7.14 * 0.144 * 0.5 * 62.4 = 

32.10 lb

Total bole biomass (eq. 3): Bodt = Bodw + Bodb = 155.92 + 32.10 = 188.12 lb

4. Component ratio method adjustment factor (CRMAdjFac)

CRM adjustment factor (eq.4): CRMAdjFac = ஻೚೏೟

ெௌ் = ଵ଼଼.ଵଶସସସ.଼଻

 = 0.42

5. Stump volume and biomass (DRYBIO_STUMP)

Stump volume (eq. 5): Svosb = గ(ௗ௕௛)మ

ସ(ଵସସ) ቂቀ(ܣെܤ(ଶ݄ + 11ܤ)ܣെܤ(ln(݄ + 1) െ ଷ଴.ଶହ

௛ାଵ

ܾ ଶቁቃܤ

ܽ

= 

గ(ଵ଴.ହ)మ

ସ(ଵସସ) ቂቀ(1 െ 0.09658)ଶ1 + 11 כ 0.09658)1 െ 0.09658)ln(1+1) െ ଷ଴.ଶହ

ଵାଵ 0.09658ଶቁ െ ቀ(1 െ

0.09658)ଶ0 + 11 כ 0.09658)1 െ 0.09658)ln(0+1) െ ଷ଴.ଶହ

଴ାଵ 0.09658ଶቁቃ = 0.97565 ft3

Svisb = గ(ଵ଴.ହ)మ

ସ(ଵସସ) ቂቀ(0.91882 െ 0.08593)ଶ1 + 11 כ 0.08593)0.91882 െ 0.08593)ln(1+1) െ

ଷ଴.ଶହ

ଵାଵ

 0.08593ଶቁ െ ቀ(0.91882 െ 0.08593)ଶ0 + 11 כ 0.08593)0.91882 െ 0.08593)ln(0+1) െ

ଷ଴.ଶହ

଴ାଵ

 0.08593ଶቁቃ = 0.81243 ft3

Stump wood biomass (eq. 6): Sodsw = Svisb * SGgw * W = 0.81243 * 0.35 * 62.4 = 17.74 lb

Stump bark biomass (eq. 7): Sodsb = (Svosb – Svisb)SGgb * W = (0.97565 - 0.81243)0.5 *

62.4 = 5.09 lb

Total stump biomass (eq. 8): Sodt = (Sodsw + Sodsb)CRMAdjFac = (17.74 + 5.09)0.42 = 

9.66 lb

6. Top and branch biomass (DRYBIO_TOP)

Top and branch biomass (eq. 9): Todt = (TAB – MST – STP – FOL) CRMAdjFac = 

(612.75 – 444.87 – 22.84 – 12.90)0.42 = 55.88 lb

7. Total aboveground biomass (CRM)

Total aboveground biomass = Bodt + Sodt + Todt = 188.12 + 9.66 + 55.88 = 253.66 lbs

8. Total aboveground carbon (CARBON_AB)

Total aboveground carbon = (Bodt + Sodt + Todt) * 0.5 = (188.12 + 9.66 + 55.88)0.5 = 

126.83 lb

Example 4: Biomass and carbon calculations for a sapling or woodland species (< 5 

inches in diameter)

Example tree information: a live (STATUSCD = 2) quaking aspen (SPCD = 746) sapling that 

is 4.5 inches d.b.h.

1. Biomass (eq. 10): Sapodt = (TAB – FOL)Sapadj = (81.10 – 1.71)0.69089 = 54.85 lb
14

CONCLUSION

Th is publication and accompanying electronic fi les on a CD-ROM present for the fi rst time 

in one report FIA’s volume models and methods to estimate volume, biomass, and carbon for 

trees in forests across the United States. Where applicable, emerging areas of research have been 

noted with continued refi nement of FIA’s modeling/estimation procedures expected in the 

future.

ACKNOWLEDGMENTS

Many individuals contributed directly and indirectly to the creation of this report. Th ere has 

been no intentional omission of authorship in this document; rather, authorship has been 

accorded to those directly contributing to and accepting responsibility for this publication. 

Special thanks are extended to those who have spent countless hours with database 

development, documentation, and sleuthing the origins of volume equations across the Nation: 

Kurt Campbell, Glenn Christensen, Mark Hansen, Mark Hatfi eld, Elizabeth LaPoint, Patrick 

Miles, Christopher Oswalt, and Karen Waddell.

LITERATURE CITED

Birdsey, R.A. 1992. Carbon storage and accumulation in United States forest ecosystems.

Gen. Tech. Rep. WO-59. Washington, DC: U.S. Department of Agriculture, Forest Service. 

51 p.

Domke, G.M.; Woodall, C.W.; Smith, J.E. In press. Accounting for density reduction and 

structural loss in standing dead trees: Implications for forest biomass and carbon stock 

estimates in the United States. Carbon Balance and Management.

Heath, L.S.; Hansen, M.H.; Smith, J.E.; Smith, W.B.; Miles, P.D. 2009. Investigation into 

calculating tree biomass and carbon in the FIADB using a biomass expansion factor 

approach. In: McWilliams, W.; Moisen, G.; Czaplewski, R., comps. 2008 Forest Inventory 

and Analysis (FIA) Symposium; 2008 October 21-23; Park City, UT. Proc. RMRS-P56CD. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain 

Research Station. 1 CD.

Heath, L.S.; Nichols, M.C.; Smith, J.E.; Mills, J.R. 2010. FORCARB2: An updated version 

of the U.S. forest carbon budget model. Gen. Tech. Rep. NRS-67. Newtown Square, PA: 

U.S. Department of Agriculture, Forest Service, Northern Research Station. 52 p.

Helms, J.A. 1998. Th e dictionary of forestry. Bethesda, MD: Th e Society of American 

Foresters. 210 p.

Jenkins, J.C.; Chojnacky, D.C.; Heath, L.S.; Birdsey, R.A. 2003. National scale biomass 

estimators for United States tree species. Forest Science. 49(1): 12-35.

Jenkins, J.C.; Chojnacky, D.C.; Heath, L.S.; Birdsey, R.A. 2004. Comprehensive database 

of diameter-based biomass regressions for North American tree species. Gen. Tech. 
15

Rep. NE-319. Newtown Square, PA: U.S. Department of Agriculture, Forest Service, 

Northeastern Research Station. 45 p. [1 CD-ROM].

Miles, P.D.; Smith, W.B. 2009. Specifi c gravity and other properties of wood and bark for 

156 tree species found in North America. Res. Note NRS-38. Newtown Square, PA: U.S. 

Department of Agriculture, Forest Service, Northern Research Station. 35 p.

Miles, P.D.; Hill, A.D. 2010. Volume equations for the Northern Research Station’s Forest 

Inventory and Analysis program as of 2010. Gen. Tech. Rep. NRS-74. Newtown Square, 

PA: U.S. Department of Agriculture, Forest Service, Northern Research Station. 50 p.

Oswalt, C.M.; Conner, R.C. 2011. Southern forest inventory and analysis volume equation 

user’s guide. Gen. Tech. Rep. SRS-138. Asheville, NC: U.S. Department of Agriculture, 

Forest Service, Southern Research Station. 22 p.

Raile, G.K. 1982. Estimating stump volume. Res. Pap. NC-224. St. Paul, MN: U.S. 

Department of Agriculture, Forest Service, North Central Forest Experiment Station. 7 p.

U.S. Department of Agriculture, Forest Service. 2010a. Forest inventory and analysis 

national program - data and tools - FIA data mart, FIADB Version 4.0. Washington, 

DC: U.S. Department of Agriculture, Forest Service. Available at http://199.128.173.17/

fi adb4-downloads/datamart.html. (Accessed 15 December 2010).

U.S. Department of Agriculture, Forest Service. 2010b. National core fi eld guide, Volume 

1: Field data collection procedures for phase 2 plots, version 4.0 and Addendum.

Washington, DC: U.S. Department of Agriculture, Forest Service. Available at http://fi a.

fs.fed.us/library/fi eld-guides-methods-proc/docs/core_ver_4-0_10_2007_p2.pdf. (Accessed 

15 December 2010).

U.S. Department of Agriculture, Forest Service. 2011. Forest Inventory and Analysis: Fiscal 

year 2010 Business Report. FS-976. Washington, DC: U.S. Department of Agriculture, 

Forest Service. 73 p.

U.S. Environmental Protection Agency. 2011. Inventory of US greenhouse gas emissions and 

sinks: 1990-2009. EPA 430-R-11-005 Washington, DC: U.S. Environmental Protection 

Agency. 459 p.

Woudenberg, S.W.; Conkling, B.L.; O’Connell, B.M.; LaPoint, E.B.; Turner, J.A.; Waddell, 

K.L. 2010. Th e Forest Inventory and Analysis Database: Database description and users 

manual version 4.0 for Phase 2. Gen. Tech. Rep. RMRS-GTR- 245. Fort Collins, CO: 

U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station. 339 p.
16
17

Appendices Printed in this Report

Appendix A.—Gross and sound cubic-foot volume equation forms for the Northern, Southern, 

Rocky Mountain, and Pacifi c Northwest (excluding AK) regions.

Appendices and Accompanying Excel Files Included on 

CD-ROM

Appendix B.—Alaska gross cubic-foot volume equation forms 

Appendix C.—Alaska sound cubic-foot volume algorithm

volcfsnd_eqn_coefs.xlsx 

volcfgrs_eqn_coefs.xlsx 

REF_SPECIES.xlsx

Selection of Previously Published Studies Cited in this 

Report and Included on CD-ROM

Publications cited in body of GTR:

Birdsey 1992: gtr_wo059

Heath et al. 2009: rmrs_p056_heath.pdf

Jenkins et al. 2004: ne_gtr319.pdf

Miles and Smith 2009: rn_nrs38.pdf

Raile 1982: rp_nc224.pdf

Volume equation publications:

Chittester and MacLean 1984: pnw_rn420.pdf

Curtis et al. 1968: pnw_rp056.pdf

Hahn 1984: rp_nc250.pdf

Hahn and Hansen 1991: Hahn_and_Hansen_1991.pdf

Larson and Winterberger 1988: pnw_rn478.pdf

Pillsbury and Kirkley 1984: pnw_rn414.pdf

Scott 1981: ne_rn304.pdf
18

APPENDIX A

Gross cubic-foot volume equation forms for the Northern, Southern, Rocky Mountain, and Pacifi c Northwest 

(excluding AK) regions. (dbh = diameter at breast height, drc = diameter at root collar, ht = total height)

Table 1.—Gross cubic-foot volume (VOLCFGRS) equation forms for the Northern region

Region/States 

(species codea

)

Form of the model:

VOLCFGRS = f(x1,x2,....,xn)

Observed items: 

(x1,x2,....,xn)

Referenceb

North Central - IA, IL, 

IN, MO (all species 

except 66) KS, ND, NE, 

SD (all species except 66 

and 122)

IF x2 = NULL

 VOLCFGRS = NULL

OTHERWISE

 VOLCFGRS = b1ݔଶ

௕మ(1 - ݁௕య௫భ

್ర

)

(IF VOLCFGRS < 0, SET TO 0)

x1 = dbh

x2 = site index

Hahn and 

Hansen 

1991

North Central - MI, MN, 

WI (all species except 66)

IF x2 = NULL OR x3 = NULL

 VOLCFGRS = NULL

OTHERWISE

 VOLCFGRS = (b0 + b1x1 + b2V1 + b3x1

2

+ b4x1

2V2 + b5V22 + b6V2V12 + b7x12V23 + 

b8x1

2V22V1)b9(b10 + b11x1) / 100,

Where V1 = top diameter outside bark = 4

And V2 = predicted bole length = b12 + b13 

(1 െ ݁ି௕భర௫భ)௕భఱݔଶ

௕భల(ܾଵ଻ െ ܸଵ

ଵݔ

)௕భఴݔଷ

௕భవ

(IF VOLCFGRS < 0, SET TO 0)

x1 = dbh

x2 = site index;

if x2 < 20, set to 20; if x2

> 120, set to 120

x3 = basal area of live 

trees on plot/condition;

if x3 < 50, set to 50; if x3

> 350, set to 350

Hahn 1984

North Central, All States 

(66)

IF V1 <= b3

 VOLCFGRS = b0 + b1V1 + b2V1

2

OTHERWISE

 VOLCFGRS = b0 + b1V1 + b2(3b3

2 – 

(2b3

3/V1)),

Where V1 = x1

2x210-3

(IF VOLCFGRS <= 0, SET TO 0.1)

x1 = drc

x2 = ht

Chojnacky 

1994

North Central - KS, ND, 

NE, SD (122)

IF x1

2x2 <= b1

 VOLCFGRS = b2 + b3x1

2x2

IF x1

2x2 > b1

 VOLCFGRS = b4 + b5x1

2x2

(IF VOLCFGRS <= 0, SET TO 0.1)

x1 = dbh

x2 = ht

Myers 

1964b

Northeast – All States (all 

species)

IF x2 = NULL

 VOLCFGRS = NULL

OTHERWISE

 VOLCFGRS = b0 + b1ݔଵ

௕మ + b3ݔଵ

௕రݔଶ௕ఱ

x1 = dbh

x2 = bole height

Scott 1981

a Species numbers refer to the codes used by FIA (Woudenberg et al. 2010)

b References in Tables 1-4 of Appendix A are listed in a separate Literature Cited section at the end of the Appendix.
19

Table 2.—Gross cubic-foot volume (VOLCFGRS) equation forms for the Southern region

Region/States 

(species codea

) 

Form of the model:

VOLCFGRS = f(x1,x2,....,xn)

Observed items:

(x1,x2,....,xn)

Referenceb

South, All States 

(All Species other than 

those listed below)

IF x1 >= 5 AND x2 ≠ NULL)

 VOLCFGRS = b0 + b1x1

2x2

OTHERWISE

 VOLCFGRS = NULL

x1 = dbh

x2 = ht

Unknown

South, All States (58, 59, 

69, 106, 140, 141)

IF V1 <= b3

 VOLCFGRS = b0 + b1V1 + b2V1

2

OTHERWISE

 VOLCFGRS = b0 + b1V1 + b2(3b3

2 – (2b33/V1)),

Where V1 = x1

2x210-3

(IF VOLCFGRS <= 0, SET TO 0.1)

x1 = drc

x2 = ht

Chojnacky 

1994

South, All States 

(61, 63, 66, 303, 321, 

755, 756, 758, 810, 843, 

846, 867, 8513)

IF V1 <= b6

 VOLCFGRS = b1 + b2V1 + b3V1

2

OTHERWISE

 VOLCFGRS = b4 + b2V1 – (b5/V1),

Where V1 = x1

2x210-3

(IF VOLCFGRS <= 0, SET TO 0.1)

x1 = drc

x2 = ht

Chojnacky 

1988

South, All States (122) IF x1 < 21

 VOLCFGRS = (b1 + b2x1

2x2) – (b3 + b4

௏భ

య௫మ

௫భ್ఱ + b6x1

2)

Where V1 = top diameter outside bark = 4

OTHERWISE

 VOLCFGRS = (b7 + b8x1

2x2) – (b9 + b10

௏భ

య௫మ

௫భ್భభ + b12x1

2)

Where V1 = top diameter outside bark = 4

(If VOLCFGRS <= 0 AND x1 >= 1, SET VOLCFGRS 

TO 0.1)

x1 = dbh

x2 = ht

Hann and 

Bare 1978

South, All States (202) VOLCFGRS = (b1 + b2x1

2x2) – (b3 + b4

௏భ

య௫మ

௫భ್ఱ + b6x1

2),

Where V1 = top diameter outside bark = 4

(IF VOLCFGRS <= 0 AND x1 >= 1, SET VOLCFGRS 

TO 0.1)

x1 = dbh

x2 = ht

Hann and 

Bare 1978

a Species numbers refer to the codes used by FIA (Woudenberg et al. 2010)

b References in Tables 1-4 of Appendix A are listed in a separate Literature Cited section at the end of the Appendix.
20

Table 3.—Gross cubic-foot volume (VOLCFGRS) equation forms for the Rocky Mountain region

Region/States (species codea

) Form of the model:

VOLCFGRS = f(x1,x2,....,xn)

Observed 

items: 

(x1,x2,....,xn)

Referenceb

AZ (All), NM (All), UT (SouthWest) (15, 17, 18, 19, 20, 21, 22, 

93, 94, 96, 101, 102, 104, 108, 

113, 114, 142, 202, 351, 352, 

353, 374, 375, 746)

RMRS, All States (103)

VOLCFGRS = (b1 + b2x1

2x2) – (b3 + b4

૚ࢂ૛࢞૜

૚࢞

࢈ ૞+ b6x1

2),

Where V1 = top diameter outside bark = 4

(IF VOLCFGRS <= 0 AND x1 >= 1, SET VOLCFGRS 

TO 0.1)

x1 = dbh

x2 = ht

Hann and 

Bare 1978 

CO (All), NV, UT (North-East), 

WY (All) (15, 17, 18, 19, 20, 21, 

22, 93, 94, 96, 101, 102, 108, 

113, 114, 142, 202, 351, 352, 

353, 374, 375, 746)

CO (East), MT (East), WY (East) 

(51, 112, 116, 118, 122, 135, 

137, 231)

CO (All), NV, WY (All) (104)

IF x1

2x2 <= b5

 VOLCFGRS = b1 + b2x1

2x2

IF x1

2x2 > b5

 VOLCFGRS = b3 + b4x1

2x2

(IF VOLCFGRS <= 0 AND x1 >= 1, SET VOLCFGRS 

TO 0.1)

x1 = dbh

x2 = ht

Myers 1964a,

Myers and 

Edminster 

1972,

Myers 1964b, 

Edminster et 

al. 1982

ID, MT (All) (Species 15, 17, 20, 

21, 22, 72, 73, 101, 102, 104, 

108, 113, 114, 142, 202)

ID, MT (West) (51, 112, 116, 

118, 122, 135, 137, 231)

AZ (South), CO (West), ID, 

MT (All), NM (South), NV, WY 

(West) (117, 119)

VOLCFGRS = V1 – (V1(b1(( ௏మ

௕మ

)௕య ݔଵ ൗ ௕ర))),

Where V1 = b5ݔଵ

௕లݔଶ௕ళ

 And V2 = top diameter outside bark = 4

(IF VOLCFGRS <= 0, SET TO 0.1)

x1 = dbh

x2 = ht

Moisen 

unpublished 

(1989)

ID, MT (All) (18, 19, 81, 93, 

94, 96, 351, 352, 353, 374, 375, 

746)

AZ (South), CO (All), ID, MT 

(All), NM (South), UT (All), WY 

(All) (242,263,264)

RMRS, All States (741, 742, 745, 

747, 748, 749)

IF x1

2x2 <= b5 OR (x1 < 21 AND b5 = 0)

 VOLCFGRS = b1 + b2x1

2x2

OTHERWISE

 VOLCFGRS = b3 + b4x1

2x2

(IF VOLCFGRS <= 0, SET TO 0.1)

x1 = dbh

x2 = ht

Kemp

(1956)

continued
21

continued

AZ (All), NM (All), UT (SouthWest) (51, 112, 116, 118, 122, 

135, 137, 231)

IF x1 < 21

 VOLCFGRS = (b1 + b2x1

2x2) – (b3 + b4

௏భ

య௫మ

௫భ

್ఱ + b6x1

2)

Where V1 = top diameter outside bark = 4

OTHERWISE

 VOLCFGRS = (b7 + b8x1

2x2) – (b9 + b10

௏భ

య௫మ

௫భ್భభ + b12x1

2)

Where V1 = top diameter outside bark = 4

(IF VOLCFGRS <= 0 AND x1 >= 1, SET VOLCFGRS 

TO 0.1)

x1 = dbh

x2 = ht

Hann and 

Bare 1978

CO (West), NV, UT (NorthEast), WY (West) (51, 112, 116, 

118, 122, 135, 137, 231)

IF x1 ≥ 5

 VOLCFGRS = b0 + b1x1

2x2

OTHERWISE

 VOLCFGRS = NULL

(IF VOLCFGRS <= 0 AND VOLCFGRS IS NOT 

NULL, SET TO 0.1)

x1 = dbh

x2 = ht

Edminster et 

al. 1980

RMRS, All States (Species 58, 

59, 62, 63, 65, 66, 69, 106, 134, 

140, 143)

IF V1 <= b3

 VOLCFGRS = b0 + b1V1 + b2V1

2

OTHERWISE

 VOLCFGRS = b0 + b1V1 + b2(3b3

2 – (2b33/V1)),

Where V1 = x1

2x210-3

(IF VOLCFGRS <= 0, SET TO 0.1)

x1 = drc

x2 = ht

Chojnacky 

1994

ID, MT (All), NV (64) VOLCFGRS = ((V1 + b1) / (b2 + b3݁௕ర௫భ)) + b5,

Where V1 = b6x1

2(b7 + b8x2 – (b9x1x2 / (x2 + b10))x2(x2/

(x2 + b10))2 -- if V1 <= 0, set V1 to 2

(IF VOLCFGRS <= 0, SET TO 1)

x1 = 

MIN(dbh,60)

x2 = ht

Chittester 

and MacLean 

1984

RMRS, All States (68, 130, 136, 

313, 361, 362, 404, 461, 462, 

492, 544, 547, 552, 602, 606, 

732, 823, 826, 901, 972, 974)

IF (SPECIES < 300 AND x1 < 9) OR

 (SPECIES >= 300 AND x1 < 11)

 VOLCFGRS = b1 + b2x1

2x2

OTHERWISE 

 VOLCFGRS = b3 + b4x1

2x2

(IF VOLCFGRS <= 0 OR x2 = NULL OR x1 < 5, SET 

VOLCFGRS TO 0.1)

x1 = dbh

x2 = ht

Unknown 

Table 3.—continued

Region/States (species codea

) Form of the model:

VOLCFGRS = f(x1,x2,....,xn)

Observed 

items: 

(x1,x2,....,xn)

Referenceb
22

RMRS, All States (133, 475) IF (x1 >= 3 AND x2 > 0 AND x3 = 1)

 VOLCFGRS = (b0 + b1(ݔଵ

ଶݔଶ)௕మ + b3)

3

IF (x1 >= 3 AND x2 > 0 AND x3 ≠ 1)

 VOLCFGRS = (b0 + b1(ݔଵ

ଶݔଶ)௕మ)

3

OTHERWISE

 VOLCFGRS = 0.1

(IF VOLCFGRS <= 0, SET TO 0.1)

x1 = drc

x2 = ht

x3 = # of 

stems

Chojnacky 

1985

AZ (All), NM (All) (322, 814)

RMRS, All States (756, 757, 758, 

803, 810, 829, 843, 846, 847)

IF (V1 <= b6)

 VOLCFGRS = b1 + b2V1 + b3V1

2

OTHERWISE

 VOLCFGRS = b4 + b2V1 – (b5/V1),

Where V1 = x1

2x210-3

(IF VOLCFGRS <= 0, SET TO 0.1)

x1 = drc

x2 = ht

Chojnacky 

1988

CO (All), ID, MT (All), NV, UT 

(All), WY (All) (322, 814)

IF (x1 >= 3 AND x2 > 0 AND x3 = 1)

 VOLCFGRS = (b0 + b1(ݔଵ

ଶݔଶ)௕మ + b3)

3

IF (x1 >= 3 AND x2 > 0 AND x3 ≠ 1)

 VOLCFGRS = (b0 + b1(ݔଵ

ଶݔଶ)௕మ)

3

OTHERWISE

 VOLCFGRS = 0

(IF VOLCFGRS < 0, SET TO 0.1)

x1 = drc

x2 = ht

x3 = # of 

stems

Chojnacky 

1985

a Species numbers refer to the codes used by FIA (Woudenberg et al. 2010)

b References in Tables 1-4 of Appendix A are listed in a separate Literature Cited section at the end of the Appendix.

Table 3.—continued

Region/States (species codea

) Form of the model:

VOLCFGRS = f(x1,x2,....,xn)

Observed 

items: 

(x1,x2,....,xn)

Referenceb
23

Table 4.—Gross cubic-foot volume (VOLCFGRS) equation forms for the Pacifi c Northwest region

Region/States 

(species codea

)

Form of the model:

VOLCFGRS = f(x1,x2,....,xn)

Observed 

items: 

(x1,x2,....,xn)

Referenceb

CA (All), OR (All), WA (All) (11, 

42, 93, 98, 231, 242, 352)

OR (East), WA (All) (15)

OR (All), WA (All) (17, 19, 22, 73, 

101, 108, 119)

OR (East) (20)

CA (All) (41, 251, 746, 747, 748, 

760, 766, 768)

WA (All) (72)

CA (All), OR (All), WA (East) (92)

OR (All), WA (West) (103)

OR (West & JJ) (113, 130)

OR (East & West) (341) 

CA (All), OR (East & JJ), WA (All) 

(351) 

CA (except Mixed-Conifer) (611)

VOLCFGRS = ((10௕భݔଵ

௕మݔଶ௕యܾସ) / ((b5(1 + b6݁

௕ళ

ೣభ

భబ

))(b8x1

2 + b9) + b10))((b11x12 – b9) / b4)

x1 = dbh

x2 = ht

Brackett 

1973,

Browne 1962

CA (All) (Species 14, 19, 22)

CA (All), OR (West & JJ) (20)

CA (All), OR (All) (21)

VOLCFGRS = b1x1

2x2V1,

Where V1 = b2 + b3

௫మ

௫భ

 

 

 -- if V1 > 0.4, set to 0.4; if V1 < 

0.3, set to 0.3

x1 = 

MAX(dbh,6)

x2 = ht

MacLean and 

Berger 1976

CA (All), OR (West & JJ) (15)

CA (All) (17)

VOLCFGRS = b1x1

2x2V1,

Where V1 = b2 + b3x2

-1 + b4

௫మ

మ

௫భ

 

 

 -- if V1 > 0.4, set to 

0.4; if V1 < 0.3, set to 0.3

x1 = 

MAX(dbh,6)

x2 = ht

MacLean and 

Berger 1976

OR (All), WA (All) (41)

CA (All) (50, 51, 54, 55)

CA (except Mixed-Conifer) (52, 

53)

CA (All), OR (All), WA (All) (81)

VOLCFGRS = b1x1

2x2V1,

Where V1 = b2 + b3x2

-1 -- if V1 < 0.27, set to 0.27

x1 = 

MAX(dbh,6)

x2 = ht

MacLean and 

Berger 1976

CA (All), OR (All) (62, 65, 66)

CA (All), OR (All), WA (All) (133, 

321, 475)

IF (x1 >= 3 AND x2 > 0 AND x3 = 1)

 VOLCFGRS = (b0 + b1(ݔଵ

ଶݔଶ)௕మ + b3)

3

IF (x1 >= 3 AND x2 > 0 AND x3 ≠ 1)

 VOLCFGRS = (b0 + b1(ݔଵ

ଶݔଶ)௕మ)

3

OTHERWISE

 VOLCFGRS = 0.1

(IF VOLCFGRS <= 0, SET TO 0.1)

x1 = drc

x2 = ht

x3 = # of stems

Chojnacky 

1985

continued
24

CA (All), OR (All), WA (All) (64) VOLCFGRS = ((V1 + b1) / (b2 + b3݁௕ర௫భ)) + b5,

Where V1 = b6x1

2(b7 + b8x2 – (b9x1x2 / (x2 + b10)))

x2(x2/(x2 + b10))2 -- if V1 <= 0, set to 2

(IF VOLCFGRS <= 0, SET TO 1)

x1 = 

MIN(dbh,60)

x2 = ht

Brackett 

1973,

Chittester 

and MacLean 

1984

CA (All) (102, 103, 104, 108, 113, 

124, 142)

CA (All), OR (All) (120)

VOLCFGRS = b1x1

2x2V1,

Where V1 = b2 + b3

௫మ

మ

௫భ

 

 

 -- if V1 > 0.4, set V1 to 0.4; if 

V1 < 0.3, set to 0.3

x1 = 

MAX(dbh,6)

x2 = ht

MacLean and 

Berger 1976

CA (All) (101, 109, 119, 127, 137)

CA (All), OR (West & JJ) (116, 

122)

CA (All), OR (All), WA (All) (117)

VOLCFGRS = b1x1

2x2V1,

Where V1 = b2 + b3x1

-1 -- if V1 > 0.4, set to 0.4; if V1

< 0.3, set to 0.3

x1 = 

MAX(dbh,6)

x2 = ht

Brackett 

1973,

MacLean and 

Berger 1976

OR (East) (116)

OR (East), WA (All) (122)

OR (East), WA (East) (202)

VOLCFGRS = ((݁

(௕భ ା ௕మ ୪୬ ௫భା௕య(୪୬ ௫మ)మା ್ర

ೣమమା ௕ఱ ୪୬ ௫మ)

b6) / ((b7(1 + b8݁(௕వ

ೣభ

భబ)

))(b10x1

2 + b11) + b12))((b13x12

– b11) / b6)

x1 = dbh

x2 = ht

Brackett 

1973, 

Summerfi eld 

unpublished 

1980,

Browne 1962

CA (All) (201, 202) VOLCFGRS = b1x1

2x2V1,

Where V1 = b2 + (b3

௫మ

௫భ

 - b4

௫మ

మ

௫భ

 

 

) -- if V1 > 0.4, set to 

0.4; if V1 < 0.3, set to 0.3

x1 = 

MAX(dbh,6)

x2 = ht

MacLean and 

Berger 1976

OR (West & JJ), WA (West & CF) 

(202)

VOLCFGRS = ((10௏భb7) / ((b8(1 + b9݁(௕భబೣభ

భబ)

))

(b11x1

2 + b12) + b13))((b14x12 – b12) / b7), where V1 = 

ܾଵ + ܾଶ logଵ଴ ݔଵ logଵ଴ ݔଶ + ܾଷ(logଵ଴ ݔଵ)ଶ +

ܾସ logଵ଴ ݔଵ + ܾହ logଵ଴ ݔଶ + ܾ଺ (logଵ଴ ݔଶ)ଶ

x1 = dbh

x2 = ht

Brackett 

1973,

Browne 1962

CA (All), OR (All) (211, 212) VOLCFGRS = ((݁(௕భା௕మ ୪୬ ௫భା௕య ୪୬ ௫మ)

ܾସ) / ((b5(1 + 

b6݁

௕ళ

ೣభ

భబ ))(b8x1

2 + b9) + b10))((b11x12 – b9) / b4)

x1 = dbh

x2 = ht

Brackett 

1973,

Krumland 

and Wensel 

1975,

Browne 1962

Table 4.—continued

Region/States (species codea

) Form of the model:

VOLCFGRS = f(x1,x2,....,xn)

Observed 

items: 

(x1,x2,....,xn)

Referenceb

continued
25

CA (All), OR (All), WA (All) (263) VOLCFGRS = ((10(௕భା ௕మ ୪୭୥భబ ௫భା ௕య ୪୭୥భబ ௫మା ௕ర௫భ)

b5) / ((b6(1 + b7݁(௕ఴ

ೣభ

భబ)

))(b9x1

2 + b10) + b11))((b12x12 – 

b10) / b5)

x1 = dbh

x2 = ht

Brackett 

1973,

Chambers and 

Foltz 1979,

Browne 1962

CA (All), OR (All), WA (All) (264, 

299) VOLCFGRS = (b1ݔଵ

௕మݔଶ௕యb4) / ((b5(1 + b6݁(௕ళ

ೣభ

భబ)

))

(b8x1

2 + b9) + b10))((b11x12 – b9) / b4)

x1 = dbh

x2 = ht

Brackett 

1973,

Browne 1962,

Bell et al. 

1981

CA (All), OR (All) (312, 313, 361, 

431, 540, 542, 815, 818, 901, 997) 

OR (West) (320)

CA (All) (330, 333, 421, 492, 500, 

600, 602, 660, 661, 730, 763, 801, 

807, 811, 826, 839, 920, 998, 999)

CA (All), OR (West & JJ) (631, 

805, 981)

CA (except Mixed-Conifer) (547, 

604, 731, 922)

CA (except Mixed-Conifer), OR 

(West), WA (East) (603)

CA (All), OR (JJ) (821)

VOLCFGRS = b1ݔଵ

௕మݔଶ௕య x1 = dbh

x2 = ht;

if species 361 

or 631, x2 = 

MIN(ht,120)

Pillsbury and 

Kirkley 1984

WA (All) (312, 313, 370, 431, 540, 

542, 815, 901, 997)

OR (West) (351, 926)

WA (West & CF) (361)

CA (All), OR (All), WA (All) (374, 

375, 591)

OR (All), WA (All) (492, 500, 602, 

660, 661, 730, 746, 747, 760, 763, 

766, 768, 920, 998, 999)

OR (West & JJ) (510)

OR (All), WA (West & CF) (600)

OR (East), WA (West & CF) (631)

WA (East) (818)

VOLCFGRS = V1((b1x1

2 – b2) / b3),

Where V1 = (b4x1

2(x2 + b5)(b6V2 + b7V2x110-3

+ b8V2x210-3 + b9V2x2x110-5 + b10V2x2

210-6 + 

b11V2ξݔଶ10-3 + b12V3

4x110-3 + b13V34x210-3 + 

b14V3

33x2x110-6 + b15V333ξݔଶ10-4 + b16V341x2210-7)

b3) / ((b17 + b18ܾଵଽ

(௫భା௕మబ)

)((b21(1 + b22݁(௕మయೣభ

భబ)

))

(b1x1

2 + b2) + b24)),

Where V2 = V3

2.5,

And V3 = (x2 + b25 - ௫భ

௕మల

 

 

) / (x2 + b5) -- if V1 <= 0, set 

to .01

x1 = dbh

x2 = 

MAX(ht,18)

Brackett 

1973, Curtis 

et al.1968,

Browne 1962

Table 4.—continued

Region/States (species codea

) Form of the model:

VOLCFGRS = f(x1,x2,....,xn)

Observed 

items: 

(x1,x2,....,xn)

Referenceb

continued
26

CA (All) (510)

CA (except Mixed-Conifer) (511)

VOLCFGRS = ((b1x1

2x2b2) / ((b3(1 + b4݁(௕ఱ

ೣభ

భబ)

))

(b6x1

2 + b7) + b8))((b9x12 – b7) / b2)

x1 = dbh

x2 = ht

Brackett 

1973,

MacLean 

unpublished 

1983,

Browne 1962

CA (All) (756)

CA (except Mixed-Conifer) (758)

CA (All), OR (East), WA (East) 

(990)

IF (V1 <= b6)

 VOLCFGRS = b1 + b2V1 + b3V1

2

Where V1 = x1

2x210-3

OTHERWISE

 VOLCFGRS = b4 + b2V1 – (b5/V1),

Where V1 = x1

2x210-3

(IF VOLCFGRS <= 0, SET TO 0.1)

x1 = drc

x2 = ht

Chojnacky 

1988

AK (All) (All Species) See Appendix B for algorithms.

a Species numbers refer to the codes used by FIA (Woudenberg et al. 2010)

b References in Tables 1-4 of Appendix A are listed in a separate Literature Cited section at the end of the Appendix.

JJ: Refers to Jackson and Josephine Counties, OR

CF: Refers to silver-fi r region of WA

Table 4.—continued

Region/States (species codea

) Form of the model:

VOLCFGRS = f(x1,x2,....,xn)

Observed 

items: 

(x1,x2,....,xn)

Referenceb
27

Table 5.—Sound cubic-foot volume (VOLCFSND) equation forms for all regions

Region/States (species codea

) Form of the model: 

VOLCFSND = f(x1,x2,....,xn)

Observed items: 

(x1,x2,....,xn)

North Central - KS, MI, MN, 

ND, NE, SD, WI (All Species)

VOLCFSND = VOLCFGRS(1 - ௕భ௕మ

ଵ଴଴ )

North Central - IA, IL, IN, MO 

(All Species)

IF x1 < b2

 VOLCFSND = VOLCFGRS(1 - ௏భ௕య

ଵ଴଴ ),

where V1 = b0 + b1x1 -- if V1 > 100, set 

to 100; if V1 < 0, set to 0

(if V1b3 > 98, set to 100)

IF x1 >= b2

 VOLCFSND = VOLCFGRS(1 - ௏భ௕య

ଵ଴଴ ),

where V1 = b0 + b1b2 -- if V1 > 100, set 

to 100; if V1 < 0, set to 0

(if V1b3 > 98, set to 100)

OTHERWISE

 VOLCFSND = 0

x1 = dbh

Northeast – All States, Rocky 

Mountain – All States, Pacifi c 

Northwest – CA, OR, WA (All 

Species)

South – All States (All Species)

VOLCFSND = 

VOLCFGRS(1 - ௫భ

ଵ଴଴)

x1 = percent of 

cubic-foot volume 

that is rotten or 

missing;

if x1 = NULL, set 

to 0; if x1 > 98, 

set to 100

Pacifi c Northwest – AK (All 

Species)

See Appendix C for algorithm.
28

LITERATURE CITED APPENDIX A

Bell, J.F.; Marshall, D.D.; Johnson, G.P. 1981. Tarif access tables for mountain hemlock 

from an equation of total stem cubic-foot volume. Res. Bull. 35. Corvallis, OR: Oregon 

State University, Forest Research Laboratory. 46 p.

Brackett, M. 1973. Notes on tarif tree volume computation. Resour. Management Rep. 24. 

Seattle, WA: State of Washington, Department of Natural Resources. 26 p.

Browne, J.E. 1962. Standard cubic-foot volume tables for the commercial tree species of 

British Columbia, 1962. Vancouver, BC, Canada: British Columbia Ministry of Forests, 

Lands and Natural Resources, Forest Surveys and Inventory. Available at http://www.for.

gov.bc.ca/hfd/library/documents/bib37482.pdf. (Accessed 15 December 2010).

Bruce, D.; DeMars, D.J. 1974. Volume equations for second-growth Douglas-fi r. Res. Note 

PNW-239. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacifi c Northwest 

Forest and Range Experiment Station. 5 p.

Bruce, D. 1984. Volume estimators for Sitka spruce and western hemlock in coastal Alaska.

In: Inventorying forest and other vegetation of the high latitude and high altitude regions, 

Proceedings of the International Symposium, SAF Regional Technical Conference; 1984 

July 23-26; Fairbanks, AK. Bethesda, MD: Society of American Foresters: 96-102.

Bruce, D. and DeMars, D. Unpublished (date unknown). FORTRAN code (DBVOL3.

FOR) created for the Anchorage Forest Sciences Laboratory, Forest Inventory and Analysis, 

Anchorage, Alaska. On fi le at USDA, Forest Service, Pacifi c Northwest Research Station, 

Portland, Oregon.

Campbell, K.R. Unpublished (2009). PL/SQL code dated April 18, 2009. On fi le at USDA, 

Forest Service, Pacifi c Northwest Research Station.

Chambers, C.J.; Foltz, B.W. 1979. Th e tariff system – revisions and additions. DNR Note 

27. Seattle, WA: State of Washington, Department of Natural Resources. 8 p.

Chittester, J.M.; MacLean, C.D. 1984. Cubic-foot tree volume equations and tables for 

western juniper. Res. Note PNW-420. Portland, OR: U.S. Department of Agriculture, 

Forest Service, Pacifi c Northwest Forest and Range Experiment Station. 8 p.

Chojnacky, D.C. 1985. Pinyon-juniper volume equations for the central Rocky Mountain 

states. Res. Pap. INT-339. Ogden, UT: U.S. Department of Agriculture, Forest Service, 

Intermountain Forest and Range Experiment Station. 27 p.

Chojnacky, D.C. 1988. Juniper, pinyon, oak and mesquite volume equations for 

Arizona. Res. Bull. INT-391. Ogden UT: U.S. Department of Agriculture, Forest Service, 

Intermountain Forest and Range Experiment Station. 11 p.
29

Chojnacky, D.C. 1994. Volume equations for New Mexico’s pinyon-juniper dryland 

forests. Res. Pap. INT-471. Ogden, UT: U.S. Department of Agriculture, Forest Service, 

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30

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Woodall, Christopher W.; Heath, Linda S.; Domke, Grant M.; Nichols, Michael C. 2011. Methods 

and equations for estimating aboveground volume, biomass, and carbon for trees in the 

U.S. forest inventory, 2010. Gen. Tech. Rep. NRS-88. Newtown Square, PA: U.S. Department 

of Agriculture, Forest Service, Northern Research Station. 30 p.

The U.S. Forest Service, Forest Inventory and Analysis (FIA) program uses numerous models 

and associated coefficients to estimate aboveground volume, biomass, and carbon for live and 

standing dead trees for most tree species in forests of the United States. The tree attribute models 

are coupled with FIA’s national inventory of sampled trees to produce estimates of tree growingstock volume, biomass, and carbon, which are available in the Forest Inventory and Analysis 

database (FIADB; http://fi atools.fs.fed.us). To address an increasing need for accurate and easy-touse documentation of relevant tree attribute models, needed individual tree gross volume, sound 

volume, biomass (including components), and carbon models for species in the United States 

are compiled and described in this publication with accompanying electronic fi les on a CD-ROM 

included with the publication. This report describes models currently in use as of 2010. These 

models are subject to change as the FIADB and associated tree attribute models are improved.

KEY WORDS: biomass equations, forest carbon, dead tree biomass, Forest Inventory and Analysis, 

volume equations, sound cubic foot, gross cubic foot

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