Conversion of Board 

Foot Scaled Logs to 

Cubic Meters in 

Washington State, 

1970–1998

Henry Spelter 

United States

Department of 

Agriculture

Forest Service 

Forest

Products

Laboratory

General

Technical

Report

FPL−GTR−131
Abstract 

The conversion factor generally used to convert logs 

measured in board feet to cubic meters has traditionally 

been set at 4.53. Because of diminishing old growth, largediameter trees, the average conversion factor has risen, as 

illustrated in this analysis of Washington state sawmill data 

over the period 1970–1998. Conversion factors for coastal 

and interior Washington were estimated at 6.76 and 5.93, 

respectively, up from 4.0 to 4.5 in the 1970s. Average sawlog diameters over the same period were estimated to have 

declined from 56 to 29 cm for coastal Washington and 

from 41 to 25 cm for interior Washington. 

Keywords: softwood, sawlogs, metric conversion factors, 

average diameters 

June 2002 

Spelter, Henry. 2002. Conversion of board foot scaled logs to cubic meters 

in Washington State, 1970–1998. Gen. Tech. Rep. FPL-GTR-131. 

Madison, WI: U.S. Department of Agriculture, Forest Service, Forest 

Products Laboratory. 6 p. 

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Conversion of Board Foot Scaled Logs to 

Cubic Meters in Washington State, 1970–1998 

Henry Spelter, Economist

Forest Products Laboratory, Madison, Wisconsin

Introduction 

In the United States, most timber is measured in terms of 

board feet. The log scales currently in use to estimate lumber 

recovery from roundwood, however, were created in the 

19th century according to sawmill technology, timber resource, and lumber sizes used at the time. Because log scales 

have not been modified since to reflect changes in these 

factors, they are outdated and inadequately serve their purpose of accurately determining recoverable lumber volumes. 

With regard to mill technology, most log rules assume 

1/4-in. for sawkerf and shrinkage, typical of 19th century 

circular head saws, but not the 1/8-in. characteristic of contemporary thin-kerf band saws. Improvements in log scanning, positioning, and cutting accuracy have allowed mills to 

boost recoveries. The advent of curve sawing means that 

logs with deductions for sweep now yield more lumber or 

some that were heretofore usable only for pulp can now be 

sawn. 

In terms of the resource, much of the large-diameter old 

growth timber has now been used up or placed off limits, 

forcing the industry to use smaller diameter thinnings and 

younger second growth. The board foot log rules determine 

recoverable volumes based on a cylinder defined by a log’s 

small end. Therefore, a bias is introduced as diameters decrease because the volume outside the cylinder becomes 

larger. Second growth trees tend to be more tapered, which 

also boosts the portion outside the core. 

Finally, with respect to lumber dimensions, size standards in 

the late 1960s were reduced, allowing boards to become 

dimensionally smaller, but the same nominal width and 

thickness designations were retained. Thus the “board feet” 

that are now produced are thinner than those upon which the 

log rules were based. 

These changes have widened the gap (known in the industry 

as the “overrun”) between log rule predictions and nominal 

lumber recoveries. Knowledgeable industry buyers know 

this and account for it in higher apparent prices where sellers 

are equally well informed. But many small timberland owners are unaware of these subtleties, and there is a perception 

that they often are at a disadvantage when selling their 

timber. 

There is a further disconnect between the board foot and 

cubic log scaling systems used in much of the rest of the 

world. The two measurement systems are fundamentally 

different. Board foot rules project only the portion recoverable as lumber based on the small end diameter, whereas 

cubic rules measure the total volume of sound wood, inclusive of lumber, chips, and sawdust, based on both end diameters. As such, the cubic rules are not affected by changes 

in sawing technology and lumber dimensions and are less 

affected by changes in log size. 

When comparing log values measured by different systems, 

the choice of conversion factor is one critical element. For 

example, in the recent dispute over softwood lumber trade 

between Canada and the United States, board foot prices in 

Washington were designated as the benchmark for comparison with cubic meter prices in British Columbia. To convert 

board foot prices to a cubic meter basis, one side advocated 

the widely used traditional conversion factor, dating back to 

at least 1950, of 4.53 m3

 per thousand board feet (MBF) of 

log. In support, they conducted dual scaling measurements in 

which a sample of logs was measured according to both 

systems. These resulted in conversion factors of 5.1 m3

/MBF 

for coastal Washington and 4.6 m3

/MBF for the interior. 

The opposing side also presented data from dual scaling log 

measurements. Conversion factors were derived for each 

species and grade (but not by diameter classes within grades) 

and the results weighted by the grade and species distribution of logs sold in Washington. Their estimated factors 

were 6.7 m3

/MBF for coastal Washington and 6.2 m3/MBF 

for the interior.1

 These differences are not inconsequential, 

because they represent a substantial amount in potential 

yearly duties on Canadian lumber imports. 

In this paper, I investigate what conversion factors from 

board feet to cubic meters are appropriate to translate present-day Washington log prices into cubic terms. 

 

1

Dual-scaling exercises were conducted in both British 

Columbia and Washington. The numbers reported here were 

results for four coastal and four interior softwood timber 

species weighted by Washington sales volumes of those 

species. 
2 

Data 

The primary data used came from 15 industry censuses 

conducted over the past 30 years by the Washington State 

Department of Natural Resources (2002). These reports 

represent the most consistent and comprehensive statistics on 

aggregate wood utilization by sawmills in Washington. 

Additional results from log yield studies conducted by the 

USDA Forest Service for the coast (Fahey and Martin 1974, 

Lane and others 1973) and for the interior (Parry 1989, 

Plank and Snellgrove 1973) were used to convert some 

descriptive industry census data into estimates of ratios of 

finished lumber to raw logs. 

Procedure 

In dual-scaling exercises, the conversion factors are derived 

from direct measurements of log samples. By contrast, the 

approach here was to work backwards from three basic 

lumber processing variables that, when multiplied together, 

collapse into the sought after conversion factors. The three 

variables are ratios of (1) actual board foot content of lumber 

to nominal board foot content, (2) nominal board feet of 

lumber recovered to scaled board foot log input (overrun), 

and (3) cubic volume of log to lumber derived from it. 

Step 1. I start with the tautological conversion of a thousand 

board feet (MBF) into cubic meters using metric equivalents 

to imperial measurements: 

1actual MBF lumber 2.36 m3 = (1) 

or a conversion factor of 

1actual MBF

2.36 m lumber 3

Step 2. The actual board foot contents of finished lumber are 

less than their nominal sizes imply. A nominal 2- by 4-in. 

surfaced dry piece, for example, is actually 1.5- by 3.5-in., 

resulting in 0.656 actual board feet for each nominal board 

foot. Using ratios between nominal and actual sizes as given 

in the American Softwood Lumber Standards definitions for 

surfaced green and surfaced dry lumber (U.S. Department of 

Commerce 1999) and weighting each size by the proportions 

reported in Western Wood Products Association production 

statistics (WWPA 2000), I calculated regional ratios. I extrapolated them over time based on the proportions of green 

and dried lumber. Multiplying Equation (1) by this variable 

I define as X yields 

1nominal MBF

2.36 m lumber

1actual MBF 1nominal MBF

2.36 m lumber actual MBF 3 3 X × X = ×

× (2) 

Step 3. The ratio between the nominal board feet of lumber 

recovered from a log and the projected recovery from the 

scale (the so-called overrun) can be determined from lumber 

output and log input figures contained in the Washington 

Mill Survey. Multiplying Equation (2) by the overrun ratio Y

gives 

1MBF, log scale

2.36 m lumber

1nominal MBF 1MBF, log scale

2.36 m lumber nominal MBF

3

3

X Y

X Y

× × =

×

× ×

 (3) 

Step 4. The cubic recovery ratio (CRR) measures the volume of finished lumber recovered from the log input. Typical sawmill CRR factors vary from as low as 0.3 to more 

than 0.6. Among the many operational factors that influence 

this, log size is one of the more important and is normally 

the variable about which a schedule of CRR values is built 

(Cahill 1984). Stud mills supplied with small logs tend to lie 

at the lower end of the range, whereas grade recovery mills 

processing large-diameter timber for high-quality lumber 

achieve higher recoveries. 

Except for a late 1960s study used to estimate residue volumes in the Washington Mill Survey, data on CRR values 

were not available. The logs utilized, however, were identified by whether they were “old growth” or “young growth,” 

defined as older or younger than 100 years. Forest Service 

lumber-yield studies (Parry 1989, Fahey and Martin 1974, 

Lane and others 1973, Plank and Snellgrove 1973) on such 

logs relate CRR values to log size. To proceed, I selected 

a combination of diameters for old and young growth 

(Table 1) whose corresponding CRR factors, weighted by 

the 1970 shares of old and young growth, approximated the 

CRR value of the late 1960s study (0.474 and 0.445 for 

coastal and interior Washington, respectively). I kept these 

CRR values and continued to weight them by the changing 

shares of old and young growth to derive subsequent CRR 

estimates, except that in 1990 I reduced the young growth 

diameter by 2.54 cm (1 in., Table 1) to reflect the increasing 

share of thinnings that began to appear with the change to 

second growth timber economy. 

Table 1—Diameter assumptions (and corresponding CRR 

ratios) used to calculate regional CRR factors (cm) 

 Old growth Young growth 

Coastal 

1970–1988 76 (0.50) 30 (0.44) 

1990–1998 76 (0.50) 28 (0.43) 

Interior 

1970–1988 56 (0.48) 25 (0.39) 

1990–1998 56 (0.48) 23 (0.37) 
3 

Multiplying Equation (3) by the inverse of the CRR (variable Z), the cubic meter to MBF log scale conversion that is 

the focus of this investigation results: 

1MBF,log scale

2.36 m log

1MBF,log scale m lumber

2.36 m lumber m log 

3

3

3 3

X Y Z

X Y Z

× × × =

×

× × ×

 (4) 

Values for X, Y, and Z are displayed in Tables 2 and 3 along 

with underlying data from the Washington Mill Survey 

characterizing the resource and product. 

Results 

A striking trend in the coastal Washington data is the decline 

of the share of old growth. By 1996, it had nearly disappeared. This contributed to the large increase in overruns 

especially evident during the past 15 years. A second outcome of smaller log sizes is a decrease in the cubic recovery 

ratio (or an increase in its inverse). Together these trends 

would have caused the conversion factor from board feet 

(Scribner long-log scale) to cubic meters to rise from approximately 4 to 4.5 in the 1970s to greater than 7 by 1998. 

However, the CRR factors used in these calculations were 

derived from 1960s-era mill studies. Improvements in sawing over the past three decades have ostensibly increased 

lumber yields, offsetting some of the yield-reducing impact 

of smaller log sizes. To what degree that occurred we can 

estimate by translating the derived log diameters into conversion factors using generalized schedules developed from 

USDA Forest Service sawmill recovery studies (Cahill 

1984) (Figs. 1 and 2). For the coast, the differences in the 

two series imply an approximate increase of 15% in the CRR 

ratio over 28 years. This results in higher conversion factors 

of about 4.7 at the beginning of the period and a lower factor 

of 6.76 in 1998 (down from 7.18). 

Trends in the log mix in interior Washington followed a 

similar course. The old growth share in the interior had not 

declined by as much as it had on the coast, hence the increase in overruns was not as large. The form of the Scribner 

scale used is also based on shorter logs, which makes this 

version of the scale more accurate, and the overruns lower, 

for the same size log. Thus the rise in the conversion factor 

from board feet (Scribner short-log scale) to cubic meters 

was more moderate, from approximately 4.5 to only 6.4 by 

1998. 

Table 2—Log and lumber characteristics for coastal Washington 

Actual to 

nominal 

lumber 

(X) 

Green 

lumber 

(%) 

Lumber 

to log 

volume 

(overrun) 

 (Y) 

Old 

growth 

logs (%) 

Ratio of 

log to 

lumber 

(1/CRR) 

(Z) 

Log 

conversion 

factor 

(m3

/MBF) 

Estimated 

average 

regional 

diameter 

(cm) 

1970 0.700 41 1.21 56 2.12 4.22 56.2 

1972 0.701 43 1.35 59 2.11 4.71 57.3 

1974 0.701 44 1.19 55 2.13 4.19 55.5 

1976 0.702 48 1.27 53 2.13 4.48 54.7 

1978 0.705 53 1.37 46 2.15 4.90 51.4 

1980 0.707 58 1.32 51 2.14 4.70 53.8 

1982 0.707 59 1.34 34 2.18 4.88 45.9 

1984 0.708 60 1.42 32 2.19 5.19 45.3 

1986 0.707 58 1.41 33 2.19 5.13 45.6 

1988 0.706 57 1.47 31 2.19 5.38 44.7 

1990 0.707 59 1.56 24 2.23 5.81 39.5 

1992 0.706 56 1.63 17 2.25 6.10 36.1 

1996 0.703 50 1.79 4 2.30 6.84 29.8 

1998 0.701 43 1.88 na 2.31 7.18 28.9 

Note: The Washington Mill Survey was not carried out in 1994. Columns 3, 4, and 5 were data reported 

in the survey. Columns 2, 6, 7, and 8 were derived from data in the survey and Forest Service yield 

studies, as described in the Procedure section. 
4 

Figure 1—Metric conversion factors from constant 

and variable cubic recovery ratio estimates, coastal 

Washington 1970–1998. 

Figure 2—Metric conversion factors from constant 

and variable cubic recovery ratio estimates, interior 

Washington 1970–1998. 

Table 3—Log and lumber characteristics for interior Washington 

Actual to 

nominal 

lumber 

(X) 

Green 

lumber 

(%) 

Lumber 

to log 

volume 

(overrun) 

(Y) 

Old 

growth 

logs (%) 

Ratio of 

log to 

lumber 

(1/CRR) 

(Z) 

Log 

conversion 

factor 

(m3

/MBF) 

Estimated 

average 

regional 

diameter 

(cm) 

1970 0.713 23 1.18 52 2.23 4.42 41.2 

1972 0.713 26 1.22 68 2.14 4.38 46.0 

1974 0.714 29 1.26 67 2.15 4.54 45.7 

1976 0.713 26 1.27 61 2.18 4.67 43.9 

1978 0.714 29 1.28 65 2.15 4.64 45.2 

1980 0.713 24 1.32 57 2.19 4.86 42.9 

1982 0.714 29 1.34 44 2.27 5.12 38.7 

1984 0.713 26 1.44 49 2.24 5.43 40.4 

1986 0.710 9 1.42 50 2.24 5.41 40.7 

1988 0.712 19 1.40 50 2.24 5.28 40.6 

1990 0.711 15 1.41 28 2.45 5.80 32.0 

1992 0.710 8 1.43 32 2.41 5.76 33.5 

1996 0.709 4 1.41 16 2.54 5.99 28.2 

1998 0.709 4 1.47 na 2.61 6.42 25.3 

Note: The Washington Mill Survey was not carried out in 1994. Columns 3, 4, and 5 were data 

reported in the survey. Columns 2, 6, 7, and 8 were derived from data in the survey and Forest 

Service yield studies, as described in the Procedure section. 

1970 1974 1978 1982 1986 1990 1996

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

Conversion factor (m3/MBF, log scale) 

CRR constant 

CRR variable 

CRR constant

1970 1974 1978 1982 1986 1990 1996

4.0

4.5

5.0

5.5

6.0

6.5

Conversion factor (m3/MBF, log scale)

CRR variable
5 

However, the diameter-derived conversion factor does not 

rise as fast as its fixed technology counterpart (Fig. 2). Overall, the implied improvement in recovery is about 12%, and 

the metric conversion factor is reduced from 6.42 to 5.93 

for 1998.2

Discussion 

These results place into perspective the conflicting conversion factors in the recent softwood lumber dispute. The 

factors advocated by one side were obtained from a large 

sample of logs scaled by both cubic and board feet. The 

results were segmented by grade and species and converted 

to a regional estimate by weighting them by Washington’s 

grade and species mix (though not by diameter class within 

the grades). The results came close to what was found here 

based on essentially the entire population of logs processed 

in the state of Washington in 1998. 

The data advocated by the other side of the dispute also 

resulted from a dual scaling exercise in which a conversion 

factor of 5.14 m3

/MBF, using coastal scaling protocols, was 

found along with an average diameter of 45 cm. The conversion factor is basically consistent with USDA Forest Service 

log conversion factors for that diameter (5.26 m3

/MBF), but 

the diameter is higher than the 29 cm that was the average 

calculated from the 1998 Washington Mill Survey. Similarly, the interior log sample scaled according to interior 

protocols had an average diameter of approximately 42 cm 

and yielded a conversion factor of 4.52. This again is consistent with USDA Forest Service conversion factors for that 

diameter (4.81 m3

/MBF), but the sample diameter is higher 

than the average of approximately 25 cm in the Washington 

Mill Survey for eastern Washington. 

Beyond the issue of softwood lumber trade is the problem of 

how to harmonize trade data where different scaling systems 

are employed. Analysts have used “standard” conversion 

factors to make North American (now exclusively U.S.) data 

compatible with data from the rest of the world, and over 

time, a factor of 4.53 m3

/MBF has become established. 

However, details on its provenance, the embedded assumptions on log size, and the type of scale used have been lost. 

A factor of 4.53 can be related to specific diameters in all 

currently used U.S. log scales, but those diameters are considerably larger than the average log sizes prevalent today. 

The results here show that a conversion factor of 4.53 was 

reasonably close for West Coast logs scaled by the Scribner 

system prior to the 1980s, when a big share of logs consisted 

of large-diameter old growth trees. Since then, however, 

 

2

These data and the submitted data in the lumber dispute 

were for different years, and the trends exhibited in the 

1970–1998 data are likely to have carried forward into 2000. 

change to a second growth timber base has made that 

standard conversion factor too low. 

The appropriateness of a standard conversion factor then has 

to be weighed according to the purposes for which it is used. 

For illustrating short-term trends in trade, the use of a standard factor may do little harm. However, longer term trends 

can become considerably biased. And for situations involving valuations requiring precision, the use of a standard 

factor irrespective of the particular circumstances is least 

appropriate. The foregoing illustrates the need for a more 

consistent and transparent log measurement system in U.S. 

timber markets. Foresters have long recognized shortcomings in the present system and have been advocating a 

change to cubic volume measurements. The results here 

underscore the confusion that can result and the costs that 

can ensue from the use of the present opaque scaling 

systems. 

Literature Cited 

Cahill, J. 1984. Log scale conversion factors. In: Snellgrove, T. and others, eds. Proceedings, User’s guide for 

cubic measurement. Seattle, WA: Published cooperatively 

by U.S. Department of Agriculture, Forest Service and University of Washington, College of Forest Resources. 

Fahey, T.; Martin, D. 1974. Lumber recovery from secondgrowth Douglas Fir. Res. Pap. PNW–177. Portland, OR: 

U.S. Department of Agriculture, Forest Service. 20 p. 

Lane, P.H.; Henley, J.W.; Woodfin, R.O., Jr.; 

Plank, M.E. 1973. Lumber recovery from old growth coast 

Douglas Fir. Res. Pap. PNW–154. Portland, OR: U.S. 

Department of Agriculture, Forest Service. 44 p. 

Parry, D. 1989. Ponderosa Pine yield study—Goldendale, 

Washington. Unpublished report on file at the USDA Forest 

Service Forest and Range Experiment Station, Portland, OR. 

Plank, M.; Snellgrove, T. 1973. Lumber yield from Western White Pine in Northern Idaho. Res. Pap. PNW–153. 

Portland, OR: U.S. Department of Agriculture, Forest 

Service. 

U.S. Department of Commerce. 1999. American Softwood 

Lumber Standard. Voluntary Product Standard DOC PS 20–

29. Washington, DC: Technology Administration, National 

Institute of Standards and Technology. 

Washington State Department of Natural Resources.

(Draft). 2002. Washington Mill Survey 1998–Series Rep. 15. 

Olympia WA: Washington State Department of Natural 

Resources. 

WWPA. 2000. Western lumber production statistics for 

analysis. Portland, OR: Western Wood Products 

Association. 
6 

Appendix—Generalized 

Equations for Converting 

Board Foot Log Volumes to 

Their Cubic Meter Equivalents 

Table 4 contains factors to convert logs measured in board 

feet (scaled by the long and short log versions of the Scribner rule) to cubic volumes. Equations (5) through (8) were 

derived from data collected in the course of extensive USDA 

Forest Service sawmill efficiency studies (Cahill 1984). 

Table 4—Conversion factors derived from 

equations for logs 15 to 41 cm in diameter 

Log diameter Factors 

in. cm Long logs Short logs 

6 15.2 8.60 8.05

 7 17.8 8.81 7.20

8 20.3 8.43 6.63

9 22.9 7.89 6.23

10 25.4 7.36 5.92

11 27.9 6.90 5.67

12 30.5 6.51 5.46

13 33.0 6.19 5.28

14 35.6 5.92 5.13

15 38.1 5.70 4.99

16 40.6 5.51 4.87

In these studies, a large population of logs was measured by 

both a customary board foot rule and a cubic scaling system, 

and relationships between the two were statistically estimated as a function of log diameter. The original cubic 

volume data and the equations derived from them were in 

terms of cubic feet. These were converted to cubic meters. 

Equations (5) through (8) were developed using inches. 

Therefore, they are only valid using inch inputs for diameter. 

Board feet (net volume basis measured by Scribner, long log 

basis) per cubic foot: 

 10.16 – 0.04 × D – 88.18/D + 290.58/D2 (5) 

where D is diameter. This is converted to m3

/1,000 board 

feet by the following conversion: 

1,000/((10.16 – 0.04 × D – 88.18/D + 290.58/D2

) × 35.31) 

 (6) 

Board feet (net volume basis measured by Scribner, short log 

basis) per cubic foot: 

 5.336 + 0.085 × D – 13.93/D (7) 

This is converted to m3

/1,000 board feet by the following 

conversion: 

 1,000/((5.336 + 0.085 × D – 13.93/D) × 35.31) (8) 

These equations result in the conversion factors in Table 4. 

for logs 15 to 41 cm in diameter.