I Relationship Of Stump Diameter To D. b. h. 

For White Oak In The Northeast 

This is the eighth report on a series of studies to 

show the relationship of stump diameter to diameter breast 

high (d.b.h. ) for commercially im~ortant tree species in the 

Northeast.+ This report is for white oak (Quercus alba). 

In this study 1,266 stump-diameter measurements were 

used, ranging from 4 inches to 46 inches. Both stump diameter and d.b.h. were measured to the nearest l/l0-inch with 

a diameter tape. To obtain diameter inside bark, bark thickness was measured with a Swedish bark g2ge. Stump heights 

were measured on the uphill side to the nearest l/l0-foot. 

It was found that 61 percent of the stumps left on 

logging operations were between 0.6 and 1.8 feet high; 10 

percent were higher than 1.8 feet; and 29 percent were lomer 

than 0.6 foot. 

In the computations, inside-bark stump diameters were 

csed to avoid inaccuracies due to unequal bark thickness, 

logging damage to bark, and bark peeling off. Stump dimeters were sorted into 2-inch classes. Stump-height rneasurements were sorted into 0. &foot classes within each stumpdiameter class. 

To develop an equation expressing the stump diameter 

--d.b.h. relationship for white oak, the method described by 

Demin@kt' was used. The following equation mas obtained: 

D.b.h. = 0.953 (stump d.i.b.) + 1.692 (stump height) - 3.645 

The irelationships developed from this eqm tion were worked 

gut as a graph (fig. 1). 

To determine the 2-inch d.b.h. class of a white-oak 

stump from this graph, you merely plot the intersection of 

the vertical ordinate (stump height) with the horizontal 
ordinate (stump diameter). For example, for a stlmp 16.0 

inches in diameter and 1.4 feet high, the t~vo lines intersect about halfway between the two limits of the 14-inch 

d.b.h. class. 

Ccmpa.rison of actual d.b.hO9s and those calculated 

with the equation showed an average weighted difference of 

0.05 inch. The standard error of estimate for all data. was 

1.192 inch. At the mea,n of stump diameters, you can expect 

60 percent of the estimates of d.b.h. to fall in the correct 

2-inch d.b.h. class. Another 31 percent can be expected to 

fall one class above or below the correct one; and 9 percent 

will fall outside this range. These errors ;re compensating. 

As the stump diameters increase beyond the mean of these 

data, the error vill also increase. These differences result 

from the irregular shape of the stump top--due often to abnormal butt s~aelling or flaring roots. 

(If you use the graph by 1-inch d.b.h. classes, this 

is what you can expect: 33 percent of the estimates should 

fall in the correct 1-inch d.b.h, class; 47 percent should 

fall one class above or below it; and 20 percent should fall 

outside this range. ) 

For all practical purposes this graph is expected to 

give reliable d.b.h. estimates for white oak any~~here in the 

Northeast. 

--FREDERICK E. HAMPF 

Forester (~ensuration) 

Division of Forest Economics 

Northeastern E'9rest Experiment Station 

Forest Service, U. S . Dept . Agriculture 

+'For earlier reports on these studies see Forest R.esearch Note No. 38 (white pine), No. 42 (sugar maple) No* 

43 (~merican beech), No. 45 (yellow birch), No. 46 (northern 

red oak), No. 55 (yellow poplar), and No. 65 (pitch pine) 

~~~Deming, W. Edwards. Sta.tistica1 adjustment of data. 

261 pp., illus. Wiley & Sons, New York. 1938. 

2 Ag~icult ure-Forest Service-Upper Darby 
STUMP DIAMETER - D. B. H RELATIONSHIP FOR 

WHITE-OAK 

IN THE NORTHEAST 

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 

STUMP HEIGHT, IN FEET