Reviewed October 1993

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How to Measure Trees and Logs

John P. Slusher
School of Forestry, Fisheries and Wildlife

Selling timber without measuring the products is like selling livestock without weighing the animals. Knowing what you have to sell and securing several bids can mean many additional dollars from your timber sales. With the assistance of a professional forester, decide which trees are ready for market, then measure them and mark them with paint spots at breast height and below stump height. If the trees are already cut, scale the logs before they are sent to the mill.

The Missouri Department of Conservation will furnish a cruising stick to any landowner free of charge. The cruising stick is a Biltmore Stick on one side and a log scaling stick on the other side. You can obtain one from your local Missouri Department of Conservation district forestry office. Your cruising stick, plus the volume tables in this publication, will enable you to compute the volume in either standing trees or logs.

Before logs or trees can be bought or sold, it is necessary to determine their content by some standard. The board foot is the most common standard used for saw logs and lumber. A board foot contains 144 cubic inches of sawed lumber or the equivalent of a board 1 inch thick, 12 inches wide and 1 foot long.

A second unit of measure is the cord. Fuel wood and pulp wood (wood used to make paper) are measured and sold by the cord. The standard cord is a pile of wood 4 feet high, 4 feet wide and 8 feet long. It occupies 128 cubic feet of space, but does not actually contain 128 cubic feet of wood because of the air spaces.

Fuel wood and pulp wood are often cut in various lengths. A pile 5 feet wide, 4 feet high and 8 feet long occupies 160 cubic feet and is called a "long cord." Similarly, a pile of wood 4 feet high and 8 feet long cut into 1- or 2-foot lengths is a "short cord," which occupies less than 128 cubic feet.

The following formula may be used to determine the number of standard cords in a stack of wood:

Number of standard cords = [length (feet) x width (feet) x height (feet)]
128

Example
Take a stack of wood that is 10 feet long, 6 feet wide and 3 feet high. Substituting these figures into the formula we get:

Number of cords = (10 x 6 x 3)
128		 180
128		 = 1.406 cords

A third unit of measure is the "cubic foot." In the United States, the cubic foot unit of measure is used chiefly in growth and yield studies or in forest inventory and research projects, but generally not in commercial dealings. It represents a block or cube of wood 1 foot high, 1 foot wide and 1 foot thick.

Another unit of measure commonly found in Missouri is the "chord foot," which is used to measure cooperage bolts. This unit is based on the length of line along the chord of the bolt. A "chord foot" is 12 inches measured along the chord, inside the bark, from "sapwood to sapwood," or from "heartwood to heartwood." Prices per chord foot depend primarily upon the quality and amount of heartwood (redwood) in the bolt and also upon the length of the bolt.

Cooperage bolts vary in length, but "stave" bolts are most commonly 39 inches long with "heading" bolts 24 inches in length. Estimated chord foot yields from sound trees are shown in Table 1.

Table 1
Stave bolt and heading volumes in standing trees

Stave bolts Number of 39-inch cuts
Diameter Breast Height, D.B.H. 1 2 3 4 5 6 7
Volume in chord feet
12 inches 1.6 3.0          
14 inches 2.8 5.4 7.0        
16 inches 3.3 6.3 8.4 10.0      
18 inches 3.9 7.4 10.7 13.7 16.5 19.1  
20 inches 4.2 8.2 12. 15.6 18.9 21.9 24.7
22 inches 4.9 9.4 13.6 17.6 21.5 25.0 28.3
24 inches 5.2 10.2 15.1 19.6 23.8 27.8 31.7
26 inches 6.0 11.6 16.8 21.8 26.7 31.2 35.4
28 inches 6.5 12.7 18.7 24.3 29.5 34.5 39.4
30 inches 9.3 16.0 22.5 28.7 34.7 40.3 45.2
32 inches 11.5 21.9 31.2 37.9 44.4 50.6 56.6
34 inches 12.2 24.1 35.6 46.0 55.3 62.0 68.5
36 inches 14.1 27.2 39.4 51.3 62.8 73.2 82.5

 

Heading bolts Number of 24-inch cuts
D.B.H. 1 2 3 4 5 6 7 8 9 10
Volume in chord feet
18 inches 4.6 9.2 13.7 18.1 22.3          
20 inches 5.1 10.2 15.2 20.1 24.9 29.5 34.0 38.4 42.7  
22 inches 5.6 11.2 16.7 22.1 27.3 32.4 37.3 42.0 46.5 50.7
24 inches 6.1 12.0 17.6 22.9 27.9 32.6 37.0 41.0 44.9 48.5
26 inches 6.7 13.1 19.2 25.0 30.5 35.7 40.6 45.2 49. 53.0
28 inches 7.2 14.1 20.7 27.0 33.0 38.7 44.1 49.2 54.0 58.5
30 inches 7.7 15.1 22.2 29.0 35.5 41.7 47.6 53.2 58.5 63.5
32 inches 8.2 16. 23.7 31.0 38.0 44.7 51.1 57.2 63.0 68.5
Data from University of Missouri AGR. EX. SVC. CIR 671 and EX. SVC. Kansas State University, 3A-574-4-500

Volume content of logs and standing trees

The volume of wood in standing trees may be estimated by obtaining two measurements and applying these to tree scale volume tables. The two measurements are diameter and merchantable height.

Once the techniques for determining tree diameter and height have been mastered, it becomes relatively easy to determine tree volume. For standing trees, this can be accomplished by checking a tree volume table (Table 2), which is simply a tabulation of volumes of trees corresponding to different tree heights and diameters.

Measuring the board-foot content of a log or a group of logs is known as log scaling. The only equipment needed to scale logs is a yardstick and a log rule (Table 3). To speed up "scaling," a log scaler uses a scaling stick. A scaling stick serves as a yardstick and has printed on it a log rule from which the contents of a log can be read as it is measured.

When calculating the volumes of standing trees, landowners should be sure they are reading from a tree volume table and when measuring logs that their volumes are from a log rule. A comparison of Tables 2 and 3 will show why this is important.

Another factor to know is the difference between various log rules. Because of certain factors, there are variations in sawed output of logs. These factors have resulted in the development of more than 50 log rules in the U.S. The International 1/4-inch Log Rule (Table 3) and the Doyle Log Rule (Table 4) are the two most commonly used rules in Missouri. The International Rule takes into account the taper in a log and probably is the most accurate, but it requires the sawmill to have a good sawyer and good equipment to cut out the volumes estimated.

Table 2
Board-foot volume of trees1 by diameter and height classes (International Rule -- Form Class 76)

D.B.H. Number of 16-foot logs in trees
1/2 1 1-1/2 2 2-1/2 3 3-1/2
Volume in board feet
10 inches 21 34 44 55      
12 inches 30 52 68 85 98    
14 inches 42 74 99 124 143 162  
16 inches 59 100 134 169 198 226 246
18 inches 74 129 175 221 259 297 325
20 inches 92 162 220 279 328 377 413
22 inches 112 198 271 344 406 467 514
24 inches 133 237 326 415 491 567 622
26 inches 158 284 392 500 592 684 755
28 inches 187 331 458 585 696 806 888
30 inches 220 381 529 677 805 933 1029
32 inches 254 435 606 776 926 1077 1192
34 inches 291 493 687 881 1054 1227 1359
36 inches 333 559 782 1006 1205 1404 1557
38 inches 374 624 874 1125 1354 1582 1754
40 inches 415 693 974 1256 1510 1764 1962
1For estimating board feet in standing trees

Table 3
The board-foot contents of logs according to the International Rule using a saw cutting 1/4-inch kerf

Diameter of log small ends, inside bark Length of logs (feet)
8 10 12 14 16
Board feet
6 inches 10 10 15 15 20
7 inches 10 15 20 25 30
8 inches 15 20 25 35 40
9 inches 20 30 35 45 50
10 inches 30 35 45 55 65
11 inches 35 45 55 70 80
12 inches 45 55 70 85 95
13 inches 55 70 85 100 115
14 inches 65 80 100 115 135
15 inches 75 95 115 135 160
16 inches 85 110 130 155 180
17 inches 95 125 150 180 205
18 inches 110 140 170 200 230
19 inches 125 155 190 225 260
20 inches 135 175 210 250 290
21 inches 155 195 235 280 320
22 inches 170 215 260 305 355
23 inches 185 235 285 335 390
24 inches 205 255 310 370 425
25 inches 220 280 340 400 460
26 inches 240 305 370 435 500
27 inches 260 330 400 470 540
28 inches 280 365 430 505 585
29 inches 305 385 465 545 630
30 inches 25 410 495 585 675

Table 4
The board-foot contents of logs according to the Doyle Log Scale

Diameter Length of log (feet)
6 8 10 12 14 16
Contents in board feet
8 inches 6 8 10 12 14 16
9 inches 9 13 16 19 22 25
10 inches 14 18 23 27 32 6
11 inches 18 25 31 37 43 49
12 inches 24 32 40 48 56 64
13 inches 30 41 51 61 71 81
14 inches 38 50 63 75 88 100
15 inches 45 61 76 91 106 121
16 inches 54 72 90 108 126 144
17 inches 63 85 106 127 148 169
18 inches 74 98 123 147 172 196
19 inches 84 113 141 169 197 225
20 inches 96 128 160 192 224 256
21 inches 108 145 181 217 253 289
22 inches 122 162 203 243 284 324
23 inches 135 181 226 271 316 361
24 inches 150 200 250 300 350 400
25 inches 165 221 276 331 386 441
26 inches 182 242 303 363 424 484
27 inches 198 265 331 397 463 529
28 inches 216 288 360 432 504 576
29 inches 234 313 391 469 547 625
30 inches 254 338 423 507 592 676

Scaling logs

The scaling of logs is the normal basis for transactions between loggers and sawmillers. Although not as accurate as the actual lumber tally after sawing, log scaling has certain advantages. It permits prompt settlement for timber cut and delivered without waiting for actual yield, and it eliminates the need for separating logs on the yard by ownership.

Scaling practices may vary in local areas. Therefore, these practices should be agreed upon before sawlogs are sold. The standard methods for obtaining log measurements are:

Diameter
measured at the small end, inside the bark and to the nearest inch. For logs that are not round, average diameters should be taken. For example, a log measuring 10.0 inches in one direction across the diameter and 11.2 inches in another direction will average 10.6 inches. This would be scaled as an 11-inch log.

Length
usually measured to an even number of feet such as 8, 10, 12, etc. If logs are cut to lengths between these even numbers, then the length is called to the smaller even number rather than to the nearest even number. For example, a log measuring 15 feet, 7 inches would be scaled as a 14-foot log rather than as a 16-foot log. In actual practice, about 3 inches additional length should be allowed. This will permit trimming the rough ends of boards sawed from the log.

Once the diameter and length have been measured, the log rule is used to determine the board-foot volume. Since log rules are constructed on the basis of sound, straight logs and no allowance is made for defect, volume loss due to defect must be calculated separately and deducted from the gross scale given by the log rule. There are guides available for estimating the amount of defect in logs.

Measuring standing timber

Timber is often sold on a stumpage basis, which means it is sold in standing trees rather than cut products such as logs, posts and pulp wood. To determine the volume of a tree, its d.b.h. (diameter breast height) and merchantable height must be determined. When these two measurements are known, the volume of the tree can be read directly from a tree volume table.

Measuring diameter at breast height (d.b.h.)

Diameter measurements of standing timber are made at breast height, which is 4-1/2 feet above the ground, because this is above the swell of the base of most trees.

The two most frequently used instruments to measure tree diameter are the diameter tape and the cruising stick. The diameter tape shows tree diameter by measuring circumference. It is based on the fact that circumference of a circle is equal to the circle's diameter multiplied by 3.14. Consequently, each division on the tape is 3.14 inches apart, with each division representing 1 inch in the tree's diameter. The diameter tape is wrapped around the tree at breast height and the diameter is read directly from the tape.

The cruising stick does not measure as accurately as the diameter tape but is much faster. It is based on a system of similar triangles (identical angles but different side lengths) to determine the distances on the stick that correspond to each inch in diameter.

To use the cruising stick, hold it horizontally, 25 inches from your eye (about arm's reach for the average person) against the tree at breast height. Be sure you have the "diameter measurement" side (front) of the stick toward you and not the log scaling side (back). Line up the zero end with the outside of the tree. Then without moving your head and using only one eye, look at the other side of the tree and read the figure nearest to where your line of sight crossed the stick and the edge of the tree. That number is the estimate of the tree's diameter at breast height.

It is important to move your eye instead of your head, or your reading will not be correct

If the tree is not round, take another reading at a right angle to the first and average the two readings.

Measuring merchantable (usable) height

Individual tree height normally is measured from a 6-inch stump to a point on the stem beyond which marketable sawlogs or other products cannot be cut. For sawlogs (a 16-foot log), the merchantable height usually is to a top diameter of not less than 8 inches. Cordwood (short logs, called "bolts") may be figured to about a 4-inch diameter. It is important to note that the merchantable top may occur at a point lower on the trunk than previously mentioned if merchantability is limited by forking, large branches or deformity.

To measure height, use that portion of the front of your cruising stick marked off as "number of 16-foot logs."

If it is necessary to go farther than 50 feet for a clear view of the tree, you may pace twice the distance and then double the reading obtained from the stick. After a little practice in timber cruising, you will find that you do not need to measure the merchantable heights of all trees. Foresters usually measure a few during a day of cruising just to "check their eye," but most of the height estimating is done by eye rather than by measurement when tallying saw timber.

Computing the volume of standing trees

Computing board feet in logs

On the back side of the Missouri Department of Conservation cruising stick is an International Log Rule. To use the rule, read from the stick the number of board feet in a log of the length you have measured. (Log lengths in feet are printed in the left-hand column on the stick and read 8, 10, 12, 14 and 16.) The diameters (in inches) are printed across the top of the stick. The point of intersection of the diameter and log length columns gives the board feet in the log if the log is straight and sound. Defects must be deducted.

Computing cordwood

Table 5 gives rough estimates of the amount of cordwood that can be produced from trees of various diameters and heights. The table is read in the same manner as the tree volume and log rule tables.

Table 5
Cord volume

D.B.H. Height in number of 8-foot bolts
1 2 3 4 5 6
Volume in cords -- unpeeled
6 inches 0.02 0.03 0.04 0.06    
8 inches 0.03 0.05 0.07 0.09 0.12 0.14
10 inches 0.05 0.07 0.10 0.13 0.17 0.20
12 inches 0.07 0.10 0.14 0.18 0.22 0.27
14 inches 0.10 0.13 0.18 0.23 0.29 0.35
16 inches 0.12 0.17 0.22 0.29 0.36 0.44
18 inches   0.20 0.27 0.35 0.44 0.53
20 inches   0.25 0.32 0.42 0.52 0.63
Taken from Technical Note 202, Lakes States Forest Experiment Station, University Farm, St. Paul, Minnesota, 1943. Volume is stem volume above one foot stump in standard unpeeled cords (standard cord is 4 feet x 4 feet x 8 feet). Height is number of usable 8-foot bolts to a variable top diameter, not less than 4 inches inside the bark.

Some woodland management tips

G5050, reviewed October 1993