How to calculate board feet of a tree
Measuring Standing Trees  Ohioline
Determining Diameter, Merchantable Height, and Volume
Randall B. Heiligmann, Extension Specialist, Forestry
Stephen M. Bratkovich, Former Extension Specialist, Forestry
Woodland owners often need to measure the merchantable boardfoot content (termed "volume") of certain trees in their woodland. In order to sell timber, for example, an estimate is needed of the quantity to be sold. If trees are to be cut to provide lumber, an estimate of volume is needed to determine what size and how many trees to cut. Using the methods described in this article, a woodland owner can estimate the boardfoot volume in one or several trees. If an estimate is needed for several acres, however, it is recommended that the woodland owner engage the services of an Ohio Department of Natural Resources Division of Forestry Service Forester, a consulting forester, or an industry forester. Methods needed to accurately and efficiently inventory timber volume on large areas are beyond the scope of this publication.
Tree Volume EstimationIn the United States, the most common measure of lumber volume is the board foot, defined as a piece of wood containing 144 cubic inches. It can most easily be visualized as a board 12 inches square and one inch thick (12" x 12" x 1" = 144 cubic inches). However, any piece of wood containing 144 cubic inches is a board foot (e.g., 3" x 4" x 12"; 2" x 6" x 12"; etc.). The boardfoot content of any board may be determined by multiplying the length by the width by the thickness, all expressed in inches, and dividing by 144 cubic inches.
The board foot is also the most common volume measure for trees and logs to be used for lumber and veneer. The boardfoot volume of a tree or log is an expression of the number of board feet of lumber that can be cut from that tree or log. The lumber volume that can be cut from a tree or a log depends on a great many variables, including how the tree is cut into logs, the dimensions of the lumber, how much of the log is lost in sawdust and waste, and the efficiency of the sawmill and workers. Because of these variables, the boardfoot volume of a tree or log cannot be measured exactly but is estimated.
Numerous methods (called "rules") have been developed to estimate boardfoot tree volume. Two boardfoot volume rules are commonly used in Ohio, the Doyle and the International 1/4Inch rules (Tables 1 and 2). Both of these rules provide an estimate of the boardfoot content of a tree based on treetrunk diameter breast high and merchantable tree height (discussed later). The Doyle rule is the most common rule in Ohio. It is used by the timber industry and many professional foresters. The International 1/4Inch rule is used by state agencies and the U.S. Forest Service.
Table 1. Standing Tree Board Foot Volumes—Doyle Rule  
Dbh (inches)  Number of 16Foot Logs  
1/2  1  11/2  2  21/2  3  31/2  4  
Board Feet  
12  20  30  40  50  60  
14  30  50  70  80  90  100  
16  40  70  100  120  40  160  180  190 
18  60  100  130  160  200  220  40  160 
20  80  130  180  220  260  300  320  360 
22  100  170  230  280  340  380  420  460 
24  130  220  290  360  430  490  540  600 
26  160  260  360  440  520  590  660  740 
28  190  320  430  520  620  710  800  880 
30  230  380  510  630  740  840  940  1,040 
32  270  440  590  730  860  990  1,120  1,220 
34  300  510  680  850  1,000  1,140  1,300  1,440 
36  350  580  780  970  1,140  1,310  1,480  1,640 
38  390  660  880  1,100  1,290  1,480  1,680  1,860 
40  430  740  990  1,230  1,450  1,660  1,880  2,080 
42  470  830  1,100  1,370  1,620  1,860  2,100  2,320 
From: Ashley, Burl S. 1980. Reference handbook for foresters. USDA NAFR15. 35 pp. 
A comparison of these two volume tables will show that they are not identical. The International 1/4Inch rule is generally considered to be the best estimate of the amount of lumber that can actually be sawn from a tree or a log under optimum conditions. The Doyle rule substantially underestimates the volume of trees in the smaller diameter classes. The International 1/4Inch rule should, therefore, be used when the most accurate estimate of yield is important, as when determining how many trees to cut to obtain a specified amount of lumber. When marketing timber stumpage, however, the choice of volume rule is less critical. Confusion on quantity should not arise as long as both buyer and seller know which rule was used to estimate volumes. Timber stumpage prices are commonly adjusted based on which rule is used.
Measuring Tree DiameterTreetrunk diameters are measured at breast height (termed diameter at breast height or DBH), defined as the diameter of the tree 4½ feet above ground on the uphill side of the tree. If a tree forks below breast height, each trunk is treated as a separate tree. DBH can be measured with a tree caliper, a Biltmore stick, a tree diameter tape, or a flexible measuring tape (e.g., cloth or steel). Tree calipers, Biltmore sticks, and treediameter tapes can be purchased through forestry equipment supply companies. The flexible measuring tape can be used to measure tree trunk circumference and circumference divided by 3.14 to determine diameter.
Table 2. Standing Tree Board Foot Volumes—International 1/4Inch Rule  
Dbh (inches)  Number of 16Foot Logs  
1/2  1  11/2  2  21/2  3  31/2  4  
Board Feet  
12  30  60  80  100  120  
14  40  80  110  140  160  180  
16  60  100  150  180  210  250  280  310 
18  70  140  190  240  280  320  360  400 
20  90  170  240  300  350  400  450  500 
22  110  210  290  360  430  490  560  610 
24  130  250  350  430  510  590  660  740 
26  160  300  410  510  600  700  790  880 
28  190  350  480  600  700  810  920  1,020 
30  220  410  550  690  810  930  1,060  1,180 
32  260  470  640  790  940  1,080  1,220  1,360 
34  290  530  730  900  1,060  1,220  1,380  1,540 
36  330  600  820  1,010  1,200  1,380  1,560  1,740 
38  370  670  910  1,130  1,340  1,540  1,740  1,940 
40  420  740  1,010  1,250  1,480  1,700  1,920  2,160 
42  460  820  1,100  1,360  1,610  1,870  2,120  2,360 
From: Ashley, Burl S. 1980. Reference handbook for foresters. USDA NAFR15. 35 pp. 
Measuring Merchantable Height
Merchantable height is the height of the tree (or the length of its trunk) up to which a particular product may be obtained, usually minus a onefoot stump height. Merchantable tree heights for sawlogs and veneer are generally estimated to the height where the trunk diameter tapers to 10 inches, or until heavy branching or defects are encountered. The merchantable height of very valuable trees, such as veneer black walnut, may be measured to the nearest foot or two feet. The merchantable height of most other trees is measured in units of 16foot logs and 8foot halflogs. Merchantable height measurements are rounded to the nearest halflog. Thus, a tree with a merchantable height of 42 feet would be measured as having 2½ logs of merchantable height.
Merchantable heights may be measured with a number of special instruments designed specifically for treeheight measurements such as clinometers, altimeters, relascopes, or hypsometers. These instruments are available through forestry equipment supply companies. Merchantable heights can also be measured with a long pole if only a few trees are being measured and they have relatively short merchantable heights. With some practice, merchantable heights in log and halflog units can be estimated quite accurately, particularly for trees with short merchantable heights.
Using the Tables to Estimate Merchantable Tree VolumeOnce the diameter at breast height and the merchantable height of a tree have been measured, Table 1 or 2 may be used to estimate its volume in board feet. For example, a 20inch DBH oak tree with a merchantable height of 2½ logs contains 260 board feet Doyle rule or 350 board feet International 1/4Inch rule.
When using these tables, it is important to remember that only that portion of the trunk that will produce a useable product should be measured. Portions of the trunk or entire trunks that are hollow, excessively crooked, rotten, etc. , should not be measured. You may hear foresters or buyers talking about gross and net volume. Gross volume is the estimated tree volume without deduction for defects (i.e., the DBH and merchantable heights of all of the trees were measured ignoring defects, volumes were determined, and the volumes were added up). Net volume is the estimated tree volume with proper deductions made for defects.
How Much Lumber in that Tree? (E2915)
There are times when a woodland owner may want to determine the board foot volume of certain trees in his or her woodlot for building purposes or for sale. Measuring the volumes of standing trees enables the property owner to select the proper combination of available trees to provide the desired amount of lumber. Volume calculations can also help the woodland owner avoid harvesting more trees than necessary and can give him or her an accurate accounting of the number of board feet for sale.
Large trees that will yield boards for lumber are called sawtimber trees. Sawtimber is measured and sold in terms of board feet. A board foot is 1 inch thick, 1 foot wide and 1 foot long. The first step in determining the board foot contents of standing trees is measuring their diameters and usable heights. Tables 2, 3 and 4 summarize these volumes using various log rule techniques.
Anyone can determine the board foot content of their trees by following a few simple steps. This bulletin describes how to estimate the amount of lumber in a tree with easytomake tools. If an estimate of the entire woodlot is needed, however, the owner should contact an area forester or a consulting forester for this service. More complex techniques are involved in estimating volumes on a large scale, which are beyond the scope of untrained individuals.
Measuring Diameter
Tree diameters are measured at breast height, which is 41 ⁄2 feet above the average ground level. Although diameter tapes are often used to take this measurement, another tool, called a Biltmore stick^{1}, is easy to construct in the home workshop. Use a straight piece of hardwood that is free from knots or other defects, as shown in Fig.1. The stick should be 30 inches long, 1 ⁄2 inch thick and 11 ⁄2 inches wide, and beveled on one edge.
Fig. 1. Dimensions of Biltmore stick designed to measure tree diameter on one side and merchantable tree height on the other side.
Sand the sides and edges of the stick smooth. The stick is then graduated on the unbeveled side according to the figures given in Table 1.
^{1}The Biltmore stick may also be purchased from forestry equipment catalogues such as Forestry Suppliers or Ben Meadows.
Table 1. Biltmore rule graduations.
Diametergraduations on a stick  Distance in inches from end of stick to diameter graduations  Diametergraduations on stick  Distance in inches from end of stick to diameter graduations 
5  4. 6  18  13.7 
6  5.4  19  14.3 
7  6.2  20  14.9 
8  7.0  21  15.5 
9  7.7  22  16.0 
10  8.  23  16.6 
11  9.2  24  17.1 
12  9.8  25  17.7 
13  10.5  26  18.2 
14  11.2  27  18.7 
15  11.8  28  19. 2 
16  12.5  29  19.7 
17  13.1  30  20.2 
Measure tree diameters with the Biltmore stick in the following way (see Fig. 2):
1. Hold the stick 25 inches from your eyes in a horizontal position. Hold the beveled edge of the stick against the trunk of the tree at breast height.
2. Look straight at the tree without moving your head from side to side. Adjust the stick so that the left or zero end is lined up with the left side of the tree.
3. Without moving your head, shift the line of sight to the righthand side of the trunk.
4. Read the diameter on the stick nearest the point at which the line of sight crosses it.
Tree diameter can also be measured using an ordinary tape measure. Wrap the tape around the circumference of the tree at 4.5 feet above its base. Divide the circumference by 3. 14 (π) to calculate the diameter of the tree.
Fig. 2. Measuring tree diameter with a Biltmore stick.
Measuring Height
Tree heights are measured in units of 16foot logs or fractions thereof. In slender, straight trees, this measurement is taken to a point on the upper trunk of the tree where the diameter inside the bark is 8 inches. With older trees, however, excessive branching or forks may reduce the usable height. One should then measure the distance between stump height and usable height.
A Merritt rule for measuring tree heights can be inscribed on the reverse side of the Biltmore stick; then both rules, one for measuring tree diameter and the other for measuring tree height, will be on the same stick.
To inscribe the Merritt rule on the stick, simply mark graduations of 6.1 inches from the zero end of the stick (see Fig. 1). Each graduation represents a 16foot log length. Inscribe halflog marks halfway between the 16foot log marks. Make the graduation for both the diameter scale and the height scale with a sharp pencil or marker. Then give the stick a coat of clear var nish or polyurethane. This will bring out the color of the indelible lead, as well as protect the stick from moisture and discoloration.
Measure tree heights with the Merritt rule by the following method (see Fig. 3):
1. Stand 66 feet from the base of the tree. Hold the stick vertically at a distance of 25 inches from your eye.
2. Adjust the stick so that the zero end is in the line of sight with the upper limit of usable height.
3. Without moving your head or the stick, shift your line of sight to the stump height at the base of the tree (usually 12 to 16 inches above ground level). From the scale, read the number of logs (or fractions of logs) in the tree.
If the ground is not level, stand on a spot that has about the same elevation as the base of the tree.
Fig. 3. Measuring tree height in 16foot log units with a Merritt rule.
Determining Tree Volume
After the diameters and heights of the trees have been measured, the board foot content for each tree can be read from a volume table. Board foot volume is estimated in many ways. Because many of these calculations were developed before the benefit of calculators, estimations are simplified formulas that are easy to tabulate by hand. Other, later formulas are more complex but ultimately more accurate in estimating the amount of useable wood. The International log rule (Table 2), one of these more recent estimation systems, gives a very accurate measure of the amount of lumber that a sound, straight tree will yield at the sawmill.
Local customs, however, sometimes require using other log rule calculations when standing timber is sold. Estimated volumes from two other log rules, Doyle and Scribner Decimal C, are given in Tables 3 and 4.
If you are going to fell the trees yourself and haul the logs to the mill, read the board foot values in Table 2, the International rule. However, if you are selling standing trees in the Lower Peninsula (and if the buyer insists), use the values in Table 3. If your trees are in the Upper Peninsula and the buyer demands it, use the values based on the Scribner Decimal C rule (Table 4).
In using these tree volume tables, increase the volumes by 10 percent for the following trees: balsam fir, spruce, white oak, yellow poplar, black cherry, beech and ash. Also, make suitable deductions for visible defects, such as rot.
Table 2. Tree volume table based on International log rule.
Diameter 4 ½ feet above ground (inches)  Number of 16foot logs
 
1  2  3  4  
Volume in board feet  
10  35  60 


11  45  75 


12  55  90  120 

13  65  110  145 

14  80  130  175 

15  90  155  200 

16 
 180  240  285 
17 
 205  280  330 
18 
 235  315  375 
19 
 265  360  425 
20 
 295  400  480 
21 
 330  450  540 
22 
 370  500  605 
23 
 405  550  665 
24 
 440  605  725 
25 
 485  665  800 
26 

 725  880 
27 

 790  950 
28 

 850  1,030 
29 

 920  1,110 
30 

 990  1,070 
Table 3. Tree volume table based on Doyle rule.
Diameter 4 ½ feet above ground (inches)  Number of 16foot logs
 
1  2  3  4  
Volume in board feet  
10  15  20 


11  20  30 


12  30  45  50 

13  40  60  70 

14  50  75  95 

15  60  95  120 

16 
 115  150  170 
17 
 140  180  210 
18 
 165  215  250 
19 
 195  255  300 
20 
 225  295  350 
21 
 260  345  400 
22 
 295  390  460 
23 
 330  445  520 
24 
 370  495  580 
25 
 415  560  660 
26 

 620  740 
27 

 685  815 
28 

 750  890 
29 

 825  980 
30 

 900  1,070 
Table 4. Tree volume table based on Scribner Decimal C rule.*
Diameter 4 ½ feet above ground (inches)  Number of 16foot logs
 
1  2  3  4  
Volume in board feet  
10  3  4 


11  4  6 


12  5  8  10 

13  6  9  12 

14  7  11  15 

15  8  14  18 

16 
 16  21  25 
17 
 18  25  29 
18 
 21  28  33 
19 
 24  32  38 
20 
 27  36  43 
21 
 30  41  49 
22 
 34  46  55 
23 
 37  51  61 
24 
 41  56  66 
25 
 45  62  74 
26 

 68  81 
27 

 74  89 
28 

 80  96 
29 

 86  104 
30 

 93  112 
*The figures shown in this table must be multiplied by 10 to obtain board foot values.
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Calculation of lumber
No construction is complete without the use of wood. Therefore, the relevant question for many future is: “How to calculate the right amount of lumber?” After all, no one wants to waste money on buying unnecessary boards. But it’s also unpleasant to lose precious construction days due to suddenly ending boards.
The price of lumber for construction is usually indicated in cubes. But the volume of construction is usually calculated in square meters. Let's try to figure out how these parameters are related.
If school knowledge is still fresh in your memory, then you can easily remember how cubic capacity is calculated. If not, we remind you:
Cubic capacity = length × width × thickness 
For calculations, it is customary to convert all parameters into meters, since it is necessary to calculate the CUBOMETER. If you have difficulty converting millimeters to meters, you can use a special calculator on the Internet by typing "millimeters to meters converter" in the search bar.
For example, let's take a board 25x120 mm and 4.5 meters long. Thus,
Board cubage = 4.5 × 0.12 × 0.025 = 0.0135 m ^{ 3 } 
Now, knowing the volume of one board, you can easily calculate how many boards fit in a cube, as well as how much one board costs.
1 m ^{ 3 } / 0.0135 m ^{ 3 } ≈ 74 pieces  so many boards in a cube 
(usually the number is a fraction and it is customary to round it down)
If the price of 1 cubic meter of boards is 2100 hryvnia, then you need to multiply this number by the cubic capacity of one board:
2100 UAH × 0. 0135 m 5 m) 
For those who do not like to count: tables and calculators
In the age of scientific and technological progress and universal standardization, it is not necessary to delve into the intricacies of calculations. The Internet will come to your aid. Enter in the search bar "calculation of boards in a cube calculator" and follow the first link. It remains only to enter the length, width and thickness of the board in the appropriate fields  and the result is ready!
In the old days, when no one had even heard of online calculators, detailed tables were compiled that helped calculate the number of pieces of wooden boards in one cube and how many square meters fit in a lumber cube.
Board length  Board width and thickness (mm)  Number of boards in a cube (pcs)  Volume 1 board (m ^{ 3 } )  square meters in 1 cube 
Twenty  
6 m  20x100  83  0. 012  50 m ^{ 2 } 
6 m  20x120  69  0.0144  50 m ^{ 2 } 
6 m  20x150  55  0.018  50 m ^{ 2 } 
6 m  20x180  46  0.0216  50 m ^{ 2 } 
6 m  20x200  41  0.024  50 m ^{ 2 } 
6 m  20x250  33  0.03  50 m ^{ 2 } 
Twentyfive  
6 m  25x100  67  0. 015  40 m ^{ 2 } 
6 m  25x120  55  0.018  40 m ^{ 2 } 
6 m  25x150  44  0.0225  40 m ^{ 2 } 
6 m  25x180  37  0.027  40 m ^{ 2 } 
6 m  25x200  33  0.03  40 m ^{ 2 } 
6 m  25x250  26  0.0375  40 m ^{ 2 } 
Thirty  
6 m  30x100  55  0. 018  33 m ^{ 2 } 
6 m  30x120  46  0.0216  33 m ^{ 2 } 
6 m  30x150  37  0.027  33 m ^{ 2 } 
6 m  30x180  30  0.0324  33 m ^{ 2 } 
6 m  30x200  27  0.036  33 m ^{ 2 } 
6 m  30x250  22  0.045  33 m ^{ 2 } 
Thirtytwo  
6 m  32x100  52  0. 0192  31 m ^{ 2 } 
6 m  32x120  43  0.023  31 m ^{ 2 } 
6 m  32x150  34  0.0288  31 m ^{ 2 } 
6 m  32x180  28  0.0346  31 m ^{ 2 } 
6 m  32x200  26  0.0384  31 m ^{ 2 } 
6 m  32x250  20  0.048  31 m ^{ 2 } 
Sorokovka  
6 m  40x100  41  0. 024  25 m ^{ 2 } 
6 m  40x120  34  0.0288  25 m ^{ 2 } 
6 m  40x150  27  0.036  25 m ^{ 2 } 
6 m  40x180  23  0.0432  25 m ^{ 2 } 
6 m  40x200  20  0.048  25 m ^{ 2 } 
6 m  40x250  16  0.06  25 m ^{ 2 } 
Pentecost  
6 m  50x100  33  0. 03  20 m ^{ 2 } 
6 m  50x120  27  0.036  20 m ^{ 2 } 
6 m  50x150  22  0.045  20 m ^{ 2 } 
6 m  50x180  18  0.054  20 m ^{ 2 } 
6 m  50x200  16  0.06  20 m ^{ 2 } 
6 m  50x250  13  0.075  20 m ^{ 2 } 
Also read: Finishing OSB (OSB) Boards
To date, edged and unedged board is the most popular lumber.
Manufacturers produce numerous variations of this material in sizes from 16x8 mm to 250x100 mm.At the same time, the width of the board is always at least twice the thickness, if the aspect ratio changes, the material is already called a beam. It is customary to measure an edged board in cubic meters, therefore, to determine the cost of work, you need to learn how to determine the weight of a cube of an edged board. Fortunately, there are readymade tables and formulas that will allow you to quickly deal with this task.
Calculation of the cubic capacity of edged boards
As a rule, most novice builders do not think about the question “a cubic meter of boards is how much1009 » , but simply use the table below. However, we strongly recommend that you learn how to calculate the cubature yourself, this will greatly simplify the work, and only in this case you can consider yourself a professional.
If we compare an edged board with an unedged or onesided edged board, there are no places on the surface of the first where the bark used to be, this parameter is called wane. A small amount of wane is generally allowed, but the smaller the amount, the better. So in terms of geometry, such a board is guaranteed to be a rectangular parallelepiped. This figure has three parameters: thickness, width, length, which are usually expressed by the letters a, b, l. These indicators are enough to know how to calculate the cubature of the board in a few seconds.
It is important to know that there is an official standard according to which boards can only be produced with the “a” parameter equal to 22, 25, 30, 40, 50, 100 mm. There are also other lumber that are made from others by planing or sawing. Their width varies from 100 to 250 mm, step 50 mm. The length of such boards can be 3, 4, 6 m.1010
Once you know all the values, you can quickly answer the question of how to calculate the cubic capacity of the board. Before calculations, you need to convert all values \u200b\u200bto meters. For example, we have a board measuring 25 mm x 10 cm x 4 m, when converted to meters, we get 0. 025, 0.1, 4. Now we multiply these parameters:
0.025 * 0.1 * 4 = 0.01
on the result obtained and find out how to calculate the cube of boards, or rather the number of boards in a cube of wood.
1 / 0.01 = 100
Thus, a cubic meter will contain 100 boards of the indicated dimensions. Now you can easily answer the question of how to calculate the cube of boards, but you need to learn how to count the amount of lumber needed to complete the work.
What is an inch board and how to calculate its cubature? To find out how many inches of an inch board are in a cube, we need to make the calculations already familiar to us, as a result of which we get 66 pieces with a board width of 10 cm, and 44 pieces with a board width of 15 cm. As a rule, one cubic meter is enough to cover an area of 40 square meters.
Calculation of the cubature of an unedged board
As already mentioned, there is also an unedged board, which is obtained as a result of longitudinal sawing of logs without processing on the sides. So it is usually somewhat more difficult to find the answer to the question of how many boards in a cube of unedged boards than in the first case. The fact is that for unedged lumber, only the width and length are accurately indicated, but the width can vary. Much depends on which part of the tree a certain board is cut from. If you are wondering how to consider the cubic capacity of an unedged board, you first need to think about the task at hand.
For example, you may need to sheathe a building, in which case you will first find out the finishing area and multiply it by the thickness of the sheathing, this will allow you to calculate the required amount of material. Let's describe this situation in numbers:
How many unedged boards 25 mm thick can be needed for the sheathing of a rectangular structure 10 * 5 meters and 3 meters high?
We calculate the entire area for finishing, for this we multiply the perimeter of the building by its height: (10 + 10 + 5 + 5) * 3 = 90 square meters. Now we multiply the obtained value by the thickness of the material: 90 * 0.025 (translate millimeters into meters) = 2.25 cubic meters.
As you can see, in this case, the width of a single cladding element practically does not matter, since this does not affect the overall cubic capacity. However, sometimes it may still be useful for you to know the average dimensions of the board, which will allow you to approximately find out how many unedged boards are in a cube. These approximate data are shown in the table:
What else you need to know when calculating the required amount of lumber
Always remember about the calculation error. The fact is that any board manufacturer always rounds the numbers in a favorable direction. For example, a board occupying a volume of 0.045 should actually be in a cubic meter of wood in the amount of approximately 22 pieces, but the manufacturer rounds 0.045 to 0.05, which results in 20 boards per cubic meter. This small margin of error may seem insignificant with volumes of a few cubic meters, but when it comes to hundreds, the difference in the number of boards seems much more significant, not to mention money.
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