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 board-foot 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 board-foot 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 Estimation

In 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 board-foot 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 board-foot 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 board-foot volume of a tree or log cannot be measured exactly but is estimated.

Numerous methods (called "rules") have been developed to estimate board-foot tree volume. Two board-foot volume rules are commonly used in Ohio, the Doyle and the International 1/4-Inch rules (Tables 1 and 2). Both of these rules provide an estimate of the board-foot content of a tree based on tree-trunk 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 1/4-Inch 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 16-Foot Logs
Dbh (inches)	1/2	1	1-1/2	2	2-1/2	3	3-1/2	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 NA-FR-15. 35 pp.

A comparison of these two volume tables will show that they are not identical. The International 1/4-Inch 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 1/4-Inch 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 Diameter

Tree-trunk 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 tree-diameter 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 1/4-Inch Rule
Dbh (inches)	Number of 16-Foot Logs
Dbh (inches)	1/2	1	1-1/2	2	2-1/2	3	3-1/2	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 NA-FR-15. 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 one-foot 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 16-foot logs and 8-foot half-logs. Merchantable height measurements are rounded to the nearest half-log. 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 tree-height 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 half-log units can be estimated quite accurately, particularly for trees with short merchantable heights.

Using the Tables to Estimate Merchantable Tree Volume

Once 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 20-inch DBH oak tree with a merchantable height of 2½ logs contains 260 board feet Doyle rule or 350 board feet International 1/4-Inch 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 easy-to-make 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 stick¹, 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.

¹The Biltmore stick may also be purchased from forestry equipment catalogues such as Forestry Suppliers or Ben Meadows.

Table 1. Biltmore rule graduations.

Diameter-graduations on a stick	Distance in inches from end of stick to diameter graduations	Diameter-graduations 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 right-hand 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 16-foot 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 16-foot log length. Inscribe half-log marks halfway between the 16-foot 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 16-foot 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 16-foot 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 16-foot 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 16-foot 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
Twenty-five
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
Thirty-two
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

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 ready-made 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 one-sided 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.