Calculating board feet

      The board footage debate rages on--Professor Wengert and others offer up methods of calculation. June 24, 2001

Q.
I just had some poplar logs cut up into 4/4, 5/5 and 6/4. I know how to figure board feet on 4/4, but what thickness do I use for 5/4 and 6/4 in the formula? What about width of 5 1/2" or 22 1/2"--do I round up? These are band saw rough-cut sizes.

Forum Responses
I think you will find the info you need by searching in the archives.

When figuring BF, the first step is always to get the surface measure (SM), which is equal to BF when the lumber is 4/4. Then total all the SM for each thickness separately--sum all the 4/4 together, then the 5/4, etc.--for the lumber that you are working with. Then multiply the SM by the thickness--x1 for 4/4; x1.25 for 5/4; x1.5 for 6/4; etc. We do not figure the BF on each piece separately when handling more than just a few pieces of lumber. (The reason involves rounding errors.)

For pieces that have a BF right on the half, you round up to the closest whole number the first time and then down the next time. However, in your example, if these are widths, we use the width (inches and fractions) and do not round the width.

Gene Wengert, forum technical advisor



At NHLA we figured board feet like this:
Length in feet x width in inches divided by 12 x thickness.

Example:
A board 5 1/2" wide x 10' long x 1 1/2" thick. 6.875 bft= 7bft.
5.5x10/12 x1.5=6.875



Whoever taught you that way to calculate BF is wrong. It is NOT the way that the NHLA uses.

It is important to round the answer after you multiply the width and length and divide by 12. This is the SM and since anyone grading hardwood lumber needs to use the SM and the NHLA always records the SM in their grading record books, I cannot image how someone involved in grading hardwood lumber would teach you the totally incorrect method. In fact, when grading, you get the SM first, grade the piece, and then finally worry about the BF. If you have the SM already, then why go back and do all the multiplication again?

Incidentally, most people use a "grading stick" or "tally stick" to measure BF. This stick does exactly what I stated here and in the previous posting automatically.

Your example, 5.5" x 10' divided by 12 equals 4.58 which is rounded to 5. Then 5 x 1.5 is 7.5. The first time it is counted as 8 BF, then next time or next piece that is at 7.5, 7 BF. But when doing many pieces, you total all the SM for the same thickness first and then multiply by the thickness.

Incidentally, if you use the incorrect method you run the risk of actually charging the customer for more footage than is really there. For example, a piece that is 7-5/8" x 10' x 1.5" is 10 BF in the incorrect method, but is actually only 9 BF. That is nearly a 10% error or over-charge. Probably illegal, to say the least!

Gene Wengert, forum technical advisor



Gene, I disagree. We cut a lot of odd cuts and special cuts and use this method a lot of the time. When we are grading truckloads, we use a tally stick or cube the load. I understood the questioner was trying to find a method of tallying without the use of a grading stick. You may disagree with this method, but it works for odd cuts and beams.


You may use your method, but it is not legal and potentially cheats the customers, as the example I gave above shows. Every mill cannot use its own definition of a board foot. The Weights and Measures people nationally and each state make sure that everyone uses the same measure--BF, gallons of gas, whatever.

I was also concerned that your initial comment indicated that it was the way that the NHLA does it. As I stated, it is NOT the way that the NHLA stipulates or teaches.

Your method is not the way that the NHLA uses and the way they teach. It is not the way addressed in the Model State Regulations adopted by the National Conference on Weights and Measures in 1977. It is not the legal and practiced definition of a board foot. It is not the way that most of the industry uses. It is not a disagreement; it is a matter of fact.

Regarding the measurement of lumber in a bulk load (that you mentioned in your response), the block tally is used, but again, each piece is measured, rounded, and then the total multiplied by the thickness.

(The questioner does not mention the use or lack of use of a tally stick or grading stick. He wanted to know what thickness to use and how to round the width.)

Para. 16 of the Rules.

...multiply the full width of the piece in inches by the standard length in feet and divide by 12, rounding to the nearest whole foot.

Para. 18 instructs that the sum of the SM is = to BF for 4/4 and thinner, and for thicker lumber, the total SM is multiplied by thickness and fractions.

Para. 13 defines the standard thicknesses.

Gene Wengert, forum technical advisor



Gene, I do not plan to cheat anybody on tally or to shortchange myself. What you have just posted is what I said to start with. If NHLA does not figure board foot this way, why do they have Para.16 multiply the full width of the piece in inches by the standard length in feet and divide by 12, rounding to the nearest whole foot? Para.18, for thicker lumber, the surface measure is multiplied by thickness and fractions.


The NHLA says that you round the answer BEFORE you multiply by the thickness. You rounded the answer afterwards, and I showed in the example how rounding at the end can lead to incorrect answers.

Your example should have said 5.5 x 10 / 12 and then round to the closest and then multiply by thickness of 1.5, which means 5.5x10/12= 4.58=5. Then 5x1.5=7.5, which is 8BF the first time and 7BF the second time you get a piece this size.

Gene Wengert, forum technical advisor



Gene, I understand what you are saying. I checked with 4 other inspectors that I have done business with, and they say they don't round off till after the thickness has been figured in. Check with NHLA. If I am wrong, I want to change the way I calculate for the thickness. I have always tried to conduct business the right way.


Para. 16 and 18 indicate how to do it and that is to round the SM and then multiply by the thickness. I checked with a former national inspector and he says that is correct and he has not seen a mill do otherwise. Lumber graders will tally the SM in their book. Each page is for a different thickness. After they are done grading, then they multiply the SM on each page (and for each grade) by the thickness. This is the way lumber grading is taught by me, the NHLA, and hopefully by all others, too. It is also the way that the lumber scaling (also called a lumber grading) stick works. You get the SM from the stick (already rounded) and then multiply by the thickness. In fact, probably 99% of all graders will use a grading stick for measuring footage. So, they may not know that they are actually rounding the SM, but it is automatic with a stick (either the wooden scale sticks or the plastic "rainbow" sticks).

Gene Wengert, forum technical advisor



Gene, I am not arguing over tallying with a grading stick. I go through 10,000' to 20,000' feet per day using the exact same method you described. But when you use the mathematical way to tally, width x length /12 x thickness, you have a more accurate number if you don't round off until the thickness has been figured in.

Example: a beam 8"x8"x20'. Rounding off first, it is 104', rounding off last, it is 107'. Tallying lumber is finding the cubic feet of the piece, correct? If you are going to find the cubic feet in this timber, which answer is closest to the actual cubic feet?

I know what you are saying and I agree, to a point. But I live in the real world and play by the rules. I am not cheating anybody, as you have alleged. It is sound business practice. You don't give lumber away. If I gave away this much lumber in every beam I sold I would have been out of business 20 years ago. If I had been cheating people, I would have been out of business 20 years ago.



You do not have a more accurate number because the rules on measurement define what accuracy is, not common sense. These rules are over 100 years old. (They do not have the objective of figuring the cubic footage.)

To quote from the INSPECTION TRAINING MANUAL, "We do not convert each piece [to board feet] as we inspect the lumber. It is all tallied as 4/4 thickness. After figuring the tally [the sum of all SMs], we multiply by the appropriate thickness."

"Example: A tally shows 618 ft. SM. If the stock is 10/4, we multiply 618 x 10/4 = 1545' board measure."

Gene Wengert, forum technical advisor



You are both forgetting that the law of averages says no matter how you do it, over time it will all be the same.

To use an above example:
an 8"x8"x20' beam rounded before is 104 bf, rounded after, is 107 bf.

BUT

an 8"x8"x19' beam rounded before is 104 bf, rounded after, is 101 bf.

So in the end, it will all come out in the wash, no appreciable difference.



I do not know of anyone using the mathematical formula for many pieces--it is used for a few pieces, in which case the "law of averages" will not work for an individual order of just a few pieces. Also, some hardwood mills make lumber specific widths and not random. Again, the "law" will not always work out. But, it is rare that anyone uses the math; they use sticks with the multiplication and rounding already done for them.

Gene Wengert, forum technical advisor



We use a tally stick most of the time, about 98% when tallying lumber. We always use the math method on timbers. Ever tried grading out a load of timbers with a tally stick? Another reason to use the math is shipping timbers. The closer you can figure the actual board footage without doing any rounding off, the closer you can figure the weight. This can get you more on a truck without going overweight.


Check out these:

Timber and Lumber Calculators

There is a board footage calculator, log volume calculator, tree value calculator and lumber and log weight calculator here.



The comments below were added after this Forum discussion was archived as a Knowledge Base article (add your comment).

Comment from contributor J:
Perhaps this will help. Board feet can be figured easily. Here's the formula: board thickness in inches x board width in inches x board length in feet divided by twelve. Here’s an example: you have a 1 1/2" thick board that is 5 1/2" wide and 8 feet long - the formula is 1.5 x 5.5 x 8 divided by 12.



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