

Rounding Issues with Woodweb's Lumber CalculatorsQuestion
Below is a report of your entries:
From Professor Gene Wengert, forum technical advisor:
If you want *hardwood* 2x4s, then the surface measure (width x length/12) is always rounded to the closest whole number, so 4x8, 4x9 and 4x10 all give 3 ft SM, which is then multiplied by the thickness (2) to give 6 BF per piece. If you have 53 pieces, then 53 x 6 = 318, which is exactly what you found.
From the original questioner: What stands out in these calculations is that a sawmill operator should not sell or mill by the board foot any 4" wide lumber that is over 8' but under 10'5" long. Has anyone ever published a table showing the extremes of the inequities to the customer or the sawyer this logic produces so both can avoid sizes that cause them to pay or sell something for nothing? How about adding a feature to your calculator that sums all the inequities so the buyer and seller know which one is losing? These rules are hard to explain to a customer while keeping a straight face and still not be taken as a crook. Customers don't like voodoo math. And no matter how legal or widely adopted you assure them the rules are, it won't make them any more comfortable. I'm not taking this out on you, Dr. Gene. I've seen debates about this before. Is there any movement in the industry away from these esoteric/arcane legacy rules?
From contributor S: Forget about that calculator. If you are charging by the board foot, tell the customer a bd/ft is width X length x thickness divided by 144. So if I was charging $.20 a ft to cut 10ft 2x4's, it would be 2"x4"x120+144=6.66 bd/ft. I'd charge him $1.33 to saw that much wood. If the customer or anyone else wants to round it off to 6 bd/ft they can go to Home Depot and try to round off the prices they charge there.
From Professor Gene Wengert, forum technical advisor: The method of calculating board feet has been with us for over 120 years and has been a standard practice for lumber mills for over a century. Further, it is adopted by all the weights and measures departments in all states. It works perfectly for billions of BF of hardwood and softwood lumber every year. If you are going to sell lumber using the term "board feet," then you must use the correct formula and correct definition. If you want to use a different calculation technique, that is certainly okay, but you cannot use the term "board feet." The definition of "board feet" is fixed and is universal. Please understand that the socalled "problem" is the result of reporting BF of hardwood lumber to the closest BF (no fractions). This means that within a given size, some pieces are a fraction more and some pieces are a fraction less than the footage. If you used decimals, you would see this, but the hassle of calculating footage using decimals for each piece would be a big headache indeed. When selling a bunch of pieces of randomwidth hardwood lumber, the fractions will average out, unless you are making a specific size, such as we do with softwoods. That is why softwoods are measured to the closest 0.01 BF for each piece. This is why Home Depot and others charge different prices for different sizes of softwood lumber... The BF is different. (Home Depot does not charge by the BF, but by the piece. However, if they did charge by the BF, they would have different prices per BF for different sizes.) If you use width x length x thickness divided by 144, as suggested above, this means that a piece 6" x 12' x 2" / 144 will be 1 BF. This is incorrect indeed, as the correct answer is 12 BF. So, perhaps you want to use the length in inches? Can you imagine measuring every piece of lumber to the closest inch in length? Sawing is hard enough without calculating the footage to the closest fraction and measuring the length to the closest inch. And also, what about thickness... Are you suggesting that if the piece is 11/8" thick that we use this thickness rather than the nominal 4/4 or 1" thickness? If you use the actual thickness (which we do not in practice), you should actually measure it to the closest 1/64" to assure that you are accurate. This seems silly to me. Rather, use the standard method of measuring footage and at the end of the day you will have the same footage with a lot less work. Note that specific sized pieces (called hardwood dimension) such as 31/2" x 24" would be totaled using the width x length / 144 formula given (with a nominal thickness), but lumber would not. What about the thickness of such pieces... Would you use the actual thickness such as 15/16"? In response to the original questioner, consider a 4.0" wide piece 1" thick. If it was 5' long it would be 2 BF (actually, 1.67 if you used fractions, so the sawmill would win on this one). If 6' long, 2 BF (actually 2.0). If 7', then 2BF (actually 2.33, a slight loss). The same pattern holds for width, as a piece 5.0" wide to 7.0" in width that is 6 ft long is 3 BF. Any piece between 5.0 up to 5.99" in width is a bit under 3.00 BF, while a piece from 6.01" to 6.99" in width is a bit over 3.00 BF. Because we make hardwood lumber random width, these apparent benefits of some sizes and losses of other sizes will average out. However, if you do have an order for specific hardwood lumber size, and that size is not to your benefit, you may wish to adjust the price a small amount to adjust for this. If you use a standard scaling stick for hardwood lumber, you will notice that within each footage box, many sticks have a line at the halfway point. This then tells you if the lumber at a given width is plus or minus within the footage. You also ask if there is a movement to change the BF measurement for hardwood lumber. The answer is no.
From contributor S: The questioner's complaint was that WOODWEB's calculator (according to his examples) was giving him the same bd/ft for a 10ft 2x4 as a 8ft 2x4. If you can get a logger to sell all his 10 ft logs as eight footers, I guess WOODWEB's calculator is valid. Also in my response, I gave all the measurements in inches... And the questioner wasn't asking about hardwood lumber sawn 11/8". I'll stand by my numbers: a 10' 2x4 has exactly 6.66666666 bd/ft. Now you can round off all you want, but if I'm sawing dimension material and charging by the foot, I'm going to charge for what I'm actually sawing. If I'm selling random width hardwood grade lumber, I use a regular board rule and something like 6.66 would be rounded up to 7 and 3.33 would go down to 3. The random widths of the boards are supposed to all even out in the end. But if you saw a whole tractor trailer load of 10 ft 2x4 and are being paid on the footage, you need to get an accurate count.
From Professor Gene Wengert, forum technical advisor: It is not that WOODWEB's calculator is incorrect. The WW calculator is using the traditional, legal and appropriate definition of the board foot. The WW calculator is perfect. The calculator and the industry and the legal system for weights and measures all give the same footage for a 2x4x8 and a 2x4x10 piece of hardwood lumber. The flaw is that hardwood lumber is seldom sold as 2x4, but is manufactured and sold as random width. Further, the length is measured to the last full foot, with all fractions dropped. I have never heard of anyone measuring hardwood lumber's length in inches, such as 120" for a 10' piece. In your formula, it would make more sense to use feet for the length and divide by 12 and not 144. But even with the simplification, the formula does not represent the historic or current, legal definition of a board foot for hardwood lumber. The answer of 6.67 is indeed correct for softwood lumber. Just to clarify, the term "dimension material" when referring to hardwoods means small piece of wood (such as 21/2" x 24" x 3/4") that can be used directly for furniture, cabinets and the like. When referring to softwoods, "dimension material" refers to 2x4, 2x6, 2x8, and so on. As stated, for dimension material (softwood), the 6.67 is the correct number. If you are sawing hardwoods and someone asks you to make a lot of hardwood 2x4x10, then you need to adjust your price accordingly and not change or alter the definition of the term "board foot."
From contributor R: I refer back to this page to find out what I have cut. https://www.csgnetwork.com/boardftcalc.html From Professor Gene Wengert, forum technical advisor: Unfortunately, the calculator referenced by contributor R is in error. For hardwoods, it is totally incorrect. The rules for hardwoods require rounding after dividing by 12 and then no decimals are included in the final answer. This is the legal definition of a board foot and is what is required to be used when selling and has been for over 100 years. The definition is fixed. For softwoods, it gives the footage to many decimals, while the correct procedure is two decimals for softwoods. This again is the legal requirement for selling by the BF in every state. Also, the definition of a board is a piece of lumber under 2" thick, so again the calculator referenced by contributor R is incorrect in that it calls all lumber a "board." Again, the definitions within our industry were determined years ago. When trade is involved, the weights and measure departments in the various states have determined what definitions will be used. We do not have the option of changing the definitions to suit our own feelings. Now, having said the above, the calculator contributor R cites can be used if you want to know what you are doing, as contributor R states. But with random hardwood lumber, the BF calculation will average out and be correct.
From Professor Gene Wengert, forum technical advisor: One point that has not been discussed is how the process works for multiple pieces of hardwood lumber. For example, assume that you have 10 pieces of 5/4 lumber and the size is 71/2" x 10'. The individual piece is 71/2 x 10 /12 = 6 (called the surface measure) times the thickness to get 7. However, with 10 pieces, the correct way is to total the surface measure of all the pieces, giving 60, and then multiply by the thickness to get 75 BF total. From the original questioner: Contributor S makes a valid point: "If you can get a logger to sell all his 10 ft logs as eight footers, I guess WOODWEB's calculator is valid." That's something that came to mind with me. A shrewd buyer could easily spec packages that allowed them to get an extra 20% of materials and labor free. Using the board foot standard you have no recourse but to eat the loss or, if you catch it in time, turn down the job. We frequently cut barn packages. This is all technically hardwood lumber. Without going through each calculation ahead of time, with the intent of spotting this potential loss for the sawyer/buyer, I have no way of knowing if someone's taking a hit. I can also easily imagine how such an inequity could surface by chance: due the width between poles/height of the eaves, etc. What to do when this surfaces on more expensive woods such as walnut or cherry? Dr Gene, where you said, "Note that specific sized pieces (called hardwood dimension) such as 31/2" x 24" would be totaled using the width x length / 144 formula given (with a nominal thickness), but lumber would not. What about the thickness of such pieces... Would you use the actual thickness such as 15/16"?" Would it seem acceptable for a small sawmill operator to change their method for charging to be based on hardwood dimension? In this modern age we have pocket calculators and even PDAs that can easily have software loaded on them for making the calculations easy. But you mentioned that there was a question about how to measure the minimum thickness on hardwood dimension. What is the current standard under hardwood dimension? Would it be acceptable to round it up to a minimum of 1" since that helps to take into account the number of cuts required/wear on machinery and people? I don't see any practical need to measure wood in less than 1/16" increments. It doesn't make sense considering wood moves. I would make it even easier and say 1/8" minimum.
From Professor Gene Wengert, forum technical advisor: Although it looks like a 2x4x10 is not a good deal for the sawyer, there are many other widths and sizes that are a good deal for the miller and not for the buyer. With a variety of sizes, it will all even out. That is the whole point and why it is done historically. It is easy and simple. As most lumber is measured with a scaling stick, it is fast, easy, simple and accurate. The deal about 10' logs is not true unless you are cutting 2x4s only. If you cut 2x6 or other sizes, it is not a problem at all and actually will sometimes benefit the sawyer. So, the comment about 10' and 8' logs is incorrect. If you have an order for 2x4 hardwood pieces or any other size that seems to benefit the buyer, then change the price. But then you will also have to change the price on pieces that benefit the sawyer, such as a 2x8x10'. Regarding stock thinner than 1.00" (in the grading area or clear cutting) for green or airdried, then it is always counted as 1 inch. This accounts for the extra sawdust, work, etc. There will not be a problem with walnut, cherry, oak, etc. as we cut random width, so the plus and minus will balance out. Further, a scaling stick makes the footage easy to obtain. That is why a PDA is not necessary, as the extra effort and work will not have any benefit. They do make automatic scaling measuring devices, but they are expensive. They make less expensive ones where you hold the device up to the end of the lumber and push a button to indicate the width. You certainly can sell lumber based on the actual size (width, length and thickness). If you use inches for all, then you will have cubic inches and then using a price per cubic inch. Just do not call the answer a board foot. (Of course, then when you get shrinkage in drying, you will lose volume more than if you use the standard BF technique.) For hardwood dimension, you might have a price based on cubic inches and not board feet. In fact, seldom is hardwood dimension sold by the BF. You and your customer would work this out.
From contributor S: I visited WOODWEB's bd/ft calculator section, and if you want to figure 2x4's or 4x4's or whatever, just use the softwood calculator. It doesn't round off. From contributor P: The smaller the job, the more valuable the wood, the more important calculations become. 100 year old formulas don't apply. Your customers should know the value of the product. If they don't, you should educate them. From Professor Gene Wengert, forum technical advisor: Although the softwood calculator does not round off, it uses the nominal size and not the actual size. Further, the answer is not the correct answer for hardwood lumber. The 100 year old method for hardwood board footage is the only legal method. It has been and still is the definition for a hardwood BF. (It would be like if we said that we did not like the definition of a mile, so we had a new one that was 5010' per mile. We cannot do that and still call it a mile.) We must use the universal and historical definition. Note that when a lot of pieces are being measured, some pieces will be rounded down and some will be rounded up, but for a bunch of pieces, it will even out. From a production point of view, I do believe it would really be awkward to have to figure out the footage of hardwood lumber while sawing if you have to include fractions and decimals. Certainly, the PDA would be helpful, but then you would have to measure the width of every piece to the closest 1/16". It is a lot easier to use the scaling stick (which is based on the 100 year old formula) and get the answer without having to measure closely. (That is, the scaling stick will show 6 BF for any piece 1" thick and 12' long between 5.5 to 6.5 inches. No need to measure 513/16" wide and get 5.8125 BF. And then have the next piece be 83/16" wide, etc.) I cannot recall ever being in a sawmill that used anything except the scaling stick for hardwood lumber. Of course, the whole purpose of measuring lumber is to get the value that is fair to the producer and fair to the buyer. We seem to be worrying about the footage, but any concerns can be offset by the pricing structure so that we get the correct and fair value.
From contributor B: "Board Feet" is a measurement of lumber volume. A board foot is equal to 144 cubic inches of wood. Actually it's easy to calculate using the following formula: (Thickness x Width x Length) / 144 = Board Feet
board foot
One board foot is the volume of a onefoot length of a "standard board" twelve inches wide by one inch thick. No where can I find that a 2x4x8 is equal to a 2x4x10. Simple elementary school math will tell you they are not the same. Does not matter what type/species of wood. A board foot is a board foot. Just because it has been done a certain way for many years doesn't make it "legal." The legal definition of 1 board foot is 12 square inches 1 inch thick. Or 144 cubic inches. Calling a 2x4x8 and 2x4x10 as equal is just like calling an 8' log the same as a 10' log. I'm sure the loggers will charge me the same for 10' logs as they would an 8'. This nonsense is one reason loggers and sawmillers have the bad reputation many people think we have. You will never convince me or most people with a little common sense that a board foot changes with the type of lumber. We don't change the volume of a gallon between different liquids. Yes, just like different species of wood, different types of liquids change by weight. But, we are talking volume with board feet, not weight. So the measurement is constant and does not vary by wood types.
From contributor J: This is a somewhat related question and I would appreciate any input. When I sell hardwoods, I round up or down, as Gene says, and get a particular number of board feet per piece. But if I sell an entire unit or "package" of hardwood, is it okay to just measure the entire unit? Example: A "package" of maple 36" wide X 24" high X 8' long. So... 24 X 36 X 8 divided by 12 = 576 BF for the unit. Will this be the exact same number if I were to measure each board individually and total them? Or close enough at least that neither seller or buyer is cheated?
From Professor Gene Wengert, forum technical advisor: Contributor J, some people do this and it is called a block tally. If buyer and seller agree, it can be used for hardwoods. The thickness, however, is based on thickness of the lumber. If the lumber is 11/8" thick, then 24" height would be about 22 layers, so you multiply the width and length times 22, not 24. We cannot do this for softwoods, as the nominal size is used for softwoods, not the actual. Contributor B, the information you have posted is incorrect for lumber. It is okay for small parts. For example, the rough size of a softwood 2x4 is not 2" x 4". We would commonly see the thickness to be around 1.83" when first made. As a further indication of this incorrectness, a 2x10 finished size is 9.25" in width, but would never be 10" when first made. I cannot believe that anyone could ever state something that is so incorrect. Also, the hardwood lumber thickness must be at least a full 1.00 inches thick in the grading area (called a cutting) for green and for airdried lumber. This means that 1" hardwood green must actually be a bit thicker than 1.00" thick when cut to allow for air drying shrinkage, if the lumber is graded after air drying. I do not know of a sawmill that would produce green hardwoods at exactly 1". But I do know softwood mills that will produce green softwood 1" lumber that is 0.88" actual when green. In all cases, the length is the last full foot with no fractions. That is not mentioned either.
Further, a hardwood board foot is not given by the formula you have quoted. In some cases the formula may work, but in others, it does not. The weights and measures department of each state as well as the various lumber grading associations have agreed about the definition of a hardwood BF and softwood BF. This definition was posted earlier. Someone who does not know what is going on can easily think one BF is 1" x 12" x 12". This person apparently wrote the definition in the Encarta Dictionary. Regarding 8' and 10' logs, did you read that this concern about the same size for hardwood lumber is for 2x4.0" x 10' lumber? Consider a 2 x 4.25" x 10'. The answer is 8 BF, not 6 BF. That is 33% more. As I have said several times, some pieces will be a little low and some a little high, but with hardwood random width, it will even out. No one is going to count 8' and 10' logs the same. I am not sure how this discussion about lumber has changed to a discussion about the price of logs. In fact, you could really go bonkers if you tried to talk about the different log scales, where one says there are 40 BF, another 48, and another 60 in the same log. But log scaling is an entirely different topic. What makes it legal is that the state weights and measure departments adopt it as the standard. Sometimes the definitions are adopted by the FTC, such as a definition of what makes furniture legal to be called solid wood even thought there are metal fasteners, staples, an MDF back or shelf, holes, grooves, etc. Look up the word "solid" and you will find a definition that cannot be applied to a piece of wood with a hole in it of a door with a raised panel insert. In other words, the basic definition must be adapted to the real world. Does the definition of a BF change with softwoods and hardwoods? It certainly does. You are incorrect when you state otherwise at the end of your note (which is not part of the dictionary definition). A softwood 2x10x12' is 1.5" x 9.25" x 12.0' actual when dried and planed. When manufactured at the sawmill, it is initially about 1.72 x 9.70 x 12'2". It is counted as 20 BF. For hardwoods, the actual size is used so it is 9 ft SM of 6/4 which is 13 or 14 BF. Those are numbers that are legal and have been held up in various court suits time and time again. The bottom line is that if anyone is going to enter the softwood or hardwood manufacturing world, they need to use the industry accepted definitions, which in the case of lumber BF have been adopted by the state weights and measure depts and therefore have the force of law.
From contributor S: I've looked at the state code here in PA and in NY and can't find anything about any legal definition of a hardwood bd/ft, rounding off to the nearest whole foot or really much at all about selling lumber. New York State does have a section about using "net tally" for kiln dried, but I couldn't find anything other than that. Since this discussion has ventured into what is legal, I was hoping someone out there might have a better way to search the state codes for references on which states define bd/ft. Also, just because I couldn't find anything in the PA weights and measures code doesn't mean there isn't anything there  I may not be searching properly.
From Professor Gene Wengert, forum technical advisor: It has to be there, as otherwise, what is to stop a person from saying that a BF is only 6" x 12" x 1"? Further, there have been cases where someone has received less lumber than they specified (hardwoods) and then the definition came into play. From contributor O: So, I've read this whole thread several times just to see if I could understand why the disagreement exists. I also went to the Canadian Federal, Ontario Provincial and Nova Scotia Provincial websites to see how they scale and what their definition of a board foot is (I realise this is primarily a US forum, but we do trade with each other). I didn't find anything earth shattering, but based on what I've read, I do think that the confusion and disagreement here is caused not by the definition of what a board foot is, but is caused by the way "rounding" to a whole number when measuring hardwood affects certain dimensions of lumber and/or volumes of piles of lumber. It seems that if we look only at one board at a time, we are either losing, or gaining, depending on the dimensions and whether we are buying or selling. As sawyers, though, we rarely sell only one board at a time to a commercial outfit, so when the scaling happens, we would be selling a volume sufficient that any errors in rounding are minimized to an unnoticeable amount? Also, as sawyers who might sell to John Q Public in small amounts, we (I'm sure) have the right to determine between us and our customer exactly how we will measure and price, and as long as we both agree on the method, there are no laws broken.
From Professor Gene Wengert, forum technical advisor: Well said. Thanks. From contributor O: Hi Gene, you're welcome, but... please don't thank me too quickly. I went back to the calculator and tried a few different ways of calculating volumes of hardwood. The variable in the case of hardwood is the rounding. If the object in measuring hardwood volume is to round to the nearest whole number, then we need to know whether we round each board first, then add up the number of boards, or do we measure the whole pile first and then round off that figure? I ask because, if we take a pile of 100 pieces of 2"x4"x10' hardwood lumber, we can arrive at two completely different volumes depending on where we introduce the rounding... You talked about this method of measuring and the discrepancies here:
However, your hardwood calculator doesn't appear to do it this way. It appears to calculate each individual board first, then add up the rounded volumes. The order of operations in the calculator appears to be wrong. Also, in your example, you round after obtaining surface measure? Whereas your calculator appears to round off after calculating each individual board volume? Please correct me if I'm wrong.
From Professor Gene Wengert, forum technical advisor: I just checked it and indeed, it does appear to add the individual BF volumes rather than total all the surface measures and then multiply by the thickness. (For example, a piece that is 77/8" x 10' x 5/4 is 7 SM and 9 BF. So, 10 pieces would be 70 SM and then 5/4 times 70 is 87.5, which could be rounded to 87 or 88. The calculator gives 90 BF.) This is a problem when you use 5/4 mainly. I am sure that the folks at WOODWEB that set up the calculator will look at this and try and fix it, as it is actually their programming. However, appreciate that you are supposed to total the SM for all pieces of all sizes that are the same thickness and then multiply by the thickness, so that would probably take quite a bit of manipulating. We will see how they do it. Thanks for your keen eye on this. Of course, for a few pieces, the error is worth noting, but with a variety of pieces of different sizes, there will be some less and some more and it will balance out on the average. Hopefully, no one uses the calculator when buying or selling, but they instead use a scaling stick which is so much faster. The stick is used within the industry to measure upwards of 20,000 feet per day. Lest we lose sight of the key point: The definition of a hardwood BF has been with us and is well defined (including calculation) for many years. We are stuck with it, even if we do not like it. So, if we do not like it, we can come up with our own specific measuring technique, but it would not be a true board foot as defined within the industry today. And of course, the end objective in not footage, but dollars. Note that the scaling stick for lumber, as well as the calculator here, both give the exact same answer (for example, 6 BF for 2x4.0x8 and 2x4.0x0 hardwood lumber). Hopefully, however, no one makes a bunch of 2x4.0x10 pieces, but rather makes a variety of widths. As mentioned, 2x41/4x10 measures 8 BF on both the scaling stick and the calculator here. So, you get another "gold star" this morning.
From Carl Hagstrom, Systems Administrator at WOODWEB: Interesting thread... particularly Gene's last note that confirms that there is a problem with the calculator programming. I looked at the code, and sure enough, at the point where the SM is rounded to the nearest full BF, the code was rounding to the nearest value ending in zero (60, 70, 80, 90, etc.) rather than the nearest single BF. I've corrected this, and in Gene's example above, the result is now 88 BF, not 90. Also wanted to mention that while I was reviewing the math behind the calculator code, I came across a note I made regarding how to handle the rounding process when there are multiple boards that are the same size, and each individual board's SM ends precisely at .5 (or 1/2) ... My notes (which, as you can imagine, were made after a conversation with Gene when I was programming the calculator) mention that in the case above (SM ends in .5 for multiple boards), the SM is rounded up for the first board, and then rounded down for the second, and so on until all the boards (of the same size) have been accounted for. This has been allowed for in the calculator computation, by the way (and it was a bit tricky to program!). As for the gold star... The knowledge of the participants at WOODWEB certainly is impressive. The last 14 years have made for many satisfying experiences as participants add their hard won knowledge to discussions (and point out less then stellar programming) at the site.
From contributor O: Thank you for the replies. If I may be so bold as to suggest the following: Given that the rounding is supposed to happen after the cumulative surface area is calculated (do I have this assumption correct or is this where I stumble?), then the formula for the calculation when all the boards are the same size can simply be: [(width"xnumber_of_boardsxlength'/12)rounded_off]xthickness From Professor Gene Wengert, forum technical advisor: Your written statement is correct, but the formula is just a bit off. The correct formula to obtain the board footage would be {(width in inches and fractions) x (standard length in feet and no fractions) / 12] rounded to a whole number} x number of pieces of this size x thickness in 1/4 inch increments rounded to a whole number. The bigger issue with this calculator is what to do when you have a lot of different sized pieces, all of the same thickness. You should sum all the SM for all the pieces and then finally multiply by the thickness to get the BF instead of getting the BF for each individual width. Because very few people will use the hardwood calculator for a lot of pieces (too cumbersome) but would use a scaling stick and tally book and because the effect is very small, I am not sure if it is worth making the change that would have little effect and little use. Thanks again for taking time. Would you like to add information to this article? Interested in writing or submitting an article? Have a question about this article? Have you reviewed the related Knowledge Base areas below?



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