Converting Board Foot Pricing to Lineal Foot Pricing

      Let's run through the arithmetic one more time. April 20, 2006

Question
After all my years in woodworking, I still can't convert board foot prices to lineal foot prices. Could someone explain it to me again?

Forum Responses
(WOODnetWORK Forum)
From contributor F:
Once you know the cost of a particular board at its price per board foot, divide that dollar amount by the number of lineal feet in the board and that will be the cost per lineal ft.

For example: an eight foot long board that is 10" wide and sells for $5.00 per brd. ft.
96"x10"=960 square inches
960 divided by 144=6.6 brd ft
6.6 brd. ft. x $5.00 =$33.00
$33.00 divided by 8(8 feet)= approx $4.12 per lineal foot



From the original questioner:
That's the problem. I don't know the cost per board in board feet. I just have a list of prices for board feet, and I'd like to convert it so I know what a lineal foot would cost.


From contributor F:
You are trying to compare apples and oranges evenly. Since as you know, a board foot calculation is based on the thickness, width and length of a piece of wood, the cost of an individual board when it is sold by the board foot is dependent on those three dimensions. On the other hand, the cost of an individual board that is sold by the lineal foot is dependent only upon the measurement of its length. Therefore, a conversion of the cost of lumber from a board foot price to a lineal foot price can only be done on a specific case by case conversion and not a blanket conversion. While it is possible to convert linear feet to board feet, the width, thickness and length must be factored in, and a board foot quantity could be converted to lineal feet if a thickness, width and length criteria were established. So, it would seem that all conversions between these two methods of measurements must be based on specifics. Naturally, the cost of lumber that is exactly 12" wide is the same price per board foot as it is per lineal foot and then it follows that lumber 6" wide will cost one half as much per lineal foot as it costs per board foot and a 3" wide board will cost one quarter as much per linear foot as it would per board foot.


From contributor L:
Sorry to be nitpicky, but this calculation only works for 4/4 stock. But you are correct in saying that he needs all of the specifications (BD FT and price) to convert into a lineal foot calculation.


From the original questioner:
Well, I have the board foot price for dimensions from 2x3, 2x4, 2x5, up to 2x12, so I'd like to know how to convert these. I know I'll have to do each one individually.


From contributor F:
Example: 2x3x8feet @ $5.00 per board ft.
3x96=288
288x2=576
576 divided by 144=4
4x$5.00= $20.00
$20.00 divided by 8 feet = $2.50 per lineal foot.


From contributor L:
You are using lumber terms that are for housing and such, but anyway.

Start with the easiest, 2x12 (8/4x12). A piece of this wood 1 foot long is equal to 2 BD FT, so the calculation would be 1' x 1' x 8/4 = 2BD FT. Then multiply 2 BD FT x Cost/BD FT to get price per lineal ft.
8/4x3 3"/12"= 1/4 therefore lineal ft x 1/4 x 8/4 x cost/bd ft
8/4x4 4"/12"= 1/3 therefore
lineal ft x 1/3 x 8/4 x coxt/bd ft
8/4x5 5"/12"= 5/12 therefore
lineal ft x 5/12 x 8/4 x cost/bd ft
8/4x12 12"/12"= 1 therefore
lineal ft x 1 x 8/4 x cost/bd ft
So... If you have 22' of 5/4 wood that is 4 1/2" wide and costs $4.23/bd ft
22' x 3/8 (4.5"/12")x 5/4 (1.25)x $4.23/bd ft= $43.62

You should be able to figure the rest out yourself.



From the original questioner:
Right on, now I got it! Thank you so much for explaining it to me. This time I'm going to put this in a Word Doc so I won't ever have to ask again.

I used those terms because I'm a builder, but I'm also a woodworker. This stock is actually 8 quarter rough sawn WR cedar, old growth KD vertical grain too. Beautiful stuff.



From contributor F:
Softwoods are usually called 1x, 2x, etc.

I want to make my formula really clear, so here you go. Take the width of any board or plank in inches and multiply that by its length, also in inches. Then take the product of that multiplication and multiply it times the thickness of the board in inches. Then, divide the result by 144 (144 is the number of square inches in a square foot). The result of that division is the total board feet in the board/timber. Now multiply the number of board feet by the dollar amount per board foot. This gives you the cost of the board. Last, divide the cost of the board by the number of feet in its length. Now you have the cost per linear foot. If the timber in question has an exact/even amount of feet, you can instead multiply the width in inches times the length in feet times the thickness in inches and divide that by 12 to get your board feet. The first method will get you exact board feet when the length is not an exact foot length.



From Gene Wengert, forum technical advisor:
The last post is correct only for softwoods and only if you use the nominal size and not the actual size. That is, for a softwood 2x6x12, you use 2 and 6 and not 1.5" and 5.5". The length is the actual length in feet (no fractions). This means that if you convert the length to inches, as contributor F suggests, it must be 60", 72", 84", etc. In fact, why use inches? Just use feet and then divide by 12 instead of 144. The answer in either case is the same. You need to use two decimals... a 2x4x8 is 5.33 BF.

The rules for hardwoods are different, in that the actual width is used including fractions, but the thickness is only in 1/4 inch increments and the length is the last full foot (no inches). The rounding rules are used for the width times length answer divided by 12 before the thickness is multiplied. The footage is always to the closest foot and does not have fractions.

Perhaps you felt that it was clear, and now after this explanation it is not so clear. This makes your question a good question indeed, as many people do not know how to calculate BF correctly. The link below (from the WOODWEB Knowledge Base) is an accurate and complete explanation.

Related article: What is a Board Foot?



From the original questioner:
Got it now. But I'm just so set in my ways... used to thinking in lineal feet.


From contributor F:
I understand what you are saying about the rules, Gene. I was trying show how you can figure the exact (actual) number of cubic inches in any piece of wood by dividing by 144, which is the number (as you know) of square inches in a square foot. I find this useful in determining the actual amount of wood that goes into a product which usually doesn't fall on an exact or even whole foot amount.

Something Gene didn't mention at length that used to give me trouble is that I always measured fewer board feet in the lumber than my supplier had billed me for, until I found out that they round boards up to the next full inch that measure a whole number plus a half an inch. They tally a board that measures 10.5" as 11". I suppose that must be in the "rounding" rules.



From contributor E:
Lumber is priced in the rough. So 8/4 would be 2" thick.


From Gene Wengert, forum technical advisor:
All my comments were pertaining to lumber and not parts or cut-up pieces. Your idea of using actual sizes and so on is certainly valid for the small pieces and gives one a good idea of the total volume of wood.

Do you mean that a piece 10.6" wide was actually counted as 11" wide for hardwoods? If so, they are cheating. The rules for measuring lumber are well documented and universally used and do not vary, except by persons who like to rip people off. Worse than that, however, is that some folks will add anywhere from 6% to 15% to account for shrinkage. This is like getting a gallon of gas, but only getting 0.95 gallons because some evaporated during processing. It is illegal in all 50 states. The most that wood shrinks is 6% anyway, so values over 6% are a rip off indeed. Note that the NHLA does not approve of this activity either.



From contributor F:
Gene, I did read with interest the recent post where woodworkers were getting less board footage than they paid for due to shrinkage. Here in Oregon, none of my suppliers have stooped to that tactic. However, I noticed that since I opened my shop here and started having hardwood delivered to my shop, my personal tally always indicated that I was measuring the loads as having fewer board feet than what the bills they gave me tallied in at. I always let it go because it was usually 4 or 5 board feet and I figured it wasn't worth the hassle. What I finally learned is that their practice is to round fractions of an inch 7/16" or less in width down to the nearest inch and 1/2" or more up to the next inch. Until your post I thought it was legal. And also, since my tallies are always less than my suppliers, I doubt that they really ever round anything down.


From contributor R:
Are you getting your lumber ripped 1 or more edges from the supplier? They will tally your total b.f. before ripping edges straight, no different then if you received it unripped. That will also account for your discrepancy, something I never noticed for my first 10 pro years in business.


From contributor F:
The answer to that is no. All I have ever bought in 4/4 material is 15/16" hit or miss rough both edges. I prefer to straight line myself and increase my yield by cross cutting boards with serious edge crook closer to net size of parts before straight lining.


From the original questioner:
My supplier just sent me this.

To dertermine LF price, multiply BF by the following:
2x3- .5
2x4- .667
2x5- .833
2x6- 1
2x8- 1.333
2x10- 1.667
2x12- 2



From Gene Wengert, forum technical advisor:
Am I missing something here? A 2x12 that is 12' long has 24 BF. Using the info above, this means 48 lf? I think that you have to divide and not multiply.

According to the hardwood grading rules, the quality of lumber is judged from the poorer side of the lumber. However, if the wood is planed, then it is graded from the best side. I wonder if getting your wood 15/16 hit and miss is worth it, as the grade will probably be lower than if you had it rough.



From contributor R:
Doc, are you telling us that the lumber we buy gets graded more than once? Even still, if it gets downgraded after hit or miss planing, the price should actually drop, since the overall quality at the best side now is less than expected, right?


From the original questioner:
Gene, have you been able to double check those figures my supplier gave me? It sure would be a handy way to figure out board to lineal feet!


From Gene Wengert, forum technical advisor:
The numbers are just fine *if you divide*.

Lumber can be graded green, then after kiln drying and then after planing. As a buyer of KD lumber, you will get the best deal if the lumber is graded after KD, but before planing.



From contributor F:
Gene, I think you were referring to me about it being better to just but it in the rough. Problem is, around here (Portland, Oregon) the suppliers won't sell it rough. I have asked why and they say the mills skip plane now so they see the color in cherry and so forth. When I was working for a furniture maker in the early 1980's, we got cherry in rough all the time.


From contributor D:
What is the formula to convert lineal ft. to board ft.?


From contributor E:
Length X width X thickness divided by 144. Remember, bd/ft pricing is based on rough measurement. 8/4 would be 2" in thickness, etc. So if you are buying 8/4 stock and having it surfaced to 1 3/4", you are paying for 2".

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