Math CentralQuandaries & Queries


Question from Darcy:

When you purchase a "bundle" of wood at the store, it is marked 0.75 cubic feet. What is the formula for figuring out that measurement for cubic feet and what fraction of a true cord of wood (128 cubic feet) is it. I would appreciate the formula so I can build a spreadsheet to help my secretaries and myself be in compliance to the law when selling firewood. Thanks.

Hi Darcy,

If each bundle was 1 cubic foot it would take 128 of them to make a cord so each would be one, one hundred and twenty-eighth of a cord.

If each bundle was 2 cubic foot it would take 128/2= 64 of them to make a cord so each would be one sixty fourth of a cord.

If each bundle was 0.5 cubic feet it would take 128/0.5 = 256 of them to make a cord so each would be one, two hundred and fifty-sixth of a cord.

If each bundle was 0.75 cubic feet it would take 128/0.75 = 171 of them to make a cord so each would be one, one hundred and seventy-first of a cord.

I'm not sure how the seller arrived at 0.75 cubic feet in a bundle. If the sticks are all approximately the same length you could tie them in a bundle to form a rough cylinder and then approximate the volume as the volume of a cylinder which is π r2 h where π = 3.14, r is the radius of the cylinder

in feet and h is the length of the sticks in feet.


Darcy wrote back

Thanks so much for the response. I have found on the internet that a formula to figure a cord (4 x 4 x 8) is length x height x width but my "answers" do not make sense. (For instance - the "answer" to 15" x 11" x 28" = 4,620.00. Do I "move" the decimal points to make it .462 cubic feet? The "bundles" in the store list the "bundle" as having 0.75 cubic feet. There are (6) pieces of wood in their bundles. There are anywhere from (24) to (28) pieces of wood in our "stack" and they measure out so much more than
the store bundles. See my quandary?

Specifically other than 24 cubic feet (1/2 of a standard pickup truck - fraction of a cord?) and 48 cubic feet (1 entire standard pickup truck fraction of a cord?), we sell a "volume" of: length of log, 15" x 11" height of logs stacked together x 28" width of logs stacked together. How many cubic feet in the "bundle" - we call them "stacks" because instead of bundling them up in plastic (which would probably not be recycled), people pick them up in their cars as a "stack" of wood. The Dept. of Weights and Measures has instructed us to "do the math" and either label them in cubic feet or label them as a fraction of a cord.

Hi again Darcy,

The measurement length × width × height does give you the volume but if you want the units to be cubic feet you need the dimensions in feet. There are 12 inches in a foot so 15 inches is 15/12 feet, 11 inches is 11/12 feet and 28 inches is 28/12 feet. Thus the volume of your stack is

15/12 × 11/12 × 28/12 = 2.67 cubic feet

which is very close to 2 2/3 cubic feet.

Notice that 2.67/0.75 = 3.6 so my calculation gives your stacks as about 3.6 bundles. You said that a bundle has 6 pieces and a stack has 24 to 28 pieces and 24/6 = 4 so each stack is 4 or more bundles. At least we are in the same "ball park".

For your truck loads, a cord is 128 cubic feet, a standard pickup is 48 cubic feet and 3 × 48 = 144 so 3 truck loads is somewhat more than a cord. Hence a truck load is a little more than a third of a cord and half a truck load is a little more than a sixth of a cord. To be more precise a truckload is 48/128 = 0.375 and hence a truckload is 0.375 of a cord.

I hope this helps,


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS