I need to calculate the number of board feet there are in a log.

Hello and thank you for your question.

I have two answers for you: one if there is no waste (so we measure
the entire volume of the log) and another where we trim the log so
that its cross section is a square (and we ignore the part of the wood
that's cut away).

A board foot is equal to 144 cubic inches of wood.
http://www.woodzone.com/tips/board_feet/board_feet.htm

Since a log is a cylinder, and if you assume that all of the wood is
useful for your purpose, its volume would be the area of its circular
cross-section times its length.

Since the area of a circle is (pi)*r*r or (pi)*(d/2)*(d/2)

The number of board feet is
(3.14)* (d * d) * (1/4) * L * (1/144)
where d is the diameter of the log in inches and L is the length of
the log in inches.

You would use calipers to measure the diameter of the log.
Alternatively, you could measure the circumference of the log (by
winding a tape measure around it), and because c = (pi) * d
d = c / pi

So in terms of circumference, the number of board feet is also
(1/3.14) * (c * c) * (1/4) * L * (1/144)
where c is the circumference of the log in inches and L is the length
of the log in inches.
---------------------
If you were looking to cut equal slabs from the log, not all of its
volume would be recoverable.  Picture a square inscribed in (set
inside) a circle.  If everything outside the square is cut away, then
the diameter of the circle becomes the diagonal of the square.

So in that case the usable volume of the log would be the area of that
square times the length of the log.
The area of a square in terms of its diagonal is
(d * d)/2
so in this case the usable board feet are
(d * d)/2 * L  * 1/144
which is about 64% of the full volume of the log

Search terms used
"board feet"

Thanks again for bringing us your question.

If you find any of my answer to be unclear, please request
clarification.  I would appreciate it if you would hold off on rating
my answer until I have a chance to respond.

Sincerely,
Google Answers Researcher
Richard-ga

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Request for Answer Clarification by christophergsmith-ga on 28 May 2004 13:39 PDT

Thank you for your rapid response.  I have at least one request for
clarification: Logs are smaller at one end than the other.  Is it best
to measure in the middle for use in calculations?

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Clarification of Answer by richard-ga on 28 May 2004 15:00 PDT

Hello again:

If you're interested in the total volume, yes, you could measure in
the middle (the exact place to measure would be the place that
represents the average width overall).

Of course, if you only wanted to measure the full-length boards that
could be cut from the log, then you'd need to measure from the narrow
end.  That would mean much more scrap, some of which could be cut into
shorter boards.

-R

clear answer and good response time.

Since the log is smaller at one end, I would take the measurements at
the smallest end AND at the largest end and use the average for my
calculations.