How To Calculate The Cubic Volume Of A Log

A straight log might not be a perfect cylinder, but it's very close. That means that if you're being asked to find the volume of a log, you can use the formula for finding volume of a cylinder to make a very close approximation. But before you can use the formula, you also need to know the log's length and either its radius or its diameter.

1. Convert Diameter to Radius

If you already know the log's radius, skip straight to Step 2. But if you've measured or been given the log's diameter, you must first divide it by 2 to get the log's radius. For example, if you've been told that the log has a diameter of 1 foot, its radius would be:

\(\frac{1\text{ foot}}{2}=0.5\text{ ft}\)

2. Measure or Discover the Log's Length

In order to work the formula for volume of a cylinder, you'll also need to know the cylinder's height, which for a log is really its length straight from one end to the other. For this example, let the log's length be 20 feet.

3. Substitute Radius and Length Into the Formula

The formula for volume of a cylinder is:

\(V=\pi r^2 h\)

where ​V​ is the volume, ​r​ is the radius of the log and ​h​ is its height (or in this case, the length of the log). After substituting the radius and length of your example log into the formula, you have:

\(V=\pi (0.5)^2\times 20\)

4. Simplify the Equation

Simplify the equation to find the volume, ​V​. In most cases, you can substitute 3.14 for π, which gives you:

\(V=3.14\times (0.5)^2\times 20=3.14\times 0.25\times 20=15.7\text{ ft}^3\)

The volume of the example log is 15.7 ft³.