Geometry+of+Trees

To keep things simple, we will assume that the trunk of a tree is a cylinder. We will then calculate the volume of this cylinder (to estimate the amount of wood).

Obviously, we will overestimate because a tree tapers and is not quite a cylinder. Professional foresters start with the same basic volume calculations that we will do, but then they run their numbers through special formulas so there is less error.

So how do we calculate the volume of a cylinder? One way to think of a cylinder is a stack of quarters. The volume of the stack of quarters shown above is 22 quarters. You might have learned volume in math class as base x height. In our example, the base is a quarter and the height is 22.

What about trees? We measured the height directly in the field with the clinometers. The base or **basal area**, though, must be calculated somehow using DBH.

In the stack of quarters, what is the basal area of a single quarter? Luckily, a quarter is a circle, and the area of all circles is a simple formula:

For our trees, we didn't measure the radius, but we do know that radius is half the diameter -- something we DID measure! Plug that into the area of a circle formula, and that is how we will figure out basal area.