Thneed Weekly – Week 2014 – 32


Thneed Weekly returns.  Back in week 2014 – 28 of Thneed Weekly we covered briefly what a D-Tape was and how the units were multiplied out to be PI units to automatically provide the user with the diameter.  This week we will derive the formula to calculate basal area of a tree.  Basal area is a metric that foresters use to determine stocking of an area among other things.  All foresters that use English units have had burned in to there brain:


But what the heck is that.  The Math penguin that usually hides in a dark office will try to shed some light on this and provide it in both English and Metric units.  Should be a good time figuring that out.

The Assumptions:


English Metric
Diameter Inches Diameter Centimeters
12 inches per foot 100 centimeters per meter
BA = Square Feet BA = Square Meters
 π = 3.1415926535


 The Problem:

You have measured a tree with a D-Tape that is 13″ (~33cm) in Diameter Breast Height.  What is the basal area of this tree?

Derive the Answer:

Basal area is an area.  We should all know that the area of a circle (the assumed shape of a tree) is


That is all fine and good but the diameter coming in and the area coming out are two different units.  inches to feet and centimeters to meters. So here goes…

English Metric Description
 EngUnit  Convert Units
 EngRad  Calculate Radius
 RadiusSq  Square Radius
 EngDerive  Multiply by Pi
EngDerivepart  Result
EngFinal Simplified