Tree Diameter Calculator
Free Tree diameter Calculator for trees & forestry. Enter variables to compute results with formulas and detailed steps.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
D = C / pi | D = sqrt(4 x BA / pi)
Tree diameter equals circumference divided by pi. Alternatively, diameter can be calculated from basal area using D = sqrt(4 x BA / pi), derived from the circle area formula BA = (pi/4) x D^2.
Worked Examples
Example 1: Pine Tree from Circumference
Problem:A pine tree has a circumference of 62.8 inches at breast height. Calculate its diameter.
Solution:D = C / pi = 62.8 / 3.14159 = 19.99 inches\nRadius = 10.00 inches\nBasal area = 0.005454 x 19.99^2 = 2.18 sq ft
Result:Diameter = 20.00 inches (50.80 cm)
Example 2: Diameter from Basal Area
Problem:A tree has a basal area of 1.77 square feet. What is its diameter?
Solution:BA in sq in = 1.77 x 144 = 254.88 sq in\nD = sqrt(4 x 254.88 / pi) = sqrt(324.00) = 18.00 inches
Result:Diameter = 18.00 inches
Frequently Asked Questions
How do you calculate diameter from circumference?
Diameter is calculated by dividing the circumference by pi (3.14159). This comes from the circle formula C = pi x D, rearranged to D = C / pi. For example, a tree with a 50-inch circumference has a diameter of 50 / 3.14159 = 15.92 inches. This assumes the trunk cross-section is perfectly circular, which is rarely exact in nature. For irregular trunks, measuring circumference and dividing by pi gives the equivalent circular diameter, which is standard practice in forestry.
Why is tree diameter important in forestry?
Tree diameter is fundamental to nearly every forestry calculation. It determines basal area, which measures stand density. Diameter is the primary input for volume estimation equations that predict how much lumber or pulpwood a tree will yield. Diameter growth rate indicates tree health and site productivity. Forest inventory protocols require DBH measurements for every sampled tree, making it the most frequently collected forest measurement in the world.
What tools are used to measure tree diameter?
The most common tools are diameter tapes (D-tapes), calipers, and Biltmore sticks. A D-tape wraps around the trunk and reads diameter directly by dividing circumference by pi on its scale. Tree calipers have two arms that measure diameter directly but are awkward for large trees. Biltmore sticks are held at a fixed distance from the eye and read diameter from a graduated scale. For research, dendrometer bands measure tiny diameter changes over time to track growth.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy