About the Tree Diameter Calculator
Tree trunks are round, so you rarely measure diameter directly — you measure the circumference (girth) by wrapping a tape around the trunk, then convert. Because a circle's circumference equals π times its diameter, you recover the diameter by dividing the girth by π (approximately 3.14159). This calculator does that conversion and also reports the radius and the cross-sectional basal area.
The formula
- Diameter = Circumference ÷ π — the core conversion, where π ≈ 3.14159265.
- Radius = Diameter ÷ 2 — half the diameter.
- Basal area = π × radius² — the area of the trunk's circular cross-section, a common forestry metric.
For example, a trunk with a circumference of 47.1 cm has a diameter of 47.1 ÷ 3.14159 ≈ 15.0 cm, a radius of 7.5 cm, and a basal area of π × 7.5² ≈ 176.7 cm².
What is DBH?
Foresters, arborists, and ecologists standardize trunk measurements as diameter at breast height (DBH): the trunk diameter measured at 1.37 m (4.5 ft) above the ground in North America, or 1.3 m in most other countries and the ISO/IUFRO standard. DBH is the single most-recorded tree dimension because it correlates strongly with a tree's age, height, volume, and biomass, and it feeds directly into growth models and carbon-stock estimates.
Diameter tapes and the π factor
A dedicated forestry "diameter tape" (d-tape) is graduated in units of π so it reads diameter directly when wrapped around the trunk — every π centimeters (about 3.14 cm) of actual girth is printed as 1 cm of diameter. If you use an ordinary sewing or measuring tape, you get circumference and must divide by π yourself, which is exactly what this tool does.
Common reference points
- A circumference of about 3.14 units always equals a diameter of 1 unit (e.g. 3.14 cm girth → 1 cm diameter).
- A 100 cm (1 m) girth corresponds to a diameter of about 31.8 cm.
- The U.S. national champion-tree and many "big tree" registries publish trunk circumference at 4.5 ft; divide by π to compare against diameter-based data.
- Because the trunk is rarely a perfect circle, a single tape reading is a good approximation but not exact — see the limitations below.