Tree Diameter Calculator
Turn trunk circumference into DBH diameter and basal area.
What it does
Foresters size trees by diameter at breast height, called DBH. Wrapping a tape gives circumference, which converts to diameter with pi. That diameter feeds basal area, volume tables, and growth tracking.
The tool above takes girth and returns DBH diameter, basal area, and radius. The defaults 100 cm match the worked example, so the page opens showing 31.8 cm. Switch to imperial for inches.
The math is direct. DBH = C / pi. Radius is half that. Basal area = pi x radius squared, the cross section at breast height. A 100 cm girth gives 31.8 cm DBH and 795.8 cm2 basal area.
Measure on the uphill side at 1.4 meters (4.5 feet), above flare and below forks where possible. Leaners, multi stems, and slope need special rules from forestry guides. Remeasure at the same marked height for growth.
This page shows the formula, one full hand checked example at 100 cm, a reference table, and practice checks that run through the tool in both unit systems.
How to use
- Pick Metric (cm) or Imperial (in).
- Wrap a tape around the trunk at breast height.
- Type the circumference reading.
- Read DBH diameter as the main result.
- Read Basal area for stand math.
- Mark the height and remeasure there next time.
Formula
- C
- Circumference at breast height.
- DBH
- Diameter at breast height.
- basal
- Cross section area at breast height.
Pi is 3.1415926535 here. Out of round trunks average two crossed diameters instead of one tape. Units stay with inputs: cm gives cm2, inches gives in2.
Worked example
Example: 100 cm around
A street tree tapes 100 cm at 1.4 m height. Find DBH.
- Write C = 100 cm.
- DBH: 100 / 3.14159 = 31.83099 cm.
- Round: 31.8 cm.
- Radius: 31.83099 / 2 = 15.915 cm.
- Basal: 3.14159 x 15.915 squared = 795.8 cm2.
- Imperial mirror: 39.4 in gives 12.54 in DBH.
Reference table
| Girth | DBH | Basal area |
|---|---|---|
| 50 cm | 15.9 cm | 198.9 cm2 |
| 100 cm | 31.8 cm | 795.8 cm2 |
| 150 cm | 47.7 cm | 1790.5 cm2 |
| 39.4 in | 12.54 in | 123.5 in2 |
Limits
- Single stem circle assumed. Flare and forks need special rules.
- Breast height only. Seedlings need other measures.
- Tape error from bark and slope carries straight into DBH.
- No age or volume here. Species tables add those.
Common mistakes
- Measuring at ground flare instead of breast height.
- Using diameter tape reading as circumference without dividing.
- Forgetting pi and reporting girth as DBH.
- Mixing cm with inches in basal math.
- Averaging multi stems as one circle.
Try it yourself
Quick checks. Answers sit tucked under each question.
50 cm around?
Diameter 15.9 cm, basal 198.9 cm2, radius 8 cm.
150 cm around?
Diameter 47.7 cm, basal 1790.5 cm2, radius 23.9 cm.
Questions
What is DBH?
Diameter at breast height, from girth over pi.
What height?
1.4 m or 4.5 ft on the uphill side.
100 cm girth DBH?
31.8 cm.
What is basal area?
Cross section at breast height, pi times radius squared.
Multi stem?
Measure each stem by guide rules, not one merged circle.
Slope?
Measure uphill side at breast height per forestry guides.