What this calculator does
Diameter at breast height is the standard forestry measurement, taken 1.3 metres above ground. Measuring a diameter directly on a standing tree is awkward, so the practical method is to measure the circumference with an ordinary tape and divide by π.
A diameter tape does exactly this: the graduations are spaced π units apart so the reading is already a diameter. Without one, a 94.2 cm circumference gives a 30 cm diameter, and the arithmetic is the only difference between the two tools.
The formula
Diameter is the circumference divided by π. The cross-sectional area is π multiplied by the square of half that diameter, which is the basal area of the individual tree. The method assumes a roughly circular trunk, which is reasonable for most species and less so for buttressed or fluted trunks.
| Term | Meaning |
|---|---|
| DBH | Diameter at breast height, measured 1.3 m above ground in most of the world and 4.5 ft in the United States. |
| Diameter tape | A tape graduated in π units so a circumference measurement reads directly as a diameter. |
| Cross-sectional area | The area of the trunk at that height, which is what stand basal area sums. |
The inputs explained
| Field | What to enter |
|---|---|
| Circumference at breast height (in) | Trunk circumference measured at breast height, with the tape level and snug against the bark. |
When to use it
Measuring without a diameter tape
An ordinary tape and a division by π gives the same answer, which is the ordinary case for anyone not carrying forestry equipment.
Recording growth over time
Circumference is the easier measurement to repeat accurately year on year, and converting to diameter makes the record comparable with published data.
Estimating tree value or volume
Timber volume tables are indexed by DBH, so a circumference has to be converted before any volume estimate can be looked up.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What diameter does each circumference give?
A range of trunk circumferences converted to diameter and cross-sectional area.
| Circumference | Diameter at breast height | Cross-sectional area | Circumference used |
|---|---|---|---|
| 31.4 in | 9.99 in | 78.46 in² | 31.4 in |
| 62.8 in | 19.99 in | 313.84 in² | 62.8 in |
| 94.2 in | 29.98 in | 706.14 in² | 94.2 in |
| 157 in | 49.97 in | 1,961.51 in² | 157.0 in |
Questions
Why is diameter measured at 1.3 metres?
It is a convention set at roughly chest height on an adult: above the root flare that swells the base of most trees, and low enough to reach without equipment. The United States uses 4.5 feet, which is about 1.37 m, so international comparisons carry a small systematic difference.
How do I convert circumference to diameter?
Divide by π, approximately 3.1416. A trunk measuring 94.2 cm around is about 30 cm in diameter. A diameter tape has that division built into its graduations, which is the only difference between it and an ordinary tape.
What if the trunk is not circular?
The circumference method assumes it is, and it overestimates the effective diameter for an oval or fluted trunk. For irregular trunks, calipers taken at two perpendicular angles and averaged give a better figure, and buttressed species are conventionally measured above the buttress instead.
Where exactly do I put the tape?
Level and perpendicular to the trunk axis at 1.3 m, snug against the bark without compressing it. On a slope, measure from the uphill side. On a leaning tree, measure perpendicular to the lean rather than to the ground.
For tree height using a clinometer, see the tree height calculator. For stand density across many trees, see the tree basal area calculator.