DBH calculator: circumference to diameter

DBH — diameter at breast height — is the number a permit threshold, an appraisal and a removal quote are all written against. It is measured at 4.5 feet above ground, on the uphill side, and almost everybody who guesses it guesses high.

Why 4.5 feet, and why it matters

Four and a half feet is the international convention for forestry and arboriculture, which is the only reason it matters — every threshold, table and formula you will meet assumes it. A measurement taken at three feet is not a conservative estimate; it is a different number that will read as a bigger tree.

Sound

A standard diameter tape reads diameter directly, because the scale is pre-divided by π. If you are using an ordinary tape measure, you measured circumference — which is what this calculator converts.

The awkward trees

SituationWhere to measureNote it as
Tree on a slope4.5 ft above ground on the uphill side"uphill side"
Swelling or burl at 4.5 ftImmediately below the swellingthe actual height used
Leaning stem4.5 ft along the stem, perpendicular to it"along stem"
Forks below 4.5 ftEach stem separately, then combine"multi-stem, n stems"
Forks above 4.5 ftOnce, below the forksingle stem

The multi-stem rule people get wrong

Adding the stem diameters together overstates the tree badly, because area scales with the square of diameter. The convention is the quadratic mean — square each diameter, add them, take the square root — which preserves total basal area and gives the diameter of the single stem that would have the same cross-section.

Three stems of 18, 12 and 9 inches sum to 39 inches, which sounds like a very large tree. Their quadratic mean is about 23.6 inches, which is the honest answer and often the difference between clearing a permit threshold and not — see the permit guide.

What to do with the number

Feed it into the removal calculator for a price band, into the appraisal calculator for a replacement value, or into the permit checker to see whether the ordinance applies. Height, if you need it, is in the height calculator.

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