Tree Diameter Calculator
Convert a trunk circumference into diameter at breast height, then estimate how the stem tapers with height and where it reaches a usable top diameter.
🌱 What is the Tree Diameter Calculator?
Tree diameter is the single most useful number in forestry, and almost nobody measures it directly. Trunks are too large to caliper accurately and too irregular for one straight-line reading to be representative, so the standard field practice is to wrap a flexible tape around the trunk and divide the resulting circumference by pi. The number that comes out is the diameter at breast height, universally abbreviated DBH, measured at 4.5 feet (1.37 m) above the ground. This calculator performs that conversion, then goes further and models how the stem narrows as it rises.
The number drives a surprising amount of real work. Timber cruisers use DBH with total height to look up merchantable volume in a species table before a sale is priced. Municipal arborists use it to decide whether a tree qualifies for heritage protection, since most preservation ordinances are written as a diameter threshold. Carbon accounting protocols convert DBH into above-ground biomass through allometric equations, which is how a woodlot becomes a tonnage of stored carbon. Consulting arborists use it in tree appraisal formulas, where trunk cross-sectional area is the size term. Homeowners use it to work out whether a leaning tree is large enough to reach the house.
The commonest mistake is measuring in the wrong place. Root flare, basal swelling and low forks all inflate a reading taken below breast height, and because cross-sectional area grows with the square of diameter, a 20 percent measurement error becomes a 44 percent error in area and in any volume or biomass figure derived from it. The second mistake is treating a taper estimate as a measurement. Stems are not perfect paraboloids, and any single equation applied to every species will be off near the butt swell and near the tip.
This calculator takes a circumference or diameter in inches or centimetres, reports DBH in both units alongside the trunk cross-sectional area in square feet, then applies a paraboloid taper model to estimate the stem diameter at any height you choose. It also solves the model backwards to find the merchantable height, the point where the stem narrows to the smallest top diameter a buyer will take. The chart draws the whole taper profile from the ground to the tip so you can see how much usable stem sits below your chosen top diameter.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Yard Maple Measured With a Tape
Circumference 60 in, total height 60 ft, diameter wanted at 20 ft, 6 in top
Example 2 — Sawlog Cruise on a Large Oak
Diameter measured directly as 24 in, total height 80 ft, diameter wanted at 40 ft, 8 in top
Example 3 — Metric Measurement of a Street Tree
Circumference 150 cm, total height 18 m, diameter wanted at 6 m, 20 cm top
Example 4 — Veteran Tree Assessed for Heritage Status
Circumference 96 in, total height 75 ft, diameter wanted at 30 ft, 10 in top
❓ Frequently Asked Questions
🔗 Related Calculators
How do you convert tree circumference to diameter?
Divide the circumference by pi (3.1416). A trunk measuring 60 inches around has a diameter of 60 divided by 3.1416, which is 19.10 inches. The same rule works in centimetres, so a 150 cm circumference is a 47.75 cm diameter.
What is DBH and where exactly is it measured?
DBH means diameter at breast height, the forestry standard reference point 4.5 feet (1.37 m) above ground level, taken on the uphill side of the trunk. It is used because it sits above most root flare, so two people measuring the same tree get comparable numbers.
How do you calculate the diameter of a tree at a given height?
This calculator uses a paraboloid taper model: d = DBH multiplied by the square root of (H minus h) divided by (H minus 4.5), with H the total height and h the height of interest, both in feet. A 19.10 inch DBH tree 60 feet tall measures about 16.21 inches at 20 feet up.
What is merchantable height?
Merchantable height is the point on the stem where the diameter falls to the smallest size a buyer will accept, called the top diameter. For a 19.10 inch DBH tree 60 feet tall with a 6 inch top, the stem reaches that top diameter at about 54.52 feet.
Why is my calculated diameter different from a caliper reading?
Circumference divided by pi gives the diameter of a perfect circle with the same perimeter. Real trunks are oval, fluted or buttressed, so a caliper measuring one axis will read higher or lower depending on where you place it. The tape-derived figure is the accepted forestry convention.
Can I use this calculator on a multi-stemmed tree?
Not directly. Standard practice is to measure each stem separately at breast height, then combine them by summing the cross-sectional areas rather than the diameters. Adding diameters would badly overstate the tree, since area grows with the square of diameter.
What is the cross-sectional area used for?
Cross-sectional area at breast height is the basal area of that single tree, in square feet. Foresters sum it across all trees on a plot to get stand basal area, which drives thinning decisions and stocking guides far better than tree counts alone.
Does bark thickness matter for these numbers?
It matters for volume, not for DBH. All the diameters here are outside bark, which is the standard for inventory and for the growth-factor age method. For log scaling, subtract about twice the bark thickness to get diameter inside bark before computing volume.
How accurate is the paraboloid taper model?
It is a reasonable first approximation for conifers and straight-stemmed hardwoods, typically within 10 to 15 percent through the merchantable portion of the stem. Species-specific taper equations fitted to local data are considerably more accurate, especially near the butt and near the tip.
How do I convert DBH in centimetres to inches?
Divide by 2.54. A 48.51 cm diameter is 19.10 inches. This calculator does the conversion automatically and reports the diameter in both units, so you can enter whichever measurement your tape gives you.
Why does the taper curve start wider than DBH at ground level?
The model is anchored at breast height, so extrapolating below 4.5 feet gives a diameter slightly larger than DBH. Real trunks flare much more sharply at the base than the curve suggests, so treat the bottom few feet of the chart as indicative only.
What top diameter should I use for sawlogs?
It depends on the mill and the product. Hardwood sawlog buyers commonly specify an 8 to 10 inch small end, softwood sawlogs often work to 6 inches, and pulpwood can go down to 3 or 4 inches. Enter the figure your buyer quotes rather than a generic value.