Tree Diameter Calculator
Convert trunk circumference to diameter at breast height, account for bark, and combine up to six stems into an equivalent diameter.
Measurements
Multi-stem circumferences
Enter the largest stems. Leave unused stems blank or zero.
Live results
Stem detail
| Stem | Circumference | Diameter over bark | Diameter under bark | Basal area |
|---|---|---|---|---|
| Equivalent | – | 22.51 cm | 20.92 cm | 397.89 cm² |
How to use this tree diameter calculator
What this calculator does
This calculator estimates diameter at breast height (DBH) from a measured trunk circumference. It handles a single stem, subtracts bark thickness to estimate the diameter of the wood inside the bark, and combines up to six stems into one area-equivalent diameter. DBH is a standard forestry measurement used in tree inventories, growth monitoring, basal-area calculations, and preliminary planning. It does not identify species, estimate total tree height, determine timber grade, or replace a professional risk assessment.
When to use it
Use it when recording trees for a woodland inventory, checking whether a tree falls into a diameter-based management class, comparing growth between measurement dates, or converting a flexible tape measurement into a diameter when calipers are unavailable. For U.S. forestry work, the usual measurement point is 4.5 feet above average ground level; the University of Minnesota Extension explains this standard in its guide to sampling and measuring timber. Other countries may use 1.3 meters or another local convention.
How to calculate
- The calculator opens with a ready-to-use demonstration: 100 cm circumference, 1 cm bark thickness, and three stems of 50, 40, and 30 cm. The example workbook is immediately available through Download Excel.
- Choose Length unit. Switching between centimeters and inches converts every current measurement and all outputs.
- For a single trunk, replace Single-tree circumference and optionally enter Single-tree bark thickness.
- For a clump or multi-stem tree, enter up to six values under Multi-stem circumferences and set Multi-stem bark thickness. Leave unused stems blank or zero.
- Read the live result cards and the Stem detail table, then download the current workbook. Reset clears the demonstration and results; Excel export remains disabled until a complete valid measurement is entered again.
Input guide
Length unit is required and accepts centimeters or inches. A unit switch changes presentation and converts existing values rather than relabeling them. Single-tree circumference is an optional positive decimal such as 100 cm; it is the tape distance around the trunk. Do not enter a diameter in this field. Single-tree bark thickness is an optional nonnegative decimal such as 1 cm, measured radially on one side. It must be less than half the calculated over-bark diameter, because bark is subtracted from both sides.
1st stem circumference through 6th stem circumference accept nonnegative decimals. At least one must be positive for a multi-stem result. Include separate stems only when treating them as components of one multi-stem tree under your chosen inventory protocol. Multi-stem bark thickness is applied to every included stem; a larger value reduces each under-bark diameter and therefore reduces the combined under-bark result. A common mistake is mixing units between stems or measuring some stems at a different height.
Output guide
Single-tree diameter over bark is circumference divided by π and is the primary DBH estimate. Single-tree diameter under bark subtracts twice the bark thickness. Single-tree basal area is the circular cross-sectional area at breast height. Equivalent multi-stem diameter preserves the sum of the individual over-bark basal areas; it is not the arithmetic average of stem diameters. Multi-stem diameter under bark combines the under-bark areas. Included stems counts positive stem entries. The Stem detail table lists each included stem's circumference, over-bark diameter, under-bark diameter, and basal area, followed by the area-equivalent totals.
Worked example
With a 100 cm single-tree circumference, the over-bark diameter is 100 ÷ π = 31.83 cm. Subtracting 2 × 1 cm of bark gives 29.83 cm under bark. Its basal area is π × (31.83 ÷ 2)² = 795.77 cm². For the three example stems, the diameters are 15.92, 12.73, and 9.55 cm. The equivalent diameter is √(15.92² + 12.73² + 9.55²) = 22.51 cm. These values match the first-open cards, table, and workbook.
Learn more
The U.S. Forest Service's guide to measuring big trees describes breast-height placement and special situations, while the FAO's tree height and diameter measurement guidance explains the 1.3 m convention used in many inventories.
How the formulas work
For an approximately circular trunk, circumference C and diameter d are related by d = C/π. Bark thickness is radial, so the under-bark diameter is d – 2t, where t is the average bark thickness on one side. The calculator rejects a bark thickness that would reduce the under-bark diameter below zero.
Basal area is the cross-sectional area at the measurement height: A = πd²/4. For a multi-stem tree, adding diameters directly would overstate size because area grows with the square of diameter. Instead, the calculator adds the stem areas, which is equivalent to computing √(d₁² + d₂² + ...). The FAO describes basal area as a core quantity in forest measurement and inventory analysis in its forest data analysis guidance.
Measurement cautions
- Keep the tape level and perpendicular to the trunk axis. On a slope, follow the applicable protocol, commonly measuring from the uphill side.
- Remove loose debris but do not compress living bark. Record whether measurements are over bark or under bark.
- For buttresses, forks, swelling, or leaning trunks, use a recognized forestry rule rather than forcing a tape through an irregular point.
- Repeat measurements at the same height and with the same unit when monitoring growth.