Tree Height Calculator
Estimate a tree's height from its shadow using a reference object and similar triangles, with the current sun angle and a height class.
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Tree Diameter (DBH) Calculator
Turn trunk circumference into diameter at breast height in inches, centimetres and feet, plus basal area, Doyle log scale and a size class.
Tree Diameter (DBH) Calculator
Chlorova · updated for 2026
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Click “Calculate” to see your results.
Diameter is derived from a single circumference wrap and assumes the trunk is roughly circular, which fluted, buttressed or lean-to trees are not, so the true diameter sits somewhere around the printed figure. Basal area and Doyle scale are standard forestry planning figures, not a grading: Doyle overestimates small-diameter logs, and mills scale their own way. Nothing here replaces a licensed arborist or a forester for trees near buildings, power lines or standing water, and many municipalities require a permit before you remove anything of this size.
Foresters, mills, permit offices and tree valuers all speak in diameter, yet almost nobody measures it directly. What you can measure is the circumference, and dividing that by pi converts it to the number everyone asks for. Diameter at breast height, usually called DBH, is the trunk width measured 4.5 ft above the ground, and it drives basal area, stand stocking, timber scale and whether your town requires a permit to cut. This calculator converts your tape reading into DBH in three units.
Measuring Diameter at Breast Height
- Stand 4.5 ft up the trunk from sound, level ground and mark that height.
- Wrap a tape around the trunk at the mark, keeping it level and snug.
- Read the circumference where the tape meets its own start point.
- Pick inches or centimetres so the units match the tape you actually used.
- Enter the circumference, never a diameter you eyeballed from the bark.
- On a slope, measure the height from the uphill side of the trunk.
- Enter how many trees the reading represents if you are cruising a stand.
- Set the log length you intend to cut before reading board feet.
- Check the size class line before you plan any tool or crew.
- Re-measure any tree that leans, forks or flares at the base twice.
The Circumference and Basal Area Math
A trunk is treated as a circle, and for any circle the circumference equals pi times the diameter. Reversing that one step gives the whole result: DBH = circumference ÷ pi. A 48-inch wrap therefore divides to 15.3 inches of diameter, and 15.3 inches is 38.8 cm or 1.27 ft. Centimetre tapes are converted first at 0.3937 in per cm, so the same 150 cm wrap becomes 59.1 in and a 18.8 in diameter.
Basal area is the cross-section of the trunk in square feet, taken from the circle area formula with the diameter in inches: 0.005454 multiplied by DBH squared. That constant is simply pi divided by four times the 144 square inches in a square foot. Doyle board-foot scale for a log is the classic (D − 4) squared times length divided by 16, and it returns nothing useful under 4 inches of diameter.
Worked Example: A 48-Inch Red Maple
- Set the unit selector to inches and enter the 48 in circumference you measured.
- Divide 48 by pi, and the diameter at breast height prints 15.3 in.
- The same trunk reads 38.8 cm, or 1.27 ft straight across.
- Basal area works out at 0.005454 times 15.3 squared, so 1.27 sq ft.
- That figure is what one tree contributes to a stand's stocking total.
- Count twenty similar trees and the stand basal area line reads 25.5 sq ft.
- Doyle scale on a 16 ft log is 11.3 squared, which prints 127 board feet.
- Halve the log length to 8 ft and the scale line drops to 64 board feet.
- The size class verdict calls it a small sawlog, worth a felling plan.
- Compare the printed diameter with any local protected-tree threshold before cutting.
Circumference to Diameter Quick Chart
Common trunk wraps converted at breast height on level ground, with the basal area each one carries and the Doyle scale for a single 16 ft log. Round your own reading to the nearest half inch, and remember that a wrap taken too low or too high shifts every column below it.
| Circumference (in) | Diameter (in) | Basal area (sq ft) | Doyle board feet |
|---|---|---|---|
| 12 | 3.8 | 0.08 | 0 |
| 24 | 7.6 | 0.32 | 13 |
| 36 | 11.5 | 0.72 | 56 |
| 48 | 15.3 | 1.27 | 127 |
| 60 | 19.1 | 1.99 | 228 |
| 72 | 22.9 | 2.86 | 358 |
| 96 | 30.6 | 5.09 | 705 |
| 120 | 38.2 | 7.96 | 1169 |
Key Terms
- DBH
- Diameter at breast height, the trunk width measured 4.5 ft above sound ground.
- Breast height
- The 4.5 ft reference line, set from the uphill side where the land slopes.
- Basal area
- Cross-sectional trunk area in square feet, the standard stocking measure per acre.
- Pole
- A small-diameter tree, roughly 4 to 10 in, that is past sapling but not yet a sawlog.
- Sawlog
- A log large and clear enough to be milled into dimension lumber.
- Doyle scale
- A simple board-foot rule that fits small logs generously and big ones poorly.
What the Diameter Number Is Really For
- Diameter decides money far more than height does, because milling rules and log grades are written against DBH, so a landowner who knows only tree height cannot compare bids.
- Basal area per acre, not tree count, is how a forester judges whether a woodlot is overstocked, and one diameter measurement feeds that figure directly.
- The Doyle scale flatters small trees and under-reads big ones, which is why two mills can pay different money for the identical log; ask for their scaling method before you judge a bid.
- Municipal tree ordinances almost always set their protection threshold at a diameter, commonly somewhere between 6 and 18 in, so the measurement decides whether a permit is required before you pick up a saw.
- A single wrap can be wrong by a tenth of an inch in diameter for every inch of tape error, which is why foresters re-measure any tree that flares, forks or leans rather than trusting one pass.
Common Mistakes & Fixes
- Measuring at 3 ft because it is comfortable, then reporting it as breast height.
- Reading the diameter off the bark rather than the tape, which biases every downstream figure.
- Entering a centimetre wrap while the selector is still set to inches.
- Ignoring a butt flare and wrapping the trunk below the swell instead of above it.
- Adding bark allowance to a softwood that was already scaled with bark on.
- Cruising a stand from one tree and calling the total basal area accurate.
When to Reach for This
Use it before you request a tree-removal permit, before you compare milling bids, when a forester asks for your stand's basal area, and any time you are deciding whether a tree is big enough to worry about. Pair it with the tree height tool for volume, the tree age tool for growth rate, and the trees per acre planner when you are designing a new planting.
Tree Diameter (DBH) Calculator: Frequently Asked Questions
How do you convert tree circumference to diameter?
Divide the circumference by pi, which is roughly 3.1416. A 48-inch wrap becomes a 15.3-inch diameter, and a 120-inch wrap becomes 38.2 inches. That single step is the entire conversion, provided the trunk is nearly round at the height where you measured.
How far off the ground is breast height?
Breast height is 4.5 ft above sound, level ground, measured up the trunk rather than out from the base. On a slope you start the measurement on the uphill side, because measuring from the downhill side inflates the height and understates the true diameter at the standard point.
Why do foresters use basal area instead of counting trees?
Basal area adds up trunk cross-section in square feet, so a large tree counts for far more than a small one, which reflects the light, water and nutrients it actually uses. A stocking guideline of 60 to 80 sq ft of basal area per acre means something a raw tree count never does.
Does bark thickness change the diameter reading?
The wrap includes bark, so DBH from circumference is a with-bark diameter. Mills often scale a tipped, debarked stick instead, and species with very thick bark such as black willow or ponderosa pine can therefore show a visible gap between your figure and the mill's.
Is the Doyle board-foot number a fair estimate of lumber?
It is a quick planning figure rather than a grade. Doyle fits small and mid-size logs generously and under-scales the largest ones, so treat the output as an order-of-magnitude check, and get a scaled bid from the mill that will actually saw the tree before you decide what it is worth.
Can I use this for a multi-trunk tree?
Measure each trunk separately at 4.5 ft and add their basal areas, because that is how a cruiser records a clump. There is no agreed single diameter for a multi-trunk tree, so if a permit ordinance hinges on one, ask the local officer how they count the clump rather than guessing.
Sources & Further Reading
- Tree Measurement for Woodland Owners — Penn State Extension. Breast-height convention, slope measurement and diameter tapes.
- Estimating Basal Area and Stand Density — University of Missouri Extension. Basis for the 0.005454 basal-area constant and stocking guidance.
- Scaling Rules and Log Rules Used by Hardwood Mills — USDA Forest Service, Northern Research Station. Doyle rule definition and its known bias on small logs.
Chlorova Gardening Team
Builds, checks and documents every tool we publish
Chlorova editorial review
Checked against extension-service publications
Formula verified against published references · Updated
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