Last updated: June 26, 2026
Tree Diameter Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
The Tree Diameter Calculator converts a measured trunk circumference into diameter at breast height (DBH) using DBH = Circumference ÷ π, because a trunk cross-section is treated as a circle. It also returns the radius (DBH ÷ 2), cross-sectional area (π × r²), and forestry basal area (0.005454 × DBH² in square feet for DBH in inches). Measurements can be entered in inches or centimetres, and the diameter is reported in both. DBH is measured 4.5 ft (1.37 m) above ground and is the foundation for tree age, volume, basal area, and value calculations.
To find tree diameter, divide the trunk circumference by pi. For example, a girth of 62.8 inches gives a diameter at breast height of about 20 inches.
Key Takeaways
- Diameter at breast height is found from girth with DBH = Circumference ÷ π
- Measure circumference at 4.5 ft (1.37 m) above ground on the uphill side
- A diameter tape (D-tape) is pre-scaled by π and reads diameter directly
- Basal area (ft²) = 0.005454 × DBH² (DBH in inches) — a 10-in tree ≈ 0.545 ft²
- Works in inches or centimetres; diameter is reported in both units
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
DBH = C ÷ π (r = DBH ÷ 2, Area = π × r²)
Where:
- DBH=Diameter at breast height(inches)
- C=Trunk circumference (girth) at 4.5 ft / 1.37 m(inches)
- r=Trunk radius(inches)
- A=Cross-sectional area(in²)
Worked Examples
Girth to Diameter
A trunk with a 62.8-inch circumference measured at breast height.
- 1Measure the circumference at breast height: 62.8 inches
- 2Apply the formula: DBH = C ÷ π = 62.8 ÷ 3.1416
- 3Result: DBH ≈ 20 inches
- 4Radius = 10 in, basal area ≈ 2.18 ft²
Metric Measurement
A trunk measured in centimetres — 160 cm girth.
- 1Circumference = 160 cm = 62.99 inches
- 2DBH = 62.99 ÷ π ≈ 20.05 inches
- 3Convert back: DBH ≈ 50.9 cm
- 4The calculator reports diameter in both inches and centimetres
Diameter to Basal Area
Working from a known 12-inch DBH to derive its basal area.
- 1Diameter (DBH) = 12 inches
- 2Circumference = π × 12 ≈ 37.7 inches
- 3Cross-sectional area = π × 6² ≈ 113.1 in²
- 4Basal area = π ÷ 576 × 12² ≈ 0.785 ft²
Introduction
The Tree Diameter Calculator converts an easy-to-take trunk circumference (girth) into the diameter at breast height (DBH) — the standard forestry measurement taken 4.5 feet (1.37 m) above the ground. Because a trunk cross-section is essentially a circle, its diameter equals the circumference divided by π: DBH = Circumference ÷ π. The calculator also reports the radius, the cross-sectional area, and the basal area used in forest inventories, and it works in both inches and centimetres. Enter a girth or a known diameter to get every derived trunk metric instantly.
How the Diameter Conversion Works
Measuring a trunk's diameter directly with calipers is awkward on a large, irregular tree, so foresters wrap a tape around the trunk to read the circumference instead. Since the circumference of a circle equals π times its diameter, dividing the girth by π recovers the diameter. From the diameter, the radius and area follow with simple geometry.
Wrap a flexible tape around the trunk at breast height to read the circumference
Diameter = Circumference ÷ π (π ≈ 3.1416)
Radius = Diameter ÷ 2
Cross-sectional area = π × radius²
Choose inches or centimetres — results are shown in both diameter units
Understanding the Formula
The relationship C = π × D is the definition of π for any circle. Rearranging gives D = C ÷ π, which is exactly what this calculator applies. A special diameter tape (D-tape) used by arborists is pre-scaled by π, so reading it around the trunk gives the diameter directly — this calculator does the same arithmetic for an ordinary tape.
The conversion assumes a roughly circular trunk. Oval, fluted, or buttressed trunks deviate from a perfect circle, so the computed diameter is the diameter of the circle with the same circumference.
How to Measure Trunk Circumference Correctly
A reliable diameter starts with a careful girth measurement. The forestry standard is breast height — 4.5 feet (1.37 m) above ground on the uphill side. Once you have the diameter you can estimate the tree's age with our tree age calculator.
Measure at 4.5 ft (1.37 m) above ground on the uphill side of the trunk
Keep the tape level and snug, perpendicular to the trunk's axis
Avoid measuring over branches, burls, or swellings that inflate the reading
For multi-stem trees, measure each stem separately or below the fork
On a leaning trunk, measure perpendicular to the lean, not horizontally
Radius, Cross-sectional Area, and Basal Area
Beyond diameter, several derived metrics are useful in forestry and arboriculture. Basal area — the cross-sectional area of the trunk at breast height expressed in square feet — is a key stand-density measure. Summing basal area across all trees on a plot tells foresters how fully a site is stocked, which you can combine with our basal area calculator.
Radius = Diameter ÷ 2 — half the trunk width
Cross-sectional area = π × radius² — the area of the trunk's circular face
Basal area (ft²) = π ÷ 576 × DBH² (DBH in inches) — the standard forestry constant 0.005454
A 10-inch DBH tree has a basal area of about 0.545 ft²
Basal area per acre is the headline metric in timber stand management
Inches, Centimetres, and Unit Conversions
Tree measurements are reported in inches in North America and centimetres in most of the world. This calculator accepts either and reports the diameter in both. Remember that the basal-area figure uses the North American convention of square feet from a diameter in inches.
1 inch = 2.54 cm; divide centimetres by 2.54 to get inches
The calculator converts your input internally before applying D = C ÷ π
Diameter is shown in both inches and centimetres for convenience
Cross-sectional area is reported in square inches
Basal area is reported in square feet (forestry standard)
Accuracy and Limitations
The geometric conversion itself is exact, but real trunks are rarely perfect circles. The diameter you obtain is the 'equivalent circular diameter' — the diameter of a circle with the same circumference. For most forestry and arboriculture purposes this is the accepted standard.
Irregular, fluted, or oval trunks deviate from a true circle
Bark thickness is included — diameter is 'outside bark' unless you measure under bark
Measuring at the wrong height is the most common source of error
Tape tension and angle affect the circumference reading
For research requiring diameter inside bark, subtract twice the bark thickness
Outside-bark DBH is the standard reported value. Only subtract bark thickness when a protocol specifically requires diameter inside bark.
When to Use This Calculator
Diameter at breast height underpins nearly every quantitative tree assessment. Once you have DBH you can drive a range of downstream calculations.
Estimate tree age with our tree age calculator
Explore height–diameter relationships with our tree height calculator
Compute stand stocking with our basal area calculator
Appraise timber or amenity value with our tree value calculator
Plan planting density using our tree spacing calculator
Record consistent DBH for forest inventories and big-tree registers
Common Mistakes to Avoid
Most diameter errors come from inconsistent measurement rather than the arithmetic. Avoid these pitfalls:
Measuring at the base instead of 4.5 ft (1.37 m) breast height
Reporting the circumference as if it were the diameter (it is π times larger)
Mixing units — entering centimetres while the selector is set to inches
Measuring over a branch collar, burl, or root flare
Letting the tape sag so it is not perpendicular to the trunk
Quick Reference Card
Tree Diameter Calculator — Quick Reference
Quick reference • Tree Diameter Calculator
DBH = C ÷ π | r = DBH ÷ 2 | Area = π × r²Valid range: Circumference 0.5–2000 in (or cm); diameter up to ~700 in
Common Values
⚠ Watch Out
- •Measure circumference at 4.5 ft (1.37 m) — not at the flared base
- •Don't report circumference as diameter — it is π times larger
- •Match the unit selector to your measurement (in vs cm)
- •Avoid measuring over burls, branches, or root flare
Pro Tips
- →A flexible tape and the ÷ π formula replace expensive calipers
- →Use a diameter tape to read DBH directly in the field
- →Pair DBH with the tree age and basal area calculators
- →Record outside-bark DBH unless a protocol says otherwise
FAQs
How do I calculate tree diameter from circumference?
Divide the circumference (girth) by π (about 3.1416). Because a trunk cross-section is a circle and a circle's circumference equals π times its diameter, Diameter = Circumference ÷ π. For example, a 62.8-inch girth gives a diameter of about 20 inches.
What is diameter at breast height (DBH)?
DBH is the trunk diameter measured 4.5 feet (1.37 m) above the ground, the international forestry standard. It is the most widely used measure of tree size and feeds into age, volume, basal area, and value calculations.
Why measure circumference instead of diameter directly?
Wrapping a flexible tape around a large, irregular trunk is far easier and more repeatable than trying to caliper its widest point. The circumference is then converted to diameter mathematically, or read directly using a π-scaled diameter tape.
What is a diameter tape (D-tape)?
A diameter tape is a measuring tape whose scale is pre-divided by π. When wrapped around a trunk it reads the diameter directly instead of the circumference. This calculator performs the same division for an ordinary tape.
How do I find basal area from diameter?
Basal area is the cross-sectional area of the trunk at breast height. In forestry units, Basal Area (ft²) = 0.005454 × DBH² where DBH is in inches. A 10-inch tree has a basal area of about 0.545 ft². The calculator reports this automatically.
Can I enter measurements in centimetres?
Yes. Choose the centimetres option in the unit selector and the calculator converts your input to inches internally, then reports the diameter in both inches and centimetres.
Does the diameter include the bark?
Yes, the standard DBH is measured outside the bark. Only subtract bark thickness (twice the thickness, since bark is on both sides) when a specific protocol requires diameter inside bark.
Is the Tree Diameter Calculator free to use?
Yes, it is completely free with no registration. You can convert as many measurements as you like, switch between circumference and diameter modes, and work in inches or centimetres.