Which formula is used?

This tool applies BA (ft²) = 0.005454 × DBH². Every figure updates live as you change the inputs.

The maths follows the stated formula precisely, but the answer is an estimate that depends on the values you enter and on rules that can change.

Can I export the result?

Yes — use the PDF button to download a branded multi-page report with your inputs, results and working.

Biology

Basal Area Calculator

Find a tree's basal area from DBH and the stand basal area per acre.

Your inputs

Change any value — everything updates instantly.

DBH in

Diameter at 4.5 ft.

Trees per acre trees

Average count of trees of this size per acre.

Try an example

Basal area per acre

78.5 ft²/ac

This means the trunks cover about 79 ft² of each acre at breast height.

Trunk cross-sectionOne acre

Slow motion1×100 trees/ac

What you are seeing

Each dot is a trunk cut at breast height.

The box is an acre (1 dot ≈ 5 trees at 100 per acre).

Together they cover 78.5 ft² per acre.

Per tree

0.785 ft²

Cross-section of one trunk.

Per tree (metric)

0.073 m²

Same area in m².

Per hectare

18.03 m²/ha

Stand basal area in metric.

Result explanation: Stand density

78.5 ft² per acre.

Real-life comparison: At 14 in DBH it would be 106.9 ft²/ac.

Low, normal or high? A moderately stocked stand.

Graph and details

Basal area per acre against DBH

How to read this chart: Basal area rises with the square of diameter, so the curve steepens.

What this calculator does

Finds each trunk's cross-section area from DBH and multiplies by trees per acre.

What your result means

78.5 ft²/ac of basal area.

Foresters use it to judge crowding and plan thinning.

Doubling DBH quadruples basal area.

The formulas

Trunk area per tree times the number of trees.

1. Basal area

BA = 0.005454 × DBH²

Symbols

DBH: Diameter at breast height (in)
0.005454: π ÷ (4 × 144) (ft²/in²)

Why this formula works

Circle area π(D/2)², converted from square inches to square feet.

Unit check

in² × ft²/in² = ft² ✓

Worked example

DBH = 12 in
0.005454 × 144
= 0.785 ft²

Common mistakes

Forgetting to square DBH.
Using circumference instead of diameter.

Working for your numbers

BA = 0.005454 × 12² = 0.7854 ft²
Per acre = 0.7854 × 100 = 78.54 ft²/ac

The stand has about 78.5 ft² of basal area per acre.

Frequently asked questions

What is basal area?

The area of trunk cross-sections at breast height.

Why use it?

It is a quick measure of how crowded a stand is.

Mixed sizes?

Run each size class separately and add them.

Prism method?

A prism or angle gauge estimates stand basal area directly in the field.

Symbols and assumptions

BA: Basal area (ft²)
TPA: Trees per acre ()

Every tree has the entered average DBH.

Sources and review

Reviewed 2026-09-25 · Next review 2027-09-25

Inventorying your forestPenn State Extension

Important limitation. An average-diameter estimate; a full inventory measures each tree.

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