Basal Area Calculator
Basal area — the cross-section of tree trunks at breast height per hectare or acre — the forester’s measure of how crowded a stand is.
A tree’s basal area is the area of a circle with its diameter at breast height (1.
How the basal area calculator works
A tree’s basal area is the area of a circle with its diameter at breast height (1.3 m or 4.5 ft): π × (DBH ÷ 2)². Multiply by the number of trees of that size per hectare for the stand. Fully stocked temperate stands run about 20–35 m²/ha (90–150 ft²/acre); much above that and thinning is due.
Formula: BA per tree (m²) = π × (DBH cm ÷ 200)²; imperial: 0.005454 × DBH in²
Worked examples
| Inputs | Stand basal area | Note |
|---|---|---|
| 300 trees of 30 cm per hectare | 21.2 | 21.2 m²/ha |
| 120 trees of 12 in per acre | 94.2 | 94.2 ft²/acre |
| One 100 cm giant | 0.8 | 0.785 m² |
FAQFrequently asked questions
What is a typical basal area?
Fully stocked temperate forests run about 20–35 m²/ha (90–150 ft²/acre); thinned or young stands 10–20; old growth and dense conifer stands can exceed 50.
How is basal area measured in the field?
Either by measuring every tree’s diameter in a sample plot, as this calculator assumes, or with a prism or angle gauge that counts “in” trees from a point — the fast method foresters use.
Why is DBH measured at 1.3 m?
Breast height (1.3 m, or 4.5 ft in the US) is a standard that clears the root flare and is easy to reach; consistency matters more than the exact height.
What if my trees are different sizes?
Run the calculator for each size class and add the results, or use the stand’s quadratic mean diameter — the diameter of the tree of average basal area.
Where these figures come from
- NCBI Bookshelf — Molecular Biology of the Cell — growth kinetics and molecular conventions
- National Human Genome Research Institute — the US genomics research institute
Last checked: September 2026. Formulas are the standard textbook forms; assumptions are stated on each page because they are where these models break.