What this calculator does
Basal area is the cross-sectional area of a trunk measured at breast height, 1.3 metres up. For a single tree it is just the area of a circle from the diameter. Summed across a stand and expressed per hectare, it becomes the standard measure of how fully a site is stocked, and it is used in preference to a stem count because it accounts for tree size as well as number.
The square relationship is what makes it useful and what catches people out. Doubling the diameter quadruples the basal area, so one 60 cm tree occupies the same basal area as four 30 cm trees. A stand of few large trees and a stand of many small ones can be equally stocked.
The formula
The diameter at breast height is halved to give a radius, and the area is π times that radius squared. The result is converted from square centimetres to square metres and square feet. Where a stems-per-hectare figure is supplied, the per-tree area is multiplied by it to give stand basal area in square metres per hectare, which assumes every tree is of the diameter entered.
| Term | Meaning |
|---|---|
| DBH | Diameter at breast height, measured 1.3 m above ground, the standard point for forestry measurement. |
| Basal area per tree | The cross-sectional area of one trunk at that height. |
| Stand basal area | The total per hectare, the usual measure of stocking. Natural forests commonly run from about 20 to 60 m² per hectare. |
| Stems per hectare | Tree count per hectare, which on its own says nothing about tree size. |
The inputs explained
| Field | What to enter |
|---|---|
| Diameter at breast height (DBH) (cm) | Trunk diameter at breast height, in centimetres. Measure the circumference and divide by π if a diameter tape is not to hand. |
| Stems per hectare (0 to skip) (trees/ha) | Stems per hectare, for the stand figure. Leave it at zero to get the per-tree area only. The calculation treats every stem as having the diameter entered, so use a mean basal area diameter rather than a mean diameter for a mixed stand. |
When to use it
Assessing how heavily stocked a stand is
Stand basal area is the figure thinning decisions are made against, since it captures the competition for light and water better than a stem count does.
Tracking growth over time
Basal area increment is a standard growth measure, and because it is an area it reflects wood volume more closely than a diameter change does.
Converting between measurement systems
Forestry in North America works in square feet per acre while most other regions use square metres per hectare, and both figures come out together here.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does basal area grow with trunk diameter?
A range of trunk diameters, each with the stand figure at a fixed 400 stems per hectare.
| DBH | Basal area per tree (m²) | Per tree (ft²) | Stand basal area |
|---|---|---|---|
| 10 cm | 0.0079 m² | 0.085 ft² | 3.14 m²/ha |
| 20 cm | 0.0314 m² | 0.338 ft² | 12.57 m²/ha |
| 30 cm | 0.0707 m² | 0.761 ft² | 28.27 m²/ha |
| 50 cm | 0.1963 m² | 2.113 ft² | 78.54 m²/ha |
| 80 cm | 0.5027 m² | 5.411 ft² | 201.06 m²/ha |
Questions
Why is diameter measured at 1.3 metres?
It is a convention chosen as roughly chest height on an adult, above the root flare that swells the base of most trees and low enough to reach comfortably. The exact height varies slightly by country, 1.3 m in most of the world and 4.5 feet in the United States, which is about 1.37 m.
What is a typical stand basal area?
Broadly 20 to 60 m² per hectare for a stocked natural forest, varying widely with species, age and site. Managed plantations are often held lower deliberately, since thinning to reduce competition produces larger individual trees.
How do I measure DBH without a diameter tape?
Measure the circumference with an ordinary tape and divide by π. A trunk measuring 94 cm around is about 30 cm in diameter. Diameter tapes simply have that division printed on them.
Can I use this for a stand of mixed sizes?
Not directly, because it applies one diameter to every stem. For a mixed stand, calculate the basal area of each size class separately and add them, or use the quadratic mean diameter, which is the diameter of the tree of average basal area rather than of average diameter.
For the diversity of the species making up a stand, see the Shannon diversity index calculator. For population growth under a site capacity limit, see the logistic growth calculator.