Basal Area Calculator (m²/ha & ft²/acre from tree diameters)

Understanding the basal area calculator — concept and principle

Basal area is the cross-sectional area of tree trunks at breast height. Foresters add it up for all trees in a sample plot and express it per hectare or acre, a key measure of stand density used to plan thinning, estimate timber volume and assess habitat.

Each trunk’s area π(d/2)² at breast height is summed and scaled to a hectare: 19.45 m²/ha.

How it is calculated

One tree: BA = π × DBH² ÷ 4. With DBH in cm, BA (m²) = 0.00007854 × DBH²; with DBH in inches, BA (ft²) = 0.005454 × DBH².
Stand basal area = sum of tree BAs ÷ plot area (m²/ha or ft²/acre); 1 m²/ha = 4.356 ft²/acre.
Trees per hectare = trees measured ÷ plot area.
Quadratic mean diameter = √(mean of DBH²), the diameter of the tree with average basal area.

The principle

A trunk's cross-section approximates a circle, so its area grows with the square of the diameter. Measuring at a fixed height, 1.3 m in many countries and 4.5 ft (1.37 m) in US forestry, avoids the flare at the base. Basal area per unit land area combines tree size and number into one figure that tracks how fully the site is occupied. The quadratic mean diameter is used instead of the arithmetic mean because basal area depends on DBH².

Worked example

Default inputs: metric, 10 trees with DBH 32, 28.5, 41, 22, 35.6, 19, 27, 30.5, 45.2 and 24 cm in a 0.04 ha plot.

Sum of tree basal areas ≈ 0.778 m² for 10 trees.
Stand basal area = 0.778 ÷ 0.04 ≈ 19.45 m²/ha, or 84.7 ft²/acre.
Trees per hectare = 10 ÷ 0.04 = 250, about 101 per acre.
Quadratic mean diameter = √(mean of DBH²) ≈ 31.5 cm (12.4 in).

Each point is the calculator re-run with only “Plot area” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Plot area	Basal area (m²/ha)
0.01	77.82
0.02	38.91
0.03	25.94
0.04	19.45
0.05	15.56
0.06	12.97
0.08	9.73

How to read the result

Compare basal area with stocking guides or management targets for your species and region. Values above the target suggest a stand that may benefit from thinning; low values indicate open stands. The same basal area can come from many small trees or a few large ones, so look at trees per hectare and QMD too.

Common mistakes

Measuring at the wrong height or on the uphill side inconsistently.
Using circumference as diameter (divide circumference by π).
Forgetting to divide by plot area.
Mixing metric and US units.

Keep in mind: Sample plots estimate the stand with sampling error. Forest management decisions should follow local guidelines and qualified foresters.

Frequently asked questions

How do you calculate basal area per hectare?

Add each tree's π × DBH² ÷ 4 in m² and divide by the plot area in hectares.

What is the basal area constant 0.005454?

π ÷ (4 × 144), converting a DBH in inches to basal area in square feet.

What is quadratic mean diameter?

The diameter of a tree with the average basal area: √(Σ DBH² ÷ n).

Sources: Avery, T. E. & Burkhart, H. E., Forest Measurements, 5th ed. McGraw-Hill · USDA Forest Service, Forest Inventory and Analysis (FIA) field guide (DBH at 4.5 ft)

Checked 9 Nov 2026. Martin A.J., “What Is Basal Area?”, University of Wisconsin–Madison Dept. of Forestry, Forestry Facts No. 43, August 1989: basal area = 3.1416 × DBH²/(4 × 144) = 0.005454 × DBH² (ft², DBH in inches), DBH measured 4½ ft above the ground.

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