About basal area
Basal area is the cross-sectional area of a tree's trunk, measured at breast height and treated as a circle. In North American forestry, breast height (DBH) is 4.5 feet above the ground; in most of the rest of the world it is 1.3 metres. Because a stem is roughly circular, its area is found from its diameter with the area-of-a-circle formula, and summing those areas over a plot gives one of the most-used measures of forest stand density.
The formula
For a single stem, basal area is the area of a circle: BA = π/4 × DBH². The convenient forestry versions bundle the unit conversion into a single constant:
- Imperial: BA (ft²) = 0.005454 × DBH(in)². The constant is (π/4) ÷ 144, because there are 144 square inches in a square foot: 0.785398 ÷ 144 = 0.0054542.
- Metric: BA (m²) = 0.00007854 × DBH(cm)². The constant is (π/4) ÷ 10,000, because there are 10,000 square centimetres in a square metre: 0.785398 ÷ 10,000 = 0.00007854.
To get stand basal area, add the basal area of every tree on a plot and divide by the plot's land area, giving square feet per acre (ft²/ac) or square metres per hectare (m²/ha).
Why basal area matters
- It measures how much of a site is occupied by tree stems, so it is a direct index of stand density and competition for light, water, and nutrients.
- Foresters use it to decide when and how heavily to thin: too high a basal area slows individual-tree growth; too low wastes growing space.
- It scales cleanly — you can measure a small sample plot and expand the per-acre value to a whole stand, which is why prism ("angle-gauge") cruising works.
Common reference points
- A 12-inch DBH tree has a basal area of 0.005454 × 12² = 0.785 ft² (about 0.073 m²).
- A 20-inch DBH tree has 0.005454 × 400 = 2.18 ft².
- Fully stocked eastern US hardwood and pine stands commonly carry roughly 80–120 ft²/ac; managed stands are often thinned to 60–90 ft²/ac.
- A single tree exactly 1 metre in diameter (100 cm) has a basal area of 0.00007854 × 10,000 = 0.785 m².