How this calculator works
Treat each trunk section as a circle measured at the same recorded breast-height convention. Sum individual areas rather than averaging diameters first, since area grows with diameter squared. Plot mode divides this sum by the sampled land area and expands to a hectare or acre. Buttresses, forks and irregular stems need an appropriate field measurement protocol; basal area is not crown cover.
Formula
BA = pi d²/4; stand BA = sum(pi d_i²/4). Stocking in m²/ha = stand BA x 10000 / plot m².
Worked example
A 20 cm stem has 0.031416 m² basal area. Two such stems in 1000 m² give 0.062832 m² total and 0.628319 m²/ha.
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Frequently asked questions
Why not use the average diameter?
Squaring a mean diameter understates area when diameters differ. Add the separate circular sections.
Where should I measure?
Use the breast height and abnormal-stem rules of your local inventory protocol and record them consistently.
Is basal area tree density?
Stem count per hectare is density. Basal area includes stem size, so equal counts can have different basal areas.