## Basal Area

Basal area per tree is the cross-sectional area of a tree at breast height. It can be calculated from Diameter at breast height (DBH) by the following English formula:

$$BA = \left( \frac{\pi}{4*144} \right) * DBH^2$$
$$BA = 0.005454154 * DBH^2$$

where:

BA is basal area per tree in square feet.
DBH is the diameter at breast height in inches.
is the constant 3.1415.

It can be calculated from Diameter at breast height (DBH) by the following metric formula:

$$BA = \left( \frac{\pi}{4*10000} \right) * DBH^2$$
$$BA = 0.00007854 * DBH^2$$

where:

BA is basal area per tree in square meters.
DBH is the diameter at breast height in centimeters.
is the constant 3.1415.

Basal area per acre is the sum of all the basal area per tree in the acre. Basal area per acre or hectare is a standard measure of the size-density relationship in a stand.

$$BA/unit = \sum_{i=1}^n BA_i w_i$$

where:

BA/ac is the Basal area per acre,
BAi is the Basal area per tree for the ith tree
Wi is the sample expansion factor weight.

Figure 1. An illustration of the basal area per acre. The basal area per tree is the cross-sectional area of each tree at breast height(the black ellipses). Basal area per acre would be the sum of these cross-sectional areas for all tree in an acre.