Wikipedia
Basal area is the area of a given section of land that is occupied by the cross-section of tree trunks and stems at the base. The term is used in forest management and forest ecology.
In most countries, this is usually a measurement taken at the diameter at breast height (1.3m or 4.5 ft) of a tree above the ground and includes the complete diameter of every tree, including the bark. Measurements are usually made for a plot and this is then scaled up for 1 hectare of land for comparison purposes to examine a forest's productivity and growth rate.
To estimate a tree's basal area BA, use the tree's diameter at breast height DBH in inches with the following formula:
$BA = \frac{\pi \times (DBH/2)^2}{144}$
(Note: The factor of 144 is there to convert from Sq Inches to Sq Feet)
This formula simplifies to: BA = 0.005454 × DBH
The result will be in ft.
For the DBH in cm use: BA = 0.00007854 × DBH
The result will be in m.
The basal area of a forest stand can be found by adding the basal areas (as calculated above) of all of the trees in an area and dividing by the area of land in which the trees were measured. Basal area is generally expressed as ft/acre or m/ha.
A wedge prism can be used to quickly estimate the basal area per hectare. To find basal area using this method, simply multiply your BAF (Basal Area Factor) by the number of "in" trees in your variable radius plot. The BAF will vary based on the prism used, common BAFs include 5/8/10, and all "in" trees are those trees, when viewed through your prism from plot centre, that appear to be in-line with the standing tree on the outside of the prism.