Basal area

The basal area (BA) of a tree can be estimated from its diameter at breast height (DBH), the diameter of the trunk as measured 1.3m (4.5 ft) above the ground. DBH is converted to BA based on the formula for the area of a circle:

${\displaystyle BA=\pi \times (DBH/2)^{2}}$ 

If ${\displaystyle DBH}$  was measured in cm, ${\displaystyle BA}$  will be in cm². To convert to m², divide by 10,000:

${\displaystyle BA(m^{2})={\frac {\pi \times (DBH(cm)/2)^{2}}{10000}}}$ 

If ${\displaystyle DBH}$  is in inches, divide by 144 to convert to ft²:

${\displaystyle BA(ft^{2})={\frac {\pi \times (DBH(inches)/2)^{2}}{144}}}$ 

The formula for BA in ft² may also be simplified as:

${\displaystyle BA(ft^{2})=0.005454\times DBH(in)^{2}}$  in English system

${\displaystyle BA(m^{2})=0.00007854\times DBH(cm)^{2}}$  in Metric system

The basal area of a forest 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 made for a plot and then scaled to m²/ha or ft²/acre to compare forest productivity and growth rate among multiple sites.

A wedge prism can be used to quickly estimate 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.^{[citation needed]}

Suppose you carried out a survey using a variable radius plot with angle count sampling (wedge prism) and you selected a Basal Area Factor (BAF) of 4. If your first tree had a diameter at breast height (DBH) of 14cm, then the standard way of calculating how much of 1ha was covered by tree area (scaling up from that tree to the hectare) would be:

(BAF/((DBH+0.5)² × π/4))) × 10,000

• BAF, in this case 4, is the BAF selected for the sampling technique.
• DBH, in this case 14 (this uses an assumed diameter, when actually used is the radius perpendicular to the tangent line)
• The + 0.5 allows under and over measurement to be accounted for.
• The π/4 converts the rest to the area.

In this case this means in every Ha there is 242 m² of tree area according to this sampled tree being taken as representative of all the unmeasured trees.

It would also be possible to survey the trees in a Fixed Area Plot (FAP). Also called a Fixed Radius Plot. In the case that this plot was 100 m². Then the formula would be

(DBH+0.5)²X π/4

1. R. Hédl, M. Svátek, M. Dancak, Rodzay A.W., M. Salleh A.B., Kamariah A.S. A new technique for inventory of permanent plots in tropical forests: a case study from lowland dipterocarp forest in Kuala Belalong, Brunei Darussalam, In Blumea 54, 2009, p 124–130. Published 30. 10. 2009.