Tree Basal Area per Acre

The Tree Basal Area per Acre calculator computes the Stand Density, which is the basal area per acre of trees based on a sample of tree breast high diameters in a plot and the plot radius.

INSTRUCTIONS: Choose units and enter the following:

• (DBH) Diameter at Breast Height samples in inches (e.g., 10.1,8.0,10.3,11.1,12.2,12.1,21.1,10.4)
• (r) Plot Radius.  Note: the default radius is for an 1/10^th of an acre sample ring.
• (PN) Plot Name. This is the sample name if desired for reporting.

Tree Basal Area per Acre (TBA): The basal area density is returned in square feet per acre (ft²/ac) and square meters per hectare (m²/ha). The calculator also returns the Basal Area (BA) for the Plot, the size of the plot (A) and the sample size (n).

The Math / Science

The basal area of a tree is a measure of the cross-sectional area of a tree trunk at breast height (typically 1.3 meters or 4.5 feet above the ground). It is commonly used in forestry to estimate the density of trees in a given area, assess forest stand structure, and calculate timber volume.

The basal area of a tree is calculated using the formula for the area of a circle:

BA  = π ⋅ DBH²/4

where:

• BA = Basal Area of a tree at breast height
• DBH = Diameter of a tree at breast height (DBH).

Unit Conversion

Basal area is often expressed in square feet per acre (ft²/ac) and square meters per hectare (m²/ha) when assessing forest stands.

Importance in Forestry:

Basal area is used to estimate the volume of timber that can be harvested.  Basal area helps in assessing the health and productivity of a forest stand. It is used in forest management practices to determine thinning and other treatments. By summing the basal areas of individual trees in a sample plot, foresters can estimate the total basal area per hectare, which is an important indicator of forest density and stand structure.

Forestry Calculators

• Tree Basal Area from Diameter: Computes the basal area of a tree based on the measurement of the tree's diameter at breast height.
• Tree Basal Area from Circumference: Computes the basal area of a tree based on the measurement of the tree's circumference at breast height.
• Basal Area per Acre: Computes the basal average per acre (ft²/ac) and basal average per hectare (m²/ha), based on samples and plot size.
• Volume of Maple Syrup from Sap: Computes the amount of maple syrup produced from an amount of sugar maple sap.
• Value of Maple Syrup Harvest: Computes the dollar amount associated with a number of sugar maple tree taps.
• Acreage Sample Ring: Compute the radius of a circle (e.g., 37 ft) where the area of the circle equates to an input area (e.g., 1/10^th acre)
• Square Meters to Acres: Converts square meters to acres.
• Simple Stats: Computes the most common observational statistics (min, max, mean, sd, sum, sort etc) for a set of comma separated numbers.

Reference

• Basal Area: A Measure Made for Management by Jim Elledge and Becky Barlow

Special Thanks

Special thanks to Luke Macaulay of the University of Maryland