Basal Area Calculator for Forest Trees

Basal Area Calculator for Forest Trees

A basal area calculator finds the cross-sectional area of a tree trunk from its diameter at breast height (DBH), then adds up the areas of several trees to get a total for a plot or stand. Basal area is a standard measurement in forestry. It tells foresters how much ground a stand's tree trunks would cover if they were cut flat at chest height.

What is basal area?

Basal area is the area of a tree's trunk cross-section, measured at breast height. The FAO defines breast height as 1.3 m above ground level, or above buttresses if these are higher. In the United States, breast height is 4½ feet (about 1.37 m). A single tree's basal area is usually given in square centimeters or square meters. A whole stand's basal area is the sum of every tree's basal area, usually reported per hectare (m²/ha) or per acre (ft²/acre).

Basal area is useful because it accounts for tree size, not just tree count. A stand with 100 thin saplings can have far less basal area than a stand with 20 large, old trees. Foresters use basal area to compare stand density, estimate timber volume, plan thinning, and track forest growth over time.

The breast-height convention sits above the flared, uneven wood near the base of most trees but is still low enough to measure without special equipment.

Basal area formula

Because a tree trunk is roughly a circle in cross-section, basal area uses the formula for the area of a circle, written in terms of diameter instead of radius:

Basal area = (π/4) × DBH²

• DBH is the diameter at breast height, in centimeters.
• π (pi) is about 3.14159.
• The result is in square centimeters (cm²).

To convert to square meters, divide by 10,000, since 1 m² equals 10,000 cm²:

Basal area (m²) = (π/4) × DBH² ÷ 10,000

For a group of trees, add up each tree's basal area:

Total basal area = sum of each tree's basal area

In US units, the same formula with DBH in inches gives square feet: π ÷ (4 × 144) × DBH², or 0.005454 × DBH². This calculator works in centimeters and square meters only.

If the trees were measured on a sample plot smaller than a hectare, divide the plot total by the plot's area in hectares to get basal area per hectare.

How to calculate basal area: worked examples

Single tree. A tree with a DBH of 30 cm has a basal area of:

(π/4) × 30² = 706.86 cm² = 0.0707 m²

Several trees. A small plot has three trees, with DBH values of 20 cm, 25 cm, and 35 cm.

The plot's total basal area is about 0.177 m². If the plot covers 0.05 hectares, the stand's basal area per hectare is 0.1767 ÷ 0.05 ≈ 3.53 m²/ha.

Using this calculator

1. Enter the DBH, in centimeters, for the first tree. Use "Add Tree" to add a row for each additional tree.
2. The calculator accepts values greater than 0 and up to 1,000 cm.
3. Each tree's basal area updates as it is entered. The total basal area for all trees appears below the list, in square meters.
4. Use "Copy Result" to copy the total for use in a spreadsheet or report.
5. To get basal area per hectare from a sample plot, divide the total by the plot's area in hectares.

Measurement notes

The formula assumes a perfectly round trunk. Real trunks are often slightly oval, especially in species with buttressed roots or storm damage. For an irregular trunk, the FAO field manual says to measure two perpendicular diameters and keep their average.

Because the formula squares the diameter, small measurement errors grow larger in the result. Reading a 30 cm tree as 32 cm, an error of only 2 cm, inflates its calculated basal area by about 14 percent. A diameter tape wrapped around the trunk is generally more accurate than calipers for field measurements.

Tree size affects basal area a great deal. A 5 cm sapling has a basal area of about 0.002 m², while a 50 cm tree has about 0.196 m², exactly 100 times more. A single old-growth tree with a 150 cm DBH has a basal area of about 1.77 m², equal to 900 trees at 5 cm DBH. This is why many forest inventories set a minimum DBH and skip smaller saplings that add little to the total. The FAO's global growing-stock figures, for example, count trees with a minimum diameter of 10 cm at breast height.

Why foresters measure basal area

Basal area supports several practical tasks in forest management.

• Comparing stand density. It lets foresters compare stands of different ages and species on the same scale, since it reflects the actual space tree trunks occupy.
• Estimating volume. Basal area correlates closely with the volume of wood in a stand, so it is a common input to timber volume formulas.
• Planning thinning. Foresters often thin a stand once its basal area passes a target value, to reduce competition for light and water among the remaining trees.
• Tracking growth. Basal area measured at two points in time shows how fast a stand is growing or how much a disturbance, such as a storm or beetle outbreak, has reduced it.

Basal area versus other density measures

Basal area does not account for how many trees make up that area. A stand with 200 large trees and a stand with 800 small trees can have the same basal area but very different structure. Stand Density Index (SDI) corrects for this by combining tree count with average tree size. Foresters also use relative density, which compares a stand's basal area to the maximum a site can typically support, to judge how close a stand is to needing thinning.

History

Austrian forester Walter Bitterlich published angle-count sampling in January 1948. The method estimates a stand's basal area per unit area by counting trees through a simple sighting device. It needs no measurement of plot areas or tree diameters.

Frequently asked questions

What is basal area in forestry? Basal area is the cross-sectional area of a tree trunk at breast height, 1.3 meters above the ground in most countries. For a stand, it is the sum of every tree's basal area, usually reported per hectare or per acre.

What is the formula for basal area? Basal area equals (π/4) times the diameter at breast height squared. With DBH in centimeters, the result is in square centimeters; divide by 10,000 to convert to square meters.

Why use basal area instead of just counting trees? Tree counts ignore size. A stand of many small saplings can have less wood and less competition than a stand of a few large trees, even with a higher tree count. Basal area reflects actual trunk size, making it a better measure of density and standing timber.

How do you measure DBH? Wrap a diameter tape around the trunk at 1.3 meters above the ground (4½ feet in the United States), measuring from the uphill side on a slope. A diameter tape reads diameter directly from the trunk's circumference.

How do I get basal area per hectare from a small plot? Divide the plot's total basal area by the plot's area in hectares. A 0.04-hectare plot with 1.2 m² of total basal area gives 1.2 ÷ 0.04 = 30 m²/ha.

Can basal area estimate timber volume? Basal area is a common input to volume equations, usually combined with tree height and a species-specific form factor. It does not give volume by itself, but it correlates strongly with it.

References

1. Food and Agriculture Organization of the United Nations. FRA 2020 Terms and Definitions. FAO FRA terms and definitions — diameter at breast height is measured over bark at 1.3 m above ground level, or above buttresses; growing stock counts trees with a minimum diameter of 10 cm at breast height.
2. Food and Agriculture Organization of the United Nations. National forest inventory field manual, section 6.2. FAO NFI field manual: tree measurements — non-circular trees measured on two perpendicular diameters and averaged; on slopes, DBH taken from the uphill side.
3. Martin, A. J. What Is Basal Area? Forestry Facts No. 43, University of Wisconsin–Madison. UW–Madison: What Is Basal Area? (PDF) — basal area = 3.1416 × DBH² ÷ (4 × 144) = 0.005454 × DBH², with DBH in inches at 4½ feet.
4. Burkhart, H. E. Remembering Walter Bitterlich. Journal of Forestry, March 2008. Remembering Walter Bitterlich (PDF) — angle-count sampling published in January 1948; estimates basal area per unit area without measuring plot areas or diameters.