Calculate tree basal area from DBH for one tree or a stand, with results in ft², m², ft²/acre, m²/ha, and stocking level.
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Basal Area Formula
Basal area is the cross-sectional area of a tree stem at breast height, usually measured at DBH. For one tree, the calculator finds the area of a circle using the tree diameter. For a stand, it adds the basal area of all entered trees and scales that total to one acre or one hectare.
One tree, DBH in inches
BA_ft2 = 0.005454 * DBH_in^2
One tree, DBH in meters
BA_m2 = pi/4 * DBH_m^2
Stand basal area from a plot
BA_acre = sum(BA_tree_ft2) / Plot_acres
BA_ha = BA_acre * 0.229568
- BA_ft2 = basal area of one tree in square feet
- BA_m2 = basal area of one tree in square meters
- DBH_in = tree diameter at breast height in inches
- DBH_m = tree diameter at breast height in meters
- sum(BA_tree_ft2) = total basal area of all measured trees in the plot
- Plot_acres = plot size converted to acres
- BA_acre = stand basal area in square feet per acre
- BA_ha = stand basal area in square meters per hectare
The one-tree mode converts your DBH entry to inches and meters, then reports basal area in both ft² and m². The stand mode calculates basal area for each diameter you enter, adds those tree values, converts the plot size to acres, and reports the result as ft²/acre and m²/ha.
Basal Area Stocking Ranges
These ranges give a general way to interpret stand basal area in ft² per acre. Exact targets vary by species, site quality, age, and management goal.
| Basal area | General interpretation | Typical meaning |
|---|---|---|
| Less than 40 ft²/acre | Understocked | Open stand with low tree cover |
| 40 to 79.9 ft²/acre | Light stocking | Common after thinning or in young stands |
| 80 to 119.9 ft²/acre | Fully stocked | Often a healthy working range |
| 120 to 159.9 ft²/acre | Heavily stocked | Trees may be approaching crowding |
| 160 ft²/acre or more | Overstocked | Competition stress is more likely |
Common Plot Size Conversions
| Plot size | Acres | Hectares |
|---|---|---|
| 1/10 acre | 0.1 acre | 0.0405 ha |
| 1/4 acre | 0.25 acre | 0.1012 ha |
| 400 m² | 0.0988 acre | 0.04 ha |
| 1000 m² | 0.2471 acre | 0.1 ha |
| 1 hectare | 2.4711 acres | 1 ha |
Basal Area Examples
Example 1: Basal area of one 12-inch tree
For a tree with a DBH of 12 inches:
BA_ft2 = 0.005454 * 12^2
BA_ft2 = 0.785 ft2
The tree has a basal area of about 0.785 ft².
Example 2: Stand basal area from a 0.1-acre plot
Suppose your plot is 0.1 acre and the measured DBH values are 10, 12.5, 8, 14, and 11 inches.
Total_BA = 0.005454*(10^2 + 12.5^2 + 8^2 + 14^2 + 11^2)
Total_BA = 3.477 ft2
BA_acre = 3.477 / 0.1 = 34.8 ft2/acre
The stand basal area is about 34.8 ft²/acre, which is in the understocked range by the general categories above.
FAQ
What is DBH?
DBH means diameter at breast height. In forestry, it is usually measured at 4.5 feet above the ground on the uphill side of the tree. Basal area depends on DBH, so a small diameter measurement error can noticeably affect the result because the formula squares the diameter.
What does basal area per acre mean?
Basal area per acre is the total cross-sectional area of tree stems on one acre of land. For example, 100 ft²/acre means that if all tree stems were cut at DBH and their cross sections were added together, they would cover 100 square feet on each acre.
Why does the stand mode use a plot size?
A plot is only a sample of the stand. Dividing the total tree basal area in the plot by the plot area scales the measurement to a per-acre or per-hectare value. If your plot is 0.1 acre, the calculator effectively multiplies the plot total by 10 to estimate ft²/acre.
