# Basal Area Calculator

Created by Julia Żuławińska
Reviewed by Purnima Singh, PhD and Steven Wooding
Last updated: Jul 18, 2022

Use the basal area calculator to find the basal area of a tree or stand density. With our calculator, you won't have to worry about converting units or remembering formulas! You can input up to 50 DBH (diameter at breast height) values and learn the stand density in seconds! And if you're new to the topic, read on to find out what basal area is and how to calculate it.

## What is basal area?

Basal area is an area of a tree's trunk if cut at the breast height. Though you calculate it for a single tree, this parameter is usually used for stand density, so it's often expressed in square meters per hectare or square feet per acre.

The basal area of a tree is calculated from its diameter at breast height (DBH). This parameter is widely used in forestry to find a tree age, production of oxygen, and others.

🙋 The breast height in DBH varies in different countries. In Australia, Canada, and Europe, it's 1.3 m (4.27 ft) above ground level. In the United States, you should measure DBH at 4.5 ft (1.37 m).

## How to calculate basal area?

The formula to calculate the basal area $BA$ of a tree is as follows:

$\footnotesize BA = \pi \times \left(\frac{DBH}{2}\right)^2$

It's the same as a formula for an area of a circle using diameter. In this equation, the unit of the result is the same as the unit of the DBH that you input. So, if you input DBH in cm, you would get the basal area in cm2.

That's why there are two other widely-used basal area formulas. If you use this first one, you can input the DBH in cm, but the basal area unit will be m2.

\footnotesize \begin{align*} BA &= \frac{\pi \times \big(\frac{DBH}{2}\big)^2}{1000}\\[1em] &= 0.00007854 \times DBH^2 \end{align*}

In the second formula, you can input DBH in inches, and the result will have a unit of square feet.

\footnotesize \begin{align*} BA &= \frac{\pi \times \big(\frac{DBH}{2}\big)^2}{144} \\[1em] &= 0.005454 \times DBH^2 \end{align*}

Here, $\footnotesize0.005454$ is the so-called foresters constant, which converts inches to square feet.

## How to calculate basal area per acre?

To calculate basal area per acre, you need to follow these steps:

1. Find a specific area representative of the density and size of trees.

2. Measure the diameter at the breast height of each tree in the chosen area.

3. Calculate the basal area of each tree with the formula:

BA = 0.005454 × DBH²

where the diameter unit is inches, and the basal area unit is square feet.

4. Add all of the tree's basal areas and divide by the area they're on (in acres).

Let's say you need to find a large forest's basal area per acre.

1. First, choose a representative area – let's say you choose a square area of 30×30 feet.

2. There are 6 trees in that square. Their DBH are (in inches): 14, 8.5, 11, 13.5, 9, 11.5.

3. Now, you need to find the basal area of each tree. The calculation for the first tree is:

BA1 = 0.005454 × 14 × 14 = 1.07 sqft

The other trees have following basal areas: BA2 = 0.39, BA3 = 0.66, BA4 = 0.99, BA5 = 0.44, BA6 = 0.72.

4. Now, we need to add all the basal areas:

Total BA = 4.27 sqft

5. Convert the chosen area to acres:
30×30 feet = 0.0207 acres, and divide these two numbers:
4.27/0.0207 = 206.28

6. The basal area per acre is equal to 206 square feet.

## How to use the basal area calculator?

Our calculator has two modes:

1. In the first mode, it calculates the basal area of one tree. For that purpose, you only need the chosen tree's diameter at breast height (DBH).

2. In the second mode, our calculator can determine basal area per acre or hectare. To use this mode, you need to measure several trees growing in a chosen, representative area and then fill in the values in the calculator. You can input DBHs of up to 50 trees.

## FAQ

### How to calculate basal area from DBH?

To calculate basal area in square feet from DBH in inches, use this formula:

basal area = 0.005454 × DBH²

If you have DBH in square centimeters, you can get a basal area in square meters with this equation:

basal area = 0.00007854 × DBH²

Julia Żuławińska
Number of trees
One tree
DBH
in
Basal area
ft²
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