Hong Life CalculatorsUnderstanding the tree diameter calculator — concept and principle
Foresters, arborists and gardeners describe tree size by the diameter at breast height (DBH). Measuring around the trunk with a tape is easier than measuring across it, so this calculator converts a trunk circumference into diameter, radius and basal area in metric and imperial units.
How it is calculated
d = C ÷ π
Radius = d ÷ 2
Basal area = π × d² ÷ 4
- C is the circumference at breast height, entered in cm, inches, m or feet and converted to cm.
- Basal area is shown in m² (d in metres) and ft² (1 ft² = 0.09290304 m²).
- In US forestry, breast height is 4.5 ft (1.37 m) above the ground; follow your own inventory standard.
The principle
A trunk cross-section is close to a circle, and for any circle the circumference equals π times the diameter. Dividing the tape measurement by π (about 3.1416) therefore gives the diameter of a circle with the same perimeter. Basal area is the cross-sectional area of that circle. Foresters add up the basal areas of all trees on a plot to describe how densely a stand is stocked, because basal area relates closely to wood volume and competition for light.
Worked example
Default input: circumference 150 cm.
- Diameter = 150 ÷ π = 47.75 cm, shown as 47.7 cm.
- In inches: 47.75 ÷ 2.54 = 18.8 in.
- Radius = 47.75 ÷ 2 = 23.9 cm.
- Basal area = π × 0.4775² ÷ 4 = 0.179 m².
- In square feet: 0.17905 ÷ 0.0929 = 1.927 ft².
| Trunk circumference at breast height | Diameter (cm) |
|---|---|
| 37.5 | 11.9 |
| 75 | 23.9 |
| 112 | 35.8 |
| 150 | 47.7 |
| 188 | 59.7 |
| 225 | 71.6 |
| 300 | 95.5 |
How to read the result
DBH is used to classify trees (for example saplings, pole timber and sawtimber), estimate volume and biomass with species equations, decide tree protection measures and estimate age with growth factors. Basal area per hectare or per acre describes stand density: higher values mean a more crowded stand. Repeating the measurement at the same marked height over years shows the tree's growth rate.
Common mistakes
- Wrapping the tape at an angle instead of level around the trunk.
- Measuring over vines, loose bark or a branch swelling.
- Measuring at a different height each time.
- Treating a strongly oval trunk as round; a diameter tape and caliper may give different readings.
Frequently asked questions
What is a diameter tape?
A forestry tape marked in units of π, so you can read diameter directly when wrapping it around the trunk.
Where is breast height on a slope?
Usually measured from the uphill side of the trunk.
How do I measure a tree that forks below breast height?
Measure each stem separately as if it were its own tree, unless your standard says otherwise.
Why is basal area useful?
It sums tree sizes on a plot into one number that relates to wood volume and stand density.
Sources: Martin A. J., "What Is Basal Area?", University of Wisconsin–Madison, Forestry Facts No. 43, 1989 · Purdue Landscape Report, "How Old Is My Tree?" (Purdue Extension)