Enter the DBH and the PRF into the calculator to determine the limiting distance for the tree line.
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Limiting Distance in Variable-Radius Sampling
The limiting distance is the maximum allowable distance from plot center to the center of a tree for that tree to be counted as in on a variable-radius plot. This calculation is most often used for borderline trees when cruising timber with a prism or angle gauge.
Core Formula
LD = DBH \times PRF
- LD = limiting distance
- DBH = diameter at breast height
- PRF = plot radius factor
DBH is typically measured at 4.5 ft above ground in U.S. forestry or 1.3 m in metric forestry. In practice, a larger tree diameter or a larger PRF produces a larger limiting distance.
Decision Rule for Borderline Trees
\text{Tree is IN if } D \le LDHere, D is the measured distance from plot center to the center of the tree. If the measured distance is greater than the limiting distance, the tree is out.
How to Calculate Limiting Distance
- Measure the tree’s DBH.
- Identify the correct PRF for your sampling setup.
- Multiply DBH by PRF.
- Compare the result to the measured tree distance from plot center.
Compatible Unit Pairings
The calculator works as long as the DBH unit and PRF unit match correctly.
| DBH Unit | PRF Unit | Resulting Limiting Distance |
|---|---|---|
| inches | ft/in | feet |
| centimeters | m/cm | meters |
| centimeters | cm/cm | centimeters |
| meters | m/m | meters |
DBH is most commonly recorded in inches or centimeters, but mathematically any consistent unit pair can be used.
Example
If a tree has a DBH of 12.5 in and the PRF is 2.5 ft/in, then:
LD = 12.5 \times 2.5 = 31.25 \text{ ft}A tree center at 31.25 ft is exactly on the limiting boundary. At 31 ft the tree is in; at 32 ft the tree is out.
Finding PRF from BAF
If your inventory design gives you a basal area factor (BAF) instead of a PRF, you can convert BAF to PRF first.
PRF_{\text{imperial}} = \frac{8.696}{\sqrt{BAF}}PRF_{\text{metric}} = \frac{0.5}{\sqrt{BAF}}Quick Imperial PRF Reference
| BAF | PRF (ft/in) | 10 in Tree LD | 20 in Tree LD |
|---|---|---|---|
| 5 | 3.889 | 38.89 ft | 77.78 ft |
| 10 | 2.750 | 27.50 ft | 55.00 ft |
| 20 | 1.944 | 19.44 ft | 38.88 ft |
| 40 | 1.375 | 13.75 ft | 27.50 ft |
Quick Metric PRF Reference
| BAF | PRF (m/cm) | 20 cm Tree LD | 30 cm Tree LD |
|---|---|---|---|
| 1 | 0.500 | 10.00 m | 15.00 m |
| 4 | 0.250 | 5.00 m | 7.50 m |
| 10 | 0.158 | 3.16 m | 4.74 m |
| 20 | 0.112 | 2.24 m | 3.36 m |
Common Field Errors
- Mixing unit systems: inches should be paired with ft/in, while centimeters should be paired with m/cm or cm/cm.
- Measuring to the wrong point: limiting distance is generally checked against the distance from plot center to the tree center, not to the bark face.
- Using circumference instead of DBH: the formula requires diameter, not trunk circumference.
- Using slope distance when horizontal distance is required: follow your cruise standard.
- Entering invalid values: DBH and PRF should both be positive.
Why the Calculation Matters
Accurate limiting-distance checks make variable-radius sampling more consistent by classifying borderline trees the same way every time. That improves downstream estimates for basal area, stand density, stocking, and timber volume.
