Forestry Prism Cruise & Basal Area Calculator
Enter variable-radius plot tallies by DBH class to estimate stand basal area, trees per acre, quadratic mean diameter, and spacing. The borderline tree section applies the selected BAF, slope, and distance reference to return an in-or-out call.
Basal area80
- Trees per acre
- 92.92
- Quadratic mean diameter
- 12.56
- Equivalent mean tree spacing
- 21.65
- Slope-corrected limiting distance
- 33.14
- Borderline tree decision
- In
Diameter class expansion
| DBH | In trees | Expansion factor | Trees per acre | Basal area |
|---|---|---|---|---|
| 8 | 10 | 28.65 | 28.65 | 10 |
| 12 | 30 | 12.73 | 38.2 | 30 |
| 16 | 30 | 7.16 | 21.49 | 30 |
| 20 | 10 | 4.58 | 4.58 | 10 |
Uses U.S. customary BAF equations and assumes all entered counts are in trees tallied across the sampled points.
How to use this calculator
- Choose the BAF stamped on the prism or angle gauge used for the cruise.
- Enter the number of points sampled and the total in-tree tally for each DBH class.
- Leave unused DBH classes at zero for both diameter and count.
- Enter the questionable tree DBH, slope percent, measured distance, and the point on the tree used for the distance.
- Read the stand estimates and compare the measured distance with the limiting distance for the borderline call.
How the prism cruise estimate is calculated
A variable-radius prism count gives each in tree the selected basal area factor. If the BAF is 10 and an average point has 8 in trees, the estimated basal area is 80 square feet per acre. This calculator applies that same rule to the total tally across all entered points.
The stand basal area formula is BA = B × (Σc ÷ P), where B is the BAF, c is the in-tree count in each diameter class, and P is the number of sampled points.
Trees per acre require DBH because small trees represent a smaller variable-radius plot than large trees. The individual tree basal area is g = 0.005454 × d², with d in inches. Each class contributes c × B ÷ g ÷ P trees per acre. The calculator sums those class contributions.
Quadratic mean diameter is then calculated from basal area and trees per acre with QMD = sqrt(BA ÷ (0.005454 × TPA)). Equivalent spacing is sqrt(43,560 ÷ TPA), which treats the estimated trees per acre as if they were evenly spaced on square acres.
Borderline trees and slope distance
The center-based plot-radius factor is R_c = 8.696 ÷ sqrt(B) feet per inch of DBH. If the field distance is measured to the nearest face at DBH, this calculator subtracts 1 ÷ 24 foot per inch to account for half the tree diameter. If the distance is measured to the tree center, it uses the center factor directly.
Slope distance is longer than horizontal distance on steep ground. The slope adjustment is K = sqrt(1 + (S ÷ 100)²), where S is percent slope. The limiting distance is L = DBH × R × K. A measured slope distance equal to or less than L is classified as in.
What moves the result most
The BAF and average count per point move basal area directly. DBH class choices matter most for trees per acre, QMD, and spacing because the expansion factor changes with diameter squared. Using broad diameter classes is acceptable for a quick stand summary, but narrower classes reduce the approximation.
What this calculator leaves out
The calculator does not estimate sampling error because it receives only total counts, not point-by-point tallies. It also does not estimate volume, merchantable height, defect, species composition, site productivity, or cruise design adequacy. Local inventory protocols may specify a different borderline-tree convention, so use the method required for the job.
Worked example
Suppose a BAF 10 prism cruise has 10 sampled points. The tallies are 10 trees at 8 inches DBH, 30 trees at 12 inches, 30 trees at 16 inches, and 10 trees at 20 inches. The total tally is 80 in trees, so basal area is 10 × (80 ÷ 10) = 80 square feet per acre.
The DBH-class expansion gives about 92.9 trees per acre. From 80 square feet per acre and 92.9 trees per acre, QMD is about 12.6 inches and equivalent spacing is about 21.7 feet.
For a 12-inch borderline tree on a 20% slope with the distance measured to the nearest face, the limiting slope distance is about 33.14 feet. A measured distance of 33 feet is classified as in because it does not exceed the limiting distance.
Common questions
What does basal area factor mean on a forestry prism?
The basal area factor is the number of square feet per acre represented by each in tree at a prism point. With BAF 10, an average of 8 in trees per point estimates 80 square feet of basal area per acre.
How is trees per acre calculated from a variable-radius plot?
Each tallied tree expands by BAF divided by that tree’s individual basal area. Because individual basal area increases with DBH squared, smaller trees have larger expansion factors than larger trees. The calculator applies that expansion to each DBH class and divides by the number of points.
Should prism distance be measured to the tree center or nearest face?
Many U.S. Forest Service field procedures measure borderline distance to the nearest face of the tree at DBH. Some teaching examples and instruments use a center-based limiting distance. Choose the reference that matches the field procedure used for the cruise.
How does slope change a prism plot limiting distance?
A slope distance is longer than the horizontal distance for the same tree. The calculator multiplies the limiting distance by the square root of 1 plus slope percent as a decimal squared. The adjustment is small on gentle slopes and more important on steep ground.
What is quadratic mean diameter?
Quadratic mean diameter is the diameter of the tree with average basal area. It is usually larger than arithmetic average DBH because basal area is proportional to diameter squared. Foresters often use QMD because it ties directly to basal area and trees per acre.
How many prism points should a forest cruise include?
There is no universal point count that fits every stand. Needed points depend on stand variability, the precision target, acreage, and the inventory protocol. This calculator summarizes the points entered; it does not decide whether the cruise design is adequate.