How it works
Smalian’s formula treats a log as a solid between two circular ends and averages their areas: cubic volume = (small-end area + large-end area) ÷ 2 × length. The area of a circle in square feet from a diameter in inches is 0.005454 × D².
It is simple and widely used for scaling, but it tends to overestimate the volume of a log that tapers strongly, because a real log is closer to a paraboloid. Measure long or tapered logs in shorter sections.
Worked example
A 16 ft log with a 12 in small end and a 16 in large end:
- Small-end area = 0.005454 × 12² = 0.785 ft²; large-end area = 0.005454 × 16² = 1.396 ft²
- Volume = (0.785 + 1.396) ÷ 2 × 16 ft = 17.45 ft³
- Total for 1 = 17.45 ft³
| Input | Value |
|---|---|
| Small-end diameter | 12 in |
| Large-end diameter | 16 in |
| Log length | 16 ft |
| Number of similar logs | 1 |
| Result | Value |
|---|---|
| Total volume | 17.45 ft³ |
| Volume of one log | 17.45 ft³ |
| Small-end area | 0.785 ft² |
| Large-end area | 1.396 ft² |
Assumptions and limits
- Circular ends and diameters measured inside bark; use the average of two perpendicular readings for an oval end.
- Smalian overestimates volume for strongly tapered or short-butted logs.
- Cubic volume is not the same as board feet; use the log scale calculator for board-foot rules.
Common questions
What is Smalian’s formula?
Cubic volume equals the average of the two end areas times the length.
Why 0.005454?
It is π ÷ 4 ÷ 144, which turns a diameter in inches into an area in square feet.
How accurate is it?
Good when the taper is under about 30%; it overestimates volume as taper increases. Use shorter sections for tapered logs.
How do I get board feet?
Use a log rule such as Doyle or International 1/4 inch in the log scale calculator.
Sources
- Smalian’s formula for log volume, as given in forest mensuration references and the BC Ministry of Forests scaling manual (V = (B + b) ÷ 2 × L).
- Area of a circle: π ÷ 4 × D²; 0.005454 converts inches to square feet.
- Read them: BC Ministry of Forests: Smalian’s formula (scaling manual)
Updated 2026-09-30