Smalian's Formula - Imperial Log Volume Calculator
The Smalian's Formula - Imperial Log Volume Calculator estimates log volume using imperial units: length in feet and diameters in inches. This calculator applies Smalian's geometric formula for approximating log volume when both end diameters are known and uses the standard conversion to cubic meters for metric reference.
Smalian's formula is named after the German forestry scientist Heinrich Christian Smalian (1800-1875), who is credited with developing one of the earliest mathematical methods for estimating the volume of a log based on its end diameters and length.
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Smalian's Formula - Imperial
Calculator
- enter the length of the log in feet
- enter the small-end diameter in inches (inside bark)
- the large-end diameter in inches (inside bark)
Results
- the volume of the log in cubic feet
- the volume of the log in cubic metres
Smalian's Formula (Imperial - Feet and Inches)
\[ V_{ft^3} = 0.005454 \cdot \left( D_s^2 + D_l^2 \right) \cdot \frac{L}{2} \]
Where:
- \( D_s \) - Small-end diameter (inches, inside bark)
- \( D_l \) - Large-end diameter (inches, inside bark)
- \( L \) - Log length in feet
Metric Conversion
\[ V_{m^3} = V_{ft^3} \cdot 0.0283168 \]
Example Calculation
Small End = 12 in, Large End = 18 in, Length = 20 ft: \[ \begin{align*} V_{ft^3} &= 0.005454 \cdot (12^2 + 18^2) \cdot \frac{20}{2} \\\\ &= 0.005454 \cdot (144 + 324) \cdot 10 \\\\ &= 0.005454 \cdot 468 \cdot 10 \\\\ &= 25.54 \, \text{ft}^3 \end{align*} \] \[ V_{m^3} = 25.54 \cdot 0.0283168 = 0.723 \, \text{m}^3 \]
This tool is ideal for log scalers and forestry professionals working in imperial units.
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