Smalian's Formula - Imperial Multi-Log Volume Calculator

Smalian's Formula - Imperial Multi-Log Volume Calculator. Image is AI generated

The Smalian's Formula - Imperial Multi-Log Calculator estimates the volume of multiple logs using imperial units: length in feet and diameters in inches. Based on Smalian's method for calculating the volume of a truncated cylinder, this calculator adds up each log's volume and returns a running total in cubic feet, with optional export to CSV and copy-to-clipboard functionality.

How to Use:

Click Add Log to enter multiple logs.
Input the length and the two diameters of each log.
Click Calculate to view board feet per log and total.
Use Copy History or Download CSV to save your results.

Looking for metric units? Switch to the Smalian's Formula - Multi-Log Calculator - Metric.

Additional Forestry Calculators:

Smalian's Formula - Imperial Multi-Log Volume Calculator

# Length (ft) Small End DIB (in) Large End DIB (in) Cubic Feet Cubic Meters Remove
Total Volume: 0 ft3 / 0 m3

Calculation History


Calculator

  1. enter the length of the log in feet
  2. enter the small-end diameter in inches (inside bark)
  3. the large-end diameter in inches (inside bark)

Results

  1. Cubic Feet Volume: calculated per log using Smalian's Formula
  2. the cubic metres volume of the log converted from the cubic foot result
  3. History: Each entry is shown in a live text for copy or download
  4. Total Board Feet: Automatically summed and displayed

Smalian's Formula - Imperial Multi-Log Volume Calculator

General Formula

Smalian's formula (imperial) for a single log's volume (in cubic feet) is given by:

\[ V \;=\; \frac{\pi}{1152}\,\bigl(D_{s}^{2} + D_{l}^{2}\bigr)\,L \]

where:

  • \(L\) = length of the log in feet (ft)
  • \(D_{s}\) = small-end diameter inside bark in inches (in)
  • \(D_{l}\) = large-end diameter inside bark in inches (in)

This formula yields volume \(V\) in cubic feet (ft³). The factor \(\tfrac{\pi}{1152}\) comes from averaging cross-sectional areas and converting square inches to square feet.

Sample Calculation

Suppose we have a single log with these measurements:

  • \(L = 8\) ft (length)
  • \(D_{s} = 10\) in (small-end diameter)
  • \(D_{l} = 12\) in (large-end diameter)

Compute step by step:

Step 1: Square the diameters (in inches):

\(D_{s}^{2} = 10^{2} = 100,\quad D_{l}^{2} = 12^{2} = 144.\)

Step 2: Sum the squared diameters:

\(D_{s}^{2} + D_{l}^{2} = 100 + 144 = 244.\)

Step 3: Multiply by length \(L = 8\) ft:

\(\bigl(D_{s}^{2} + D_{l}^{2}\bigr)\,L = 244 \times 8 = 1952.\)

Step 4: Multiply by \(\tfrac{\pi}{1152}\):

\[ V = \frac{\pi}{1152} \times 1952 = \pi \times \frac{1952}{1152} = \pi \times 1.6944\ldots \approx 1.6944 \times 3.1416 = 5.3228\ldots \]

Numerically, \(1.6944 \times \pi \approx 5.323\).

Step 5: Final volume (rounded to three decimals):

\[ V \approx 5.323 \;\text{ft³}. \]

Summary of sample result:

  • Volume in imperial: \(5.323 \;\text{ft³}\)

This tool is ideal for log scalers and forestry professionals working in imperial units.

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