Smalian's Formula - Metric Multi-Log Volume Calculator

Smalian's Formula - Metric Multi-Log Volume Calculato. AI generated image

This calculator uses Smalian's formula to estimate the volume of multiple logs in cubic metres (m³) and also converts each result to cubic feet (ft³).

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

Prefer imperial measurements? Try the Smalian's Formula - Multi-Log Calculator - Imperial.

More useful forestry calculators:

Smalian's Formula - Metric Multi-Log Volume Calculator

# Length (m) Small End DIB (cm) Large End DIB (cm) Cubic Metres Cubic Feet Remove
Total Volume : 0 m³ / 0 ft³

Calculation History


Calculator

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

Results

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


Accurate diameter and length measurements ensure reliable volumes for inventory, transportation planning, and sales calculations.

Smalian's Formula - Metric Multi-Log Volume Calculator

General Formula

Smalian's formula (metric) for a single log's volume is given by:

\[ V \;=\; \frac{\pi}{80000} \,\bigl(D_{s}^{2} + D_{l}^{2}\bigr)\,L \]

where:

  • \(L\) = length of the log in metres (m)
  • \(D_{s}\) = small-end diameter inside bark in centimetres (cm)
  • \(D_{l}\) = large-end diameter inside bark in centimetres (cm)

This formula yields volume \(V\) in cubic metres (m³).

Sample Calculation

Suppose we have a single log with these measurements:

  • \(L = 2.50\) m (length)
  • \(D_{s} = 30\) cm (small-end diameter)
  • \(D_{l} = 35\) cm (large-end diameter)

Compute step by step:

Step 1: Square the diameters (in cm):

\(D_{s}^{2} = 30^{2} = 900,\quad D_{l}^{2} = 35^{2} = 1225.\)

Step 2: Sum the squared diameters:

\(D_{s}^{2} + D_{l}^{2} = 900 + 1225 = 2125.\)

Step 3: Multiply by length \(L = 2.50\) m:

\(\bigl(D_{s}^{2} + D_{l}^{2}\bigr)\,L = 2125 \times 2.50 = 5312.5.\)

Step 4: Multiply by \(\pi/80000\):

\[ V = \frac{\pi}{80000} \times 5312.5 = \pi \times \frac{5312.5}{80000} = \pi \times 0.06640625 \approx 0.2087 \]

Numerically, \(0.06640625 \times \pi \approx 0.2087.\)

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

\[ V \approx 0.209 \;\text{m³}. \]

To convert this result to cubic feet (ft³), multiply by 35.3147:

\[ V_{\text{ft?}} = 0.2087 \times 35.3147 \approx 7.37 \;\text{ft³}. \]

Summary of sample result:

  • Volume in metric: \(0.209 \;\text{m³}\)
  • Equivalent in imperial: \(7.37 \;\text{ft³}\)
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