1. What is the Board Foot and Lumber Piece Calculator?
Definition: The Board Foot and Lumber Piece Calculator estimates the total board feet of a log using various log scaling rules and calculates the number of lumber pieces based on the desired lumber size and length, supporting multiple units (inches, feet, yards, centimeters, meters).
Purpose: This tool assists loggers, sawmill operators, and woodworkers in determining lumber yield from logs, enabling accurate material planning and cost estimation across different measurement units.
2. How Does the Calculator Work?
The calculator uses log scaling rules to estimate board feet and calculates lumber pieces with the following formulas:
\( D_{\text{in}} = D \times U_{\text{dim}} \text{ or } \frac{C \times U_{\text{dim}}}{\pi} \)
\( L_{\text{log, ft}} = \frac{L_{\text{log}} \times U_{\text{log}}}{12} \)
\( L_{\text{lumber, ft}} = \frac{L_{\text{lumber}} \times U_{\text{lumber}}}{12} \)
\( TBF = f(D_{\text{in}}, L_{\text{log, ft}}, \text{Rule}) \)
\( BF = \frac{T \times W \times L_{\text{lumber, ft}}}{12} \)
\( N = \left\lceil \frac{TBF}{BF} \right\rceil \)
Where:
- \( D \): Dimension input (diameter or circumference);
- \( D_{\text{in}} \): Diameter in inches;
- \( C \): Circumference;
- \( U_{\text{dim}} \): Dimension unit conversion factor (e.g., 1 for inches, 12 for feet);
- \( L_{\text{log}} \): Log length in selected unit;
- \( L_{\text{log, ft}} \): Log length in feet;
- \( U_{\text{log}} \): Log length unit conversion factor;
- \( L_{\text{lumber}} \): Lumber length in selected unit;
- \( L_{\text{lumber, ft}} \): Lumber length in feet;
- \( U_{\text{lumber}} \): Lumber length unit conversion factor;
- \( T \): Thickness in inches (actual, based on nominal size);
- \( W \): Width in inches (actual, based on nominal size);
- \( TBF \): Total board feet;
- \( BF \): Board feet per piece;
- \( N \): Number of pieces;
- \( f \): Log rule function (e.g., Doyle: \( \frac{(D_{\text{in}} - 4)^2 \times L_{\text{log, ft}}}{16} \)).
Unit Conversions:
- 1 inch = 1 inch
- 1 foot = 12 inches
- 1 yard = 36 inches
- 1 centimeter = 0.393701 inches
- 1 meter = 39.3701 inches
Log Rules:
- Champlain: \( TBF = 0.62832 \times (D_{\text{in}}^2 - D_{\text{in}}) \times \frac{L_{\text{log, ft}}}{12} \)
- Clements: \( TBF = 0.7854 \times (D_{\text{in}}^2 - 2D_{\text{in}}) \times \frac{L_{\text{log, ft}}}{16} \)
- British Columbia: \( TBF = 0.0476 \times (D_{\text{in}} - 1.5)^2 \times L_{\text{log, ft}} \)
- Brereton: \( TBF = 0.06545 \times D_{\text{in}}^2 \times L_{\text{log, ft}} \)
- Doyle: \( TBF = \frac{(D_{\text{in}} - 4)^2 \times L_{\text{log, ft}}}{16} \)
- Ontario: \( TBF = (0.55 \times D_{\text{in}}^2 - 1.2 \times D_{\text{in}}) \times \frac{L_{\text{log, ft}}}{12} \)
- Scribner: \( TBF = (0.0494 \times D_{\text{in}}^2 - 0.124 \times D_{\text{in}} - 0.269) \times L_{\text{log, ft}} \)
- Spaulding: \( TBF = (0.778 \times D_{\text{in}}^2 - 1.125 \times D_{\text{in}} - 13.482) \times \frac{L_{\text{log, ft}}}{16} \)
Steps:
- Select dimension input type (diameter or circumference), enter the dimension, and choose its unit.
- Enter log length, select its unit, and choose a log scaling rule.
- Enter lumber length, select its unit, and choose nominal lumber size.
- Convert dimension to inches: \( D_{\text{in}} = D \times U_{\text{dim}} \) or \( \frac{C \times U_{\text{dim}}}{\pi} \).
- Convert log and lumber lengths to feet: \( L_{\text{ft}} = \frac{L \times U}{12} \).
- Calculate total board feet using the selected log rule.
- Calculate board feet per piece: thickness times width times lumber length (in feet) divided by 12.
- Calculate number of pieces: ceiling of total board feet divided by board feet per piece.
- Display results to four decimal places, using scientific notation for values less than 0.0001.
3. Importance of the Board Foot Calculation
Calculating board feet from logs is essential for:
- Yield Estimation: Determines the lumber volume obtainable from a log.
- Cost Planning: Facilitates pricing and budgeting for logging and milling operations.
- Resource Management: Optimizes lumber production and inventory planning.
4. Using the Calculator
Example (Diameter in Meters, Doyle Rule): Calculate board feet and pieces for a log with a 0.508-meter diameter, 4.8768 meters long, using the Doyle rule, cut into 2x4 lumber (1 1/2 x 3 1/2 inches), 2.4384 meters long:
- Input: Dimension: 0.508 (diameter, meters); Log Length: 4.8768 (meters); Log Rule: Doyle; Lumber Length: 2.4384 (meters); Nominal Size: 2 x 4.
- Diameter: \( 0.508 \times 39.3701 \approx 20 \) inches.
- Log Length: \( \frac{4.8768 \times 39.3701}{12} \approx 16 \) feet.
- Lumber Length: \( \frac{2.4384 \times 39.3701}{12} \approx 8 \) feet.
- Total Board Feet: \( \frac{(20 - 4)^2 \times 16}{16} = 256.0000 \).
- Board Feet per Piece: \( \frac{1.5 \times 3.5 \times 8}{12} \approx 3.5000 \).
- Number of Pieces: \( \left\lceil \frac{256}{3.5} \right\rceil = 74 \).
- Result: Total Board Feet: 256.0000; Board Feet per Piece: 3.5000; Number of Pieces: 74.
Example (Circumference in Centimeters, Scribner Rule): Calculate board feet and pieces for a log with a 159.59 cm circumference, 365.76 cm long, using the Scribner rule, cut into 1x6 lumber (3/4 x 5 1/2 inches), 304.8 cm long:
- Input: Dimension: 159.59 (circumference, cm); Log Length: 365.76 (cm); Log Rule: Scribner; Lumber Length: 304.8 (cm); Nominal Size: 1 x 6.
- Diameter: \( \frac{159.59 \times 0.393701}{\pi} \approx 20 \) inches.
- Log Length: \( \frac{365.76 \times 0.393701}{12} \approx 12 \) feet.
- Lumber Length: \( \frac{304.8 \times 0.393701}{12} \approx 10 \) feet.
- Total Board Feet: \( (0.0494 \times 20^2 - 0.124 \times 20 - 0.269) \times 12 \approx 209.2440 \).
- Board Feet per Piece: \( \frac{0.75 \times 5.5 \times 10}{12} \approx 3.4375 \).
- Number of Pieces: \( \left\lceil \frac{209.2440}{3.4375} \right\rceil = 61 \).
- Result: Total Board Feet: 209.2440; Board Feet per Piece: 3.4375; Number of Pieces: 61.
5. Frequently Asked Questions (FAQ)
Q: What is a board foot?
A: A board foot is a unit of lumber volume, equal to 144 cubic inches (1 foot long, 1 foot wide, 1 inch thick).
Q: Why are different log rules used?
A: Log rules account for variations in sawing efficiency, log shape, and regional standards, providing different estimates of usable lumber.
Q: How are units converted?
A: All inputs are converted to inches (for diameter/circumference) or feet (for lengths) using standard conversion factors before calculations.
6. Commercial Standard Lumber Sizes Table Chart
| Nominal Size |
Actual Size |
Weight / Foot |
| 1 X 3 |
.75 X 2.5 |
0.47 |
| 1 X 4 |
.75 X 3.5 |
0.64 |
| 1 X 6 |
.75 X 5.5 |
1.00 |
| 1 X 8 |
.75 X 7.25 |
1.32 |
| 1 X 10 |
.75 X 9.25 |
1.69 |
| 1 X 12 |
.75 X 11.25 |
2.05 |
| 2 X 3 |
1.5 X 2.5 |
0.94 |
| 2 X 4 |
1.5 X 3.5 |
1.28 |
| 2 X 6 |
1.5 X 5.5 |
2.00 |
| 2 X 8 |
1.5 X 7.25 |
2.64 |
| 2 X 10 |
1.5 X 9.25 |
3.37 |
| 2 X 12 |
1.5 X 11.25 |
4.10 |
| 2 X 14 |
1.5 X 13.25 |
4.83 |
| 3 X 3 |
2.5 X 2.5 |
1.52 |
| 3 X 4 |
2.5 X 3.5 |
2.13 |
| 3 X 6 |
2.5 X 5.5 |
3.34 |
| 3 X 8 |
2.5 X 7.25 |
4.41 |
| 3 X 10 |
2.5 X 9.25 |
5.62 |
| 3 X 12 |
2.5 X 11.25 |
6.84 |
| 3 X 14 |
2.5 X 13.25 |
8.05 |
| 3 X 16 |
2.5 X 15.25 |
9.27 |
| 4 X 4 |
3.5 X 3.5 |
2.98 |
| 4 X 6 |
3.5 X 5.5 |
4.68 |
| 4 X 8 |
3.5 X 7.25 |
6.17 |
| 4 X 10 |
3.5 X 9.25 |
7.78 |
| 4 X 12 |
3.5 X 11.25 |
9.57 |
| 4 X 14 |
3.5 X 13.25 |
11.28 |
| 4 X 16 |
3.5 X 15.25 |
12.98 |
| 6 X 6 |
5.5 X 5.5 |
7.35 |
| 6 X 8 |
5.5 X 7.5 |
10.03 |
| 6 X 10 |
5.5 X 9.5 |
12.70 |
| 6 X 12 |
5.5 X 11.5 |
15.37 |
| 6 X 14 |
5.5 X 13.5 |
18.05 |
| 6 X 16 |
5.5 X 15.5 |
20.72 |
| 6 X 18 |
5.5 X 17.5 |
23.29 |
| 8 X 8 |
7.5 X 7.5 |
13.67 |
| 8 X 10 |
7.5 X 9.5 |
17.32 |
| 8 X 12 |
7.5 X 11.5 |
20.96 |
| 8 X 14 |
7.5 X 13.5 |
24.61 |
| 8 X 16 |
7.5 X 15.5 |
28.26 |
| 8 X 18 |
7.5 X 17.5 |
31.90 |
| 10 X 10 |
9.5 X 9.5 |
21.94 |
| 10 X 12 |
9.5 X 11.5 |
26.55 |
| 10 X 14 |
9.5 X 13.5 |
31.17 |
| 10 X 16 |
9.5 X 15.5 |
35.79 |
| 10 X 18 |
9.5 X 17.5 |
40.41 |
| 12 X 12 |
11.5 X 11.5 |
32.14 |
| 12 X 14 |
11.5 X 13.5 |
37.73 |
| 12 X 16 |
11.5 X 15.5 |
43.33 |
Board Foot Calculator for Lumber© - All Rights Reserved 2025
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