Rafter Length Calculator

This rafter length calculator determines the total length of a roof rafter based on the building width, overhang, ridgeboard thickness, and roof pitch. The tool accepts mixed number and decimal inputs for accurate calculations in both feet and inches.

Calculator

1. enter the width of the building in feet and inches
2. the roof overhang in inches
3. the ridge board thickness in inches
4. roof pitch as a rise-over-run ratio

Results

1. the roof angle in degrees
2. the slope multiplier for calculating rafter length
3. the corresponding factor for hip and valley rafters
4. the rafter length in decimal feet
5. the rafter length in standard feet and fractional inches format
6. the total rafter length in inches

Rafter Length Calculation - Formulas and Example

\( \textbf{Formulas} \) 1. \( \text{Half Span} \): \[ \text{Half Span} = \frac{W}{2} \text{ (converted to feet)} \] 2. \( \text{Adjusted Overhang} \): \[ \text{Adjusted Overhang} = \frac{O}{12} \text{ (converted to feet)} \] 3. \( \text{Adjusted Ridgeboard} \): \[ \text{Adjusted Ridgeboard} = \frac{R}{2} \div 12 \text{ (converted to feet)} \] 4. \( \text{Slope Factor} \): \[ S = \frac{\sqrt{P^2 + 12^2}}{12} \] 5. \( \text{Rafter Length} \): \[ \text{Rafter Length} = \left( \frac{W}{2} + \frac{O}{12} - \frac{R}{2} \div 12 \right) \times S \] \( \textbf{Example Calculation} \) \( \text{Given Inputs:} \) - \( W = 20 \) feet \( = 240 \) inches - \( O = 16 \) inches - \( R = 1.5 \) inches - \( P = 6 \) (6:12 roof pitch) \( \text{Conversions:} \) \[ \text{Half Span} = \frac{240}{2} = 10 \text{ feet} \] \[ \text{Adjusted Overhang} = \frac{16}{12} = 1.33 \text{ feet} \] \[ \text{Adjusted Ridgeboard} = \frac{1.5}{2} = 0.75 \text{ inches} = \frac{0.75}{12} \text{ feet} = 0.0625 \text{ feet} \] \( \text{Calculate the Slope Factor:} \) \[ S = \frac{\sqrt{6^2 + 12^2}}{12} = \frac{\sqrt{36 + 144}}{12} = \frac{\sqrt{180}}{12} \approx 1.118 \] \( \text{Compute the Rafter Length:} \) \[ \text{Rafter Length} = \left( 10 + 1.33 - 0.0625 \right) \times 1.118 \] \[ = (11.2675) \times 1.118 \] \[ = 12.60 \text{ feet} \] \( \text{Convert to Feet and Inches:} \) \[ 12.60 \text{ feet} = 12 \text{ feet} + (0.60 \times 12) \text{ inches} \] \[ = 12 \text{ feet } 7.214 \text{ inches} \] \[ \approx 12 \text{ feet } 7\frac{3}{16} \text{ inches} \] \( \textbf{Final Result:} \) The rafter length is 12 feet 7 3/16 inches.

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