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Roof Rise, Run, Rafter & Pitch Geometry
Relate rise, horizontal run, geometric rafter length, angle, percentage slope and rise per 12 units of run.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
Rise 3 and run 4 give geometric rafter length 5, a 75% slope, and 9 units of rise per 12 units of run.
Rafter² = rise² + run²; slope = rise/run = tan(angle); x:12 rise = 12 × slope
Worked example
Enter these known values and leave the other values blank.
- Rise
- 3 m
- Run length
- 4 m
- Geometric rafter length
- 5 m
- Roof pitch
- 36.87 deg
- Slope percentage
- 75 %
- Rise per 12 units of run
- 9 :12
Assumptions and limitations
- Run is horizontal distance, not the sloped length. Rise is the vertical difference over that run.
- Rise and slope can be zero; run and rafter length must be positive. Angles are from zero up to, but not including, 90°.
- The hypotenuse is geometric length. Overhangs, ridge details, joints and cuts affect an actual rafter’s finished dimensions.
- This geometry does not determine rafter section size, structural capacity or roofing-system minimum slope.
- Arithmetic uses 64 significant decimal digits. Displayed results use the configured rounding.
Common questions
Is 9:12 pitch equal to 9% slope?
No. Nine units of rise per twelve of run is 9/12 = 75% slope.
References
Bookify accepts a horizontal zero-rise boundary while retaining positive run/rafter lengths, the upper angle bound and every captured geometric equation.
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