How do you calculate rafter or roof length from the pitch?
Short answer. Sloped length equals the horizontal run times the pitch multiplier, which is √(rise² + 144) ÷ 12. A 14 foot run at 8/12 (multiplier 1.202) gives about 16.8 feet of roof length from the wall line to the ridge, before adding the overhang.
The formula
Length = run × √(rise² + 144) ÷ 12
Or use the Pythagorean theorem with real numbers: length = √(run² + rise²), where rise = run × pitch ÷ 12.
Worked example: 28 foot wide gable at 8/12
- Run is half the width: 14 feet.
- Multiplier for 8/12: 1.202.
- Length to the ridge line: 14 × 1.202 = 16.83 feet.
- Add a 1.5 foot overhang (measured level): 1.5 × 1.202 = 1.80 feet.
- Total sloped length: about 18.6 feet, so framers would buy 20 foot stock.
Quick multipliers
- 4/12: 1.054
- 5/12: 1.083
- 6/12: 1.118
- 7/12: 1.158
- 8/12: 1.202
- 9/12: 1.250
- 10/12: 1.302
- 12/12: 1.414
Framing details
- Framers subtract half the ridge board thickness, measured level, from the run before calculating.
- Rafter tails and plumb cuts add their own small adjustments.
- Trusses come engineered, so no rafter math is needed for them.
Double check by measuring an existing rafter in the attic if you can; real framing sometimes differs a little from plans.
For roofing material
Sloped length tells you how many shingle courses fit from eave to ridge and how long underlayment runs are. For full roof area, multiply plan area by the same factor. See how roofers measure a roof and roof anatomy explained.