Roof Pitch & Rafter Length Calculator

Roof pitch (x/12), angle and ridge rise from a building span, plus common rafter length including the eave overhang and ridge board.

For a gable roof the run of each rafter is half the span.
/12
Inches of rise per 12 in of horizontal run, e.g. 6 for a 6/12 roof.
Measured level, from the outside of the wall to the end of the rafter tail.
Half of it is deducted from each rafter’s run. 1½ in for a 2× ridge board; 0 if rafters meet tip to tip.
Common rafter length (incl. overhang)
14.46
Line length along the slope from the ridge board face to the tail. Buy the next longer stock length to allow for the plumb cut at the ridge.
Roof pitch
6/12
Roof angle
26.57
Ridge rise above wall plates
6.00
Rafter run (to ridge board face)
11.94
Pitch multiplier (slope length ÷ run)
1.118
Slope as a percentage
50.0 %
Notes
Steep roof (over 4/12 under OSHA 29 CFR 1926.500): use fall protection and roof brackets when working on it.

Estimate generated with SortedSums: https://sortedsums.com/roof-pitch-calculator/. For informational purposes only; verify before relying on it.

Estimate only. This tool is for informational and educational purposes. Results depend on your inputs and simplifying assumptions, and are not a substitute for professional engineering, design or financial advice. Always verify with a qualified professional and applicable codes before purchasing, building or making decisions.

How it’s calculated

Roof pitch is the rise in inches for every 12 in of horizontal run. A rafter is the hypotenuse of a right triangle whose legs are its run and rise, so its length is the run times the pitch multiplier √(1 + (pitch ÷ 12)²).

Run = span ÷ 2 − ridge thickness ÷ 2 Pitch multiplier = √(1 + (pitch ÷ 12)²) Rafter length = (run + overhang) × multiplier Angle = arctan(pitch ÷ 12) Ridge rise = (span ÷ 2) × pitch ÷ 12 Pitch from rise = rise ÷ (span ÷ 2) × 12

Example: a 24 ft span with a 6/12 pitch, 12 in overhang and a 1½ in ridge board. Run = 144 − 0.75 = 143.25 in. Multiplier = √(1 + 0.5²) = 1.1180. Rafter = (143.25 + 12) × 1.1180 = 173.58 in = 14.46 ft, so buy 16 ft stock. Angle = arctan(0.5) = 26.57°; ridge rise = 12 × 0.5 = 6 ft.

PitchAngleMultiplier
4/1218.43°1.0541
6/1226.57°1.1180
8/1233.69°1.2019
12/1245.00°1.4142

This gives geometry only. Rafter size and spacing depend on span, snow and wind loads; use the span tables in your local building code or an engineer.

Frequently asked questions

How do I convert roof pitch to degrees?

Take the arctangent of the pitch divided by 12. A 6/12 roof is arctan(0.5) = 26.57°; a 12/12 roof is 45°.

How long is a rafter for a 24 ft wide house with a 6/12 roof?

Each rafter runs about 12 ft horizontally; × 1.118 = 13.42 ft to the ridge line, or about 14.46 ft including a 12 in overhang and allowing for a 1½ in ridge board.

What is a low-slope roof?

OSHA defines a low-slope roof as one with a slope of 4 in 12 or less, and a steep roof as anything over 4 in 12. Asphalt shingles need at least 2 in 12.

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Sources

Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.

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