Free tool
Roof pitch calculator
Enter the rise and run, or the angle. Get the pitch, the angle in degrees and the pitch multiplier. Add the footprint to get the roof squares with waste.
Pitch
6/12
Angle
26.6°
Multiplier
1.118
One pitch over the whole roof. Roofs with mixed pitches need each section worked out on its own and added up.
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How the math works
Pitch
Pitch is how many inches the roof climbs for every 12 inches across. Pitch = 12 × rise ÷ run. A rise of 3 over a run of 6 is the same slope as 6 over 12, so it is a 6/12.
Angle
The angle is the arctangent of rise ÷ run. For 6/12 that is the arctangent of 0.5, about 26.6 degrees. Going the other way, pitch = 12 × tan(angle).
Pitch multiplier
A sloped roof has more surface than the flat ground it covers. The multiplier is the square root of 1 + (pitch ÷ 12)². For 6/12 that is the square root of 1.25, about 1.118: the roof is 11.8% bigger than its footprint.
Squares and waste
Roof area = footprint × multiplier. Squares = roof area ÷ 100. Then add waste for cuts and starter: squares × (1 + waste ÷ 100).
Worked example
A 2,000 sq ft footprint at 6/12: 2,000 × 1.118 = 2,236 sq ft of roof, which is 22.36 squares. With 10% waste, order about 24.60 squares.
Measure the footprint flat, including the overhangs, not just the walls. These are estimates for planning and quoting; confirm measurements before you order materials.
Roof pitch chart
Common pitches with their angle and multiplier.
| Pitch | Angle | Multiplier |
|---|---|---|
| 1/12 | 4.8° | 1.003 |
| 2/12 | 9.5° | 1.014 |
| 3/12 | 14.0° | 1.031 |
| 4/12 | 18.4° | 1.054 |
| 5/12 | 22.6° | 1.083 |
| 6/12 | 26.6° | 1.118 |
| 7/12 | 30.3° | 1.158 |
| 8/12 | 33.7° | 1.202 |
| 9/12 | 36.9° | 1.250 |
| 10/12 | 39.8° | 1.302 |
| 11/12 | 42.5° | 1.357 |
| 12/12 | 45.0° | 1.414 |
Questions
What does a 6/12 roof pitch mean?
The roof rises 6 inches for every 12 inches it runs across. That is about 26.6 degrees, and the roof surface is about 1.118 times the flat footprint.
How do I measure roof pitch?
From a ladder at the gable end, hold a level flat against the roof edge, mark 12 inches along it, and measure straight up from that mark to the roof. That number is the rise. An angle app on a phone laid on the rafter or the roof also works: enter the angle instead.
What is a roofing square?
100 square feet of roof surface. A roof with 2,236 square feet of surface is about 22.4 squares before waste.
How much waste should I add?
About 10% for a simple gable roof and 15% or more for a cut-up roof with hips, valleys and dormers. Check your supplier's and the shingle maker's guidance for the product you are ordering.
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