Roof Pitch Calculator
Converts roof pitch between the three ways it gets described — rise over run, degrees and ratio — and gives the slope factor you need for area calculations.
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The formula
angle = arctan(rise ÷ run) slope factor = √(1 + (rise ÷ run)²) rise per 12 = (rise ÷ run) × 12
The slope factor is Pythagoras applied to a unit triangle: a run of 1 and a rise of r gives a hypotenuse of √(1 + r²). That hypotenuse is how much roof sits above each unit of ground, which is why it converts footprint into real area.
What to watch out for
The same roof gets described three different ways depending on who is talking:
- Rise over run — "6/12". Standard in the US and on American plans.
- Degrees — the usual European convention, and what a pitch gauge or phone app reads.
- Ratio — "1:2", common on UK drawings.
The slope factor is the whole trick. A roof's footprint — the area it covers on the ground — is always smaller than its actual surface. Multiply by √(1 + (rise ÷ run)²) and you get the real area to cover.
At 6/12 that factor is 1.118, so a 100 m² footprint is 112 m² of roof. At 12/12 it is 1.414, and the difference is 41%. Ordering against the footprint is the most common way to run short of materials on a roof.
Pitch also decides what you can put on the roof. Most tiles have a minimum pitch below which wind-driven rain gets under them, typically 15–22.5°; slates want more; shingles generally need 4/12 or above unless detailed specially.
Frequently Asked Questions
What is a 6/12 roof pitch in degrees?
26.57°. The conversion is arctan(6 ÷ 12), and the slope factor that goes with it is 1.118.
How do I convert roof pitch to degrees?
Take the arctangent of rise divided by run. A 4/12 pitch is arctan(4/12) = 18.43°; a 12/12 pitch is 45°.
What is the slope factor and why do I need it?
It is the number that converts a flat footprint into the real sloping area — √(1 + (rise ÷ run)²). At 6/12 it is 1.118, so a 100 m² footprint is 112 m² of roof. Ordering materials against the footprint leaves you 12% short.
What is the minimum roof pitch?
It depends entirely on the covering. Standing-seam metal and single-ply membranes go almost flat; most interlocking tiles want 15–22.5°; plain tiles and slates want more; asphalt shingles generally need 4/12 or steeper unless specially detailed.