Free tool
Roof pitch calculator: rise, run and angle
Convert between rise and run, pitch in 12, degrees and percent grade, and turn a horizontal run into a length along the slope. Rise and run can be in any unit, as long as they match.
Any unit, as long as rise and run match.
From the wall line to below the ridge, in any unit.
Pitch
6 in 12
26.57° · 50% grade · 1 in 2 · slope factor 1.118
Geometry only. It converts the measurements you enter; it does not say what pitch a roof or a roofing product needs, size rafters, or replace a framing layout. The slope length is before overhang, ridge allowance and cuts.
The arithmetic, in full
Pitch from rise and run. Pitch in 12 = rise ÷ run × 12. A rise of 6 over a run of 12 is 6 in 12, which is 50% grade and 1 in 2.
Angle. Angle = arctan(rise ÷ run). 6 in 12 is 26.57°; 45° is 12 in 12.
Metric. A 250 mm rise over 1000 mm of run is 3 in 12, or 14.04°.
Length along the slope. Slope length = run × √(1 + (rise ÷ run)²). At 4 in 12 the factor is 1.0541, so a 14 ft horizontal run is 14.757 ft along the slope, before overhang and cuts.
What each input means
- Rise
- Vertical height gained, measured with a level and tape, in any unit.
- Run
- Horizontal distance for that rise, in the same unit as the rise. It must be greater than zero.
- Pitch in 12
- Rise per 12 of run, the North American way of stating pitch.
- Angle
- From horizontal, from 0 up to but not including 90 degrees.
- Horizontal run for slope length
- Optional. The horizontal distance you want converted into a length along the roof, in any unit; the answer comes back in that unit.
Frequently asked questions
- How do I calculate roof pitch?
- Measure the rise (vertical) over a known run (horizontal), in the same unit, and scale it to a run of 12. A roof that rises 6 in over 12 in of run is a 6 in 12 pitch. In metric, a 250 mm rise over 1000 mm of run is the same ratio as 3 in 12.
- How do I convert pitch to degrees?
- The angle is the arctangent of rise ÷ run. A 6 in 12 pitch is arctan(0.5) = 26.57°. 12 in 12 is exactly 45°. Going the other way, rise per 12 = 12 × tan(angle).
- What is the slope factor?
- The length along the roof for one unit of horizontal run: √(1 + (rise ÷ run)²). Multiply a horizontal run by it to get the length along the slope. It is geometry only: overhangs, the ridge allowance and plumb cuts still have to be added or taken off.
- What pitch does my roofing need?
- That is set by the roofing manufacturer and the building code, not by this calculator. Shingles, metal and low-slope membranes each have minimum slopes and underlayment rules. Check the product's installation instructions.
- Can I measure pitch from the attic or a ladder?
- Yes, if you measure a true vertical rise over a true horizontal run. A level and a tape over 12 in of run is the usual method. Measuring along the roof surface instead of horizontally gives the wrong number, and the calculator cannot tell the difference.
Getting it into a priced estimate
Use the slope length to measure the roof area for sheathing and roofing, then price those lines on the estimate. The plywood calculator takes the sloped dimensions directly.
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