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Roof Pitch Calculator

Enter the rise and run to get the roof angle, slope, pitch ratio and rafter length.

How it is calculated

Enter the vertical rise and the horizontal run in the same unit (the labels say metres, but the angle, slope and ratio come out the same in any unit). The tool computes angle = atan(rise ÷ run) in degrees, slope % = rise ÷ run × 100 and the x:12 pitch rise ÷ run × 12, the number of units the roof climbs for every 12 units of run. The rafter length is the hypotenuse, √(rise² + run²). Both values must be above zero, so a flat roof gives no result. The rafter is the sloping length from the wall line to the ridge only: overhang, ridge thickness and cuts are not added.

Worked example

A roof section that rises 2.1 m over a run of 4.5 m. The ratio rise ÷ run is 2.1 ÷ 4.5 = 0.4667. The angle is atan(0.4667) = 25.02°. The slope is 0.4667 × 100 = 46.67%. The x:12 pitch is 0.4667 × 12 = 5.60, so about 5.6:12. The rafter length is √(2.1² + 4.5²) = √(4.41 + 20.25) = √24.66 ≈ 4.97 m, before adding any overhang.

Try this example →

Common mistakes

  • Using the full span of the building as the run. For a symmetrical gable roof, the run is half the span, from the wall to the point below the ridge.
  • Measuring the sloping length instead of the vertical rise. The rise is straight up from the wall plate to the ridge, not along the rafter.
  • Mixing units, such as rise in centimetres and run in metres. The angle will then be wrong; use one unit for both.
  • Confusing slope percent with degrees. A 100% slope is 45 degrees, not 100, and 46.67% is only about 25 degrees.
  • Taking the rafter length as the cut length. The tool adds no eave overhang, ridge board or birdsmouth allowance, so lengthen it for the real rafter.

About this calculator

Roof pitch describes how steep a roof is, most commonly expressed in the US as an x:12 ratio — how many inches the roof rises for every 12 inches of horizontal run. From the rise and run, the roof angle is simply the arctangent of rise divided by run, the slope percentage is (rise ÷ run) × 100, and the rafter length for that section of roof comes straight from the Pythagorean theorem: the square root of rise squared plus run squared.

Roofers, carpenters and architects rely on these figures for very practical reasons: pitch determines which roofing materials are suitable (very low-slope roofs need different membrane systems than steep-slope shingle roofs), rafter length drives lumber ordering and framing layout, and steeper pitches shed rain and snow more effectively, which is why building codes in snowy regions often specify a minimum pitch.

Enter the rise and run of your roof section, and the calculator returns the roof angle, slope percentage, the x:12 pitch ratio and the rafter length.

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