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Roof Pitch Calculator

Find your roof pitch angle and ratio.

How it is calculated

Roof pitch compares how far the roof rises with how far it runs horizontally. The tool computes the angle as angle = arctan(rise ÷ run) in degrees, the ratio as rise:run (both rounded to whole numbers for the label), and a rafter length multiplier √(rise² + run²) ÷ run. Rise and run must use the same unit, such as inches or centimetres, and the run must be above zero while the rise cannot be negative. Multiply the horizontal run of your roof by the multiplier to get the sloped rafter length along the roof surface. The multiplier does not include overhang, ridge board thickness or cutting allowances.

Worked example

Take a roof that rises 6 units for every 12 units of run, a common 6:12 pitch. Angle: arctan(6 ÷ 12) = arctan(0.5), which is 26.57 °. The ratio is shown as 6:12. Multiplier: √(6² + 12²) ÷ 12 = √180 ÷ 12 = 13.416 ÷ 12 = 1.1180. A half-span of 4 m therefore needs a rafter about 4 × 1.118 = 4.47 m long, before overhang.

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Common mistakes

  • Mixing units for rise and run, such as rise in inches and run in feet. The ratio and angle will be wrong; use one unit for both.
  • Entering the full roof span as the run. For a symmetric gable roof the run is half the span, from wall to ridge.
  • Using the rise over the rafter length instead of the horizontal run. Pitch is measured against the horizontal, not along the slope.
  • Treating the degrees as a percentage grade. A 6:12 pitch is 26.57 °, but its slope grade is 50%.
  • Entering decimals and expecting them in the label. The ratio text rounds to whole numbers, while the angle and multiplier use the exact values.

About this calculator

This calculator converts a roof's rise and run into its pitch ratio (e.g. 6:12), angle in degrees, and rafter length multiplier — the pitch ratio expresses how many inches the roof rises for every 12 inches of horizontal run, the standard way roofing is specified in the US.

Roofers and contractors use it to order the right amount of roofing material (steeper pitches need more material per square foot of footprint) and to select fasteners and shingles rated for that slope, while DIYers building a shed or extension use it to figure out rafter lengths before cutting lumber.

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Comments (1)

  • Editorial team

    The ratio label simply echoes the rise and run you type, rounded to whole numbers, so entering 3 and 6 shows 3:6 rather than 6:12. For the familiar form, type 12 as the run and the rise per 12 as the rise. Note that the angle and multiplier stay exact even when the label rounds. Which pitch are you working with, a low shed roof or a steeper gable?

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