acalculator

What is my roof pitch?

Enter the rise and run of the roof, or a pitch such as 6/12, or an angle. See the pitch, the angle, the percent slope, the rafter length and the slope factor.

Your numbers

Units
I know
Pitch
6

The roof pitch is 6 in 12, an angle of 26.57°.

Angle
26.57°
Slope
50%
Rise
6 ft 0 in
Rafter length
13.416 ft
Slope factor
1.118

Pitch: 6. The roof pitch is 6 in 12, an angle of 26.57°.

How to calculate

Computes a roof’s pitch as rise in 12, its angle, its percent slope, the rafter length and the slope factor, from the rise and run, from a pitch, or from an angle.

Example with the default inputs (I know Rise and run, Rise 6 ft 0 in, Run 12 ft 0 in): The roof pitch is 6 in 12, an angle of 26.57°.

Method: slope = rise ÷ run (or pitch ÷ 12, or tan angle); pitch = 12 × slope; angle = arctan(slope); percent = 100 × slope; rafter = run × √(1 + slope²)

  • The run is the horizontal distance, not the sloped length. For a simple gable it is half the building’s width.
  • The rafter length is the line from the wall plate to the ridge over the run. It adds nothing for overhang, ridge board thickness or cuts.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. I know Rise and run, Rise 6 ft, Run 12 ft 0 in gives Pitch (rise in 12) 6, Angle 26.57°, Slope 50%, Rafter length 13.416 ft, Slope factor 1.118034.Source: hand calculation in content.mdx: 12 × 6 ÷ 12 = 6; arctan(0.5) = 26.57°; √(6² + 12²) = 13.416 ft; √1.25 = 1.1180
  2. I know Rise and run, Rise 4.5 ft, Run 15 ft 0 in gives Pitch (rise in 12) 3.6, Slope 30%, Angle 16.7°.Source: hand calculation in content.mdx: 12 × 4.5 ÷ 15 = 3.6; 30%; arctan(0.3) = 16.70°
  3. I know Pitch, Pitch (rise in 12) 2, Run 10 ft 0 in gives Slope 16.666667%, Rise 1.667 ft, Angle 9.46°.Source: IRC 2021 R905.2.2 gives 2:12 as the minimum slope for asphalt shingles; hand calculation in content.mdx: 2 ÷ 12 = 16.67%, arctan(1/6) = 9.46°, rise 10 × 2/12 = 1.667 ft
  4. I know Angle, Angle 45°, Run 8 ft 0 in gives Pitch (rise in 12) 12, Rise 8 ft, Slope factor 1.414214.Source: hand calculation in content.mdx: tan 45° = 1, so the pitch is 12/12, the rise equals the run, and the factor is √2

How it works

Every result comes from the slope, the rise for each unit of run:

  • From rise and run: slope = rise ÷ run.
  • From a pitch: slope = pitch ÷ 12.
  • From an angle: slope = tan(angle).

Then:

  • Pitch = 12 × slope, the inches of rise for every 12 inches of run (a 6/12 roof has pitch 6).
  • Angle = arctan(slope), in degrees above horizontal.
  • Percent slope = 100 × slope.
  • Rise = slope × run.
  • Rafter length = √(rise² + run²) = run × √(1 + slope²). This is the sloped length over the run, with nothing added for an overhang or ridge board.
  • Slope factor = √(1 + slope²).

The run is the horizontal distance, never the length along the slope.

Worked examples by hand

Rise 6 ft over a 12 ft run. Slope 6 ÷ 12 = 0.5. Pitch 12 × 0.5 = 6/12. Angle arctan(0.5) = 26.57°. Percent slope 50%. Rafter √(6² + 12²) = √180 = 13.416 ft. Slope factor √1.25 = 1.1180.

Rise 4.5 ft over a 15 ft run. Slope 0.3, so pitch 12 × 0.3 = 3.6/12, 30%, and arctan(0.3) = 16.70°.

A 2/12 roof over a 10 ft run (the IRC minimum for asphalt shingles). Slope 2 ÷ 12 = 0.1667, so 16.67% and arctan(0.1667) = 9.46°. The rise is 10 × 2 ÷ 12 = 1.667 ft.

A 45° roof over an 8 ft run. tan 45° = 1, so the pitch is 12/12, the rise is 8 ft, and the slope factor is √2 = 1.4142.

Other questions people ask

How do I calculate roof pitch?

Divide the rise by the run and multiply by 12. A roof that rises 6 ft over a 12 ft run has a pitch of 12 × 6 ÷ 12 = 6, written 6/12 or 6:12: it rises 6 inches for every 12 inches across.

How do I convert roof pitch to degrees?

Take the arctangent of pitch ÷ 12. A 6/12 roof is arctan(0.5) = 26.57°. A 12/12 roof is 45°.

What is the lowest pitch for asphalt shingles?

The International Residential Code (IRC 2021, R905.2.2) allows asphalt shingles on slopes of 2 units vertical in 12 horizontal (2:12) or more. From 2:12 up to 4:12 it requires a double layer of underlayment.

How do I find the run of my roof?

The run is the horizontal distance from the outside of the wall to the point under the ridge. On a simple gable roof it is half the width of the building. It is not the length along the slope.

What is the slope factor used for?

The slope factor is the rafter length per unit of run, √(1 + (rise ÷ run)²). Multiply the flat plan area of a roof by it to get the sloped roof area. For a 6/12 roof it is 1.118.

How do I measure pitch from the attic?

Hold a level horizontal against a rafter, mark 12 in along the level, and measure straight up from that mark to the underside of the rafter. That measurement in inches is the pitch.