# What is my roof pitch?

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.

- Page: https://www.acalculator.org/construction/roof-pitch-calculator
- JSON spec: https://www.acalculator.org/construction/roof-pitch-calculator.json
- Version: 8febc55ea8dd

## Default answer

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°.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| know | I know | Whether you know the rise and run, the pitch, or the angle. |
| rise | Rise | How far the roof goes up over the run. |
| run | Run | The horizontal distance the roof covers, from the wall to below the ridge. |
| pitch | Pitch (rise in 12) | The rise for every 12 units of run, such as 6 for a 6/12 roof. |
| angle | Angle | The angle of the roof above horizontal. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| pitch | Pitch | The rise for every 12 units of run: 12 × rise ÷ run. |
| angle | Angle | The angle above horizontal: arctan(rise ÷ run). |
| grade | Slope | The rise as a percent of the run. |
| rise | Rise | The rise over the run: run × rise ÷ run. |
| rafter | Rafter length | The sloped length over the run: √(rise² + run²), before any overhang. |
| factor | Slope factor | The rafter length for each unit of run: √(1 + (rise ÷ run)²). Multiply a plan area by it for the roof area. |

## Method

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

## Assumptions

- 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.

## Worked examples

1. know = rise-run, rise = 1.8288, run = 3.6576 gives pitch = 6, angle = 0.463648, grade = 50%, rafter = 4.089321, 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. know = rise-run, rise = 1.3716, run = 4.572 gives pitch = 3.6, grade = 30%, angle = 0.291457. Source: hand calculation in content.mdx: 12 × 4.5 ÷ 15 = 3.6; 30%; arctan(0.3) = 16.70°.
3. know = pitch, pitch = 2, run = 3.048 gives grade = 16.666667%, rise = 0.508, angle = 0.165149. 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. know = angle, angle = 0.785398, run = 2.4384 gives pitch = 12, rise = 2.4384, 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.

## FAQ

### 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.

## Sources

- International Code Council, International Residential Code 2021, R905.2.2 Slope: asphalt shingles on slopes of 2 units vertical in 12 units horizontal or greater. https://codes.iccsafe.org/s/IRC2021P3/chapter-9-roof-assemblies/IRC2021P3-Pt03-Ch09-SecR905.2.2