Pitch, angle and slope
Roof pitch says how steep a roof is, written as how many inches it rises for every 12 inches it runs level: a 6/12 roof climbs 6 inches per foot. Builders, roofers and suppliers use pitch, while plans and some materials use the angle in degrees, so it helps to switch between them.
This roof pitch calculator converts a pitch to an angle and a percentage grade, finds the pitch from a measured rise and run or from an angle, and gives the rafter multiplier. Add the footprint of the roof and it estimates the sloped area in square feet and in roofing squares.
How to use it
- Choose From a pitch if you know it, From a rise and run to measure one, or From an angle.
- To measure, hold a level horizontally against the roof, mark 12 inches along it, and measure straight up to the roof surface. That number is the rise in 12.
- Optionally enter the footprint area the roof covers, overhangs included.
- Read the pitch, angle, grade and multiplier, and the roof area if you gave a footprint.
Measure from a ladder or the attic where you can work safely; never on a steep or wet roof.
The roof pitch formulas
pitch = rise ÷ run × 12
angle = arctan(pitch ÷ 12)
rafter multiplier = √(1 + (pitch ÷ 12)²)
sloped roof area = footprint × rafter multiplier; 1 roofing square = 100 sq ftThe multiplier is how much longer the sloped surface is than the level run beneath it. Multiply a rafter run or a footprint area by it to get the real length or area along the slope.
Worked example: a 6/12 roof over 1,500 sq ft
- Angle: arctan(6 ÷ 12) = 26.57°
- Grade: 6 ÷ 12 = 50%
- Rafter multiplier: √(1 + 0.25) = 1.118
- Roof area: 1,500 × 1.118 = 1,677 sq ft, or 16.77 squares
A 6/12 roof is 26.57° steep, and the roof over a 1,500 sq ft footprint is about 1,677 sq ft. Order roofing materials with extra for waste, ridges and valleys; your supplier can advise how much.
Common pitches
| Pitch | Angle | Multiplier |
|---|---|---|
| 3/12 | 14.04° | 1.0308 |
| 4/12 | 18.43° | 1.0541 |
| 5/12 | 22.62° | 1.0833 |
| 6/12 | 26.57° | 1.118 |
| 7/12 | 30.26° | 1.1577 |
| 8/12 | 33.69° | 1.2019 |
| 9/12 | 36.87° | 1.25 |
| 10/12 | 39.81° | 1.3017 |
| 12/12 | 45° | 1.4142 |
A 12/12 pitch is a 45° roof. Low pitches shed water slowly and need materials made for them; roofing makers state the lowest pitch each product suits.
Related tools
- For rafter lengths and cuts, see the rafter calculator.
- The slope calculator handles any rise and run as a slope or grade.
- For floor area under the roof, use the square footage calculator.
- For a roof with several slopes, find the footprint of each section and run them one at a time.
Frequently asked questions
How do I convert roof pitch to degrees?
Divide the rise by 12, then take the arctangent. A 6/12 pitch is arctan(0.5), which is 26.57°. A 4/12 pitch is about 18.43°, and a 12/12 pitch is exactly 45°. Enter any pitch above and the calculator shows the angle, the grade and the rafter multiplier.
How do I measure my roof pitch?
Hold a level horizontally with one end touching the roof surface, mark 12 inches along it, and measure straight up from that mark to the roof. The measurement in inches is your pitch in 12. You can also measure on a rafter in the attic, which is safer.
What is a rafter multiplier?
It is how much longer a sloped length is than the level run under it. For a 6/12 roof it is 1.118, so a rafter over a 10 foot run is about 11.18 feet long before overhangs. The same number turns a flat footprint into the sloped roof area.
What is a roofing square?
A roofing square is 100 square feet of roof surface. Shingles and other roofing are often priced and sold by the square. A 1,677 square foot roof is 16.77 squares, before adding extra for waste, ridges and valleys. The calculator shows squares whenever you give a footprint.
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