Roof pitch is the rise of a roof in inches for every 12 inches of level run. A roof that climbs 5 ft over 12 ft of run is a 5/12 pitch: 22.62°, a 41.7% grade, and every foot of level run becomes 1.0833 ft of roof surface. Enter any two measurements you have and the calculator gives the rest, including the multiplier roofers use to turn a floor plan into roof square footage.
How roof pitch is calculated
Pitch is a ratio, so the unit you measure in does not matter as long as rise and run use the same one. Divide the rise by the run and multiply by 12. The angle is the arctangent of rise over run, the grade is rise over run times 100, and the pitch multiplier is the length of the sloped side of a right triangle whose level side is 1.
Pitch = rise ÷ run × 12 · Angle = arctan(rise ÷ run) · Multiplier = √(1 + (rise ÷ run)²)
Worked example with the defaults: 5 ft of rise over 12 ft of run is 5 ÷ 12 = 0.4167. Times 12 gives 5/12. The arctangent of 0.4167 is 22.62°, the grade is 41.7%, and the multiplier is √(1 + 0.4167²) = 1.0833. A 1,344 sq ft footprint (house plus overhangs) under that roof has 1,344 × 1.0833 = 1,456 sq ft of roof.
Measuring pitch on a real roof
From the ground or the attic you rarely see the whole triangle, so measure a piece of it. Hold a level against the underside of a rafter (or on the shingles with a straight board), mark 12 inches along the level, and measure straight up from that mark to the rafter. That vertical distance in inches is the pitch. A 4 ft level gives a better average: measure the rise at 48 inches and divide by 4.
If you know the whole building, use span and height instead. The span is outside wall to outside wall, and the run of a gable is half of it. A 24 ft wide house whose ridge line sits 5 ft above the wall plates is 5 ÷ 12 × 12 = 5/12.
Lean-to and single slope roofs
A shed or lean-to roof has one plane, so the run is the full distance between the low and high walls, not half. Switch on "Single slope" and enter the width the roof crosses and how much higher the upper wall is. A 10 ft deep lean-to that rises 30 in has 30 ÷ 120 × 12 = 3/12.
Roof pitch from a picture or an angle
A phone level or angle finder laid on the roof gives degrees. Enter them in the angle tab: 26.57° is 6/12, 45° is 12/12. From a photo, pick one taken square to the gable end, draw a level line and a vertical line on the image, and measure both in pixels: the ratio is the same as on the roof. Photos taken at an angle distort the result, so check it on site before ordering.
Pitched roof calculator: roof angle, pitch and multiplier
A pitched roof is any roof that slopes, and there are three ways people describe the slope: as a pitch in x/12, as an angle in degrees, or as a percent grade. The calculator converts between all of them, so if you measured 30° with a phone level you get 6.93/12 and a multiplier of 1.1547. Use that multiplier on the footprint: 1,344 sq ft under a 30° roof is 1,344 × 1.1547 = 1,552 sq ft of roof, which is 15.52 roof squares.
| Roof angle | Pitch | Roof pitch multiplier | Roof for 1,344 sq ft of footprint |
|---|---|---|---|
| 20° | 4.37/12 | 1.0642 | 1,430 sq ft |
| 25° | 5.60/12 | 1.1034 | 1,483 sq ft |
| 30° | 6.93/12 | 1.1547 | 1,552 sq ft |
| 35° | 8.40/12 | 1.2208 | 1,641 sq ft |
| 40° | 10.07/12 | 1.3054 | 1,754 sq ft |
| 45° | 12.00/12 | 1.4142 | 1,901 sq ft |
Whether you call it the roof angle, the pitch or the pitch multiplier, the multiplier is 1 ÷ cos(angle): the length of roof for every 1 unit of level distance.
Pitch chart and multiplier
The pitch multiplier (also called the pitch factor) turns level measurements into sloped ones. The hip and valley factor does the same for a hip or valley rafter on a roof where both planes share the pitch. The full chart from 1/12 to 24/12 sits under the calculator; the common range is here.
| Pitch | Angle | Grade | Multiplier | Hip / valley |
|---|---|---|---|---|
| 3/12 | 14.04° | 25.0% | 1.0308 | 1.4361 |
| 4/12 | 18.43° | 33.3% | 1.0541 | 1.4530 |
| 5/12 | 22.62° | 41.7% | 1.0833 | 1.4743 |
| 6/12 | 26.57° | 50.0% | 1.1180 | 1.5000 |
| 8/12 | 33.69° | 66.7% | 1.2019 | 1.5635 |
| 10/12 | 39.81° | 83.3% | 1.3017 | 1.6415 |
| 12/12 | 45.00° | 100.0% | 1.4142 | 1.7321 |
HomeAdvisor's roofing cost guide calls slopes of 9/12 and more exceptionally steep, since they need extra safety gear and slow the crew down. That is where the roof replacement cost calculator adds a steep-roof charge.
Which roofing suits which pitch
The 2021 International Residential Code sets a minimum slope for every roof covering in Section R905:
- Asphalt shingles need at least 2/12 (R905.2.2), and from 2/12 up to 4/12 they need two layers of underlayment.
- Clay and concrete tile need 2½/12 (R905.3.2), again with double underlayment up to 4/12.
- Wood shingles and wood shakes need 3/12 (R905.7.2, R905.8.2), metal shingles 3/12 (R905.4.2), slate 4/12 (R905.6.2).
- Metal panels with lapped seams and no sealant need 3/12; with lap sealant ½ in 12; standing seam ¼ in 12 (R905.10.2).
Manufacturers can ask for more than the code. Metal Sales lists 3/12 as the minimum for its Classic Rib exposed-fastener panel and 3/12 over open framing (1/12 over a solid deck) for its Vertical Seam standing seam.
What to work out next
With the pitch in hand, the roofing calculator turns your house footprint into roof square feet, squares and a shingle list, and the shingle calculator goes straight from squares to bundles. Framing the roof yourself? The rafter calculator gives the rafter length and birdsmouth for this pitch, and the roof truss calculator counts and draws trusses. For a low pitch, compare panels in the metal roof calculator. To turn the roof area into a shingle order, use the roof square calculator.