Roof Pitch Calculator

A roof pitch says how steep a roof is. It is the rise (how far the roof goes up) divided by the run (how far it goes across, measured level). On a roof that is the same on both sides, the run is half the span. Everything else, from the angle to the rafter length, comes from that one number.

The formula

slope = rise ÷ run (run = span ÷ 2)
pitch = slope × 12, written x/12 · percent = slope × 100 · ratio 1 : x, where x = run ÷ rise
angle = arctan(slope) · slope from an angle = tan(angle)
pitch multiplier = √(1 + slope²)
rafter = (run − half the ridge board + level overhang) × multiplier
ridge height = run × slope · gable end = span × rise ÷ 2
hip or valley rafter = run × √(2 + slope²) · hip pitch = slope ÷ √2
birdsmouth heel = seat cut × slope · height above plate = rafter depth × multiplier − heel
roof area = footprint (with overhangs) × multiplier · squares = sq ft ÷ 100

Worked example

A roof spans 30 ft from wall to wall and rises 7 ft 6 in from the top of the walls to the ridge. The run is half the span: 30 ÷ 2 = 15 ft. The slope is 7.5 ÷ 15 = 0.5, so the pitch is 0.5 × 12 = 6/12. The angle is arctan(0.5) = 26.57°, the grade is 0.5 × 100 = 50%, the ratio is 1 : (15 ÷ 7.5) = 1 : 2, and the rise is 7.5 ÷ 30 = 1/4 of the span. The pitch multiplier is √(1 + 0.5²) = √1.25 = 1.118. Each rafter from the wall line to the ridge centre is 15 × 1.118034 = 16.77 ft, about 16 ft 9 1/4 in.

With the Advanced figures: a 1½ in ridge board takes ¾ in off the run, and a 12 in level overhang adds 12 in, so the rafter covers 15 ft − ¾ in + 1 ft = 191.25 in of run. Times 1.118034 that is 213.82 in, about 17 ft 9 13/16 in, so you buy an 18 ft board. A 3½ in seat cut gives a heel of 3.5 × 0.5 = 1¾ in. A 7¼ in rafter measures 7.25 × 1.118034 = 8.11 in plumb, so the height above the plate is 8.11 − 1.75 = 6.36 in. A roof 42 ft by 32 ft seen from above is 1,344 sq ft flat and 1,344 × 1.118034 = 1,502.64 sq ft sloped, or 15.03 squares.

Pitch, angle and multiplier chart

The chart in the calculator lists 2/12 to 18/12. A few more: 1/12 is 4.76°, 3½/12 is 16.26°, 7½/12 is 32.01° and 24/12 is 63.43°. Common house roofs sit between 4/12 and 9/12.

How to measure a roof pitch

• 12-inch method: in the loft, hold a level flat with one end touching the underside of a rafter. Mark 12 in along the level, then measure straight up from the mark to the rafter. If it is 6 in, the pitch is 6/12. In metric, use a 1 m level and measure in mm: 500 mm up over 1,000 mm across is 1 : 2, the same as 6/12. Pick Rise and run above.
• Phone level: most phones have a level or measure app. Lay the phone along a rafter or the gable trim and read the angle, then pick Angle. Check it on two or three rafters.
• From the ground: at a gable end, measure the span of the house and estimate the height of the ridge above the wall tops (count siding courses or bricks). Pick Rise and span.
• On the roof: only if it is safe. A level and tape on the shingles works the same as in the loft.

Minimum pitch by material

United States, International Residential Code (2021, chapter 9): asphalt shingles 2/12, with two layers of underlayment from 2/12 to under 4/12; clay and concrete tile 2½/12, with two layers of underlayment below 4/12; slate and wood shakes 4/12; wood shingles 3/12; metal standing seam ¼/12; lapped metal sheets ½/12 with sealant in the laps, or 3/12 without; built-up and single-ply membranes ¼/12. Typical UK maker figures: plain clay tiles 35°, interlocking concrete tiles about 22.5° (some down to 12.5°), natural slate about 20° and up, depending on the slate size and how exposed the roof is. These are typical figures to plan with, not checked against your local rules; the maker's figure for the product you buy always wins.

Plumb and seat cut angles follow the speed-square convention: set the square to the pitch angle (or the common number, e.g. 6) for the plumb cut; the seat cut is square to it. The one-third limit on the birdsmouth notch is a common rule of thumb, not a code figure. Board lengths are typical stock sizes (8 to 20 ft or 2.4 to 6.0 m).