Roof Pitch Calculator

What roof pitch means

Roof pitch is how many inches a roof rises for every 12 inches it runs level. A 6/12 roof climbs 6 inches over each foot measured horizontally. Builders in the US quote pitch this way because it matches the framing square: the 12 is always the run, and only the rise changes.

You need the pitch to order roofing — every product has a minimum slope it can be installed on — to work out rafter lengths, and to turn a house's footprint into real roof area. A steeper roof has more surface than its footprint, so the same house at 12/12 needs about 26% more shingles than at 6/12 (multiplier 1.414 vs 1.118).

The calculator accepts any run, not just 12. If you can only hold a 24 inch level against the roof, enter the rise over 24 inches and the pitch is scaled to 12 for you. In reverse mode, type the angle from a phone inclinometer or angle finder and it converts the angle to pitch.

The roof pitch formulas

Pitch = rise ÷ run × 12, written as x/12.
Angle = arctan(rise ÷ run), in degrees.
Angle → pitch (reverse) = tan(angle) × 12.
Slope % = rise ÷ run × 100.
Rafter multiplier = √(rise² + run²) ÷ run. Multiply a level run by it to get the sloped length.

Pitch, angle and slope percent are the same number expressed three ways, so you can switch between them with no loss. The rafter multiplier is what the "length per foot of run" row on a framing square's rafter table gives you, divided by 12.

Worked example: a 7/12 garage roof

In the attic, a level held against the underside of a rafter, with a mark at 12 inches, shows7 inches from the mark up to the rafter. The garage is 28 ft wide with a gable roof, so each rafter runs 14 ft level from wall plate to ridge, and the eaves overhang 18 inches (1.5 ft).

Pitch = 7 ÷ 12 × 12 = 7/12.
Angle = arctan(7 ÷ 12) = 30.26°.
Slope = 7 ÷ 12 × 100 = 58.3%.
Multiplier = √(7² + 12²) ÷ 12 = √193 ÷ 12 = 1.158. That matches the framing-square figure the US Navy's carpentry manual gives: a 7-inch rise makes a rafter 13.89 inches long per foot of run (13.89 ÷ 12 = 1.158).
Rafter length = (14 + 1.5) × 1.1577 = 17.94 ft before the ridge-board allowance. The rafter length calculator takes that off and gives cut angles.

At 7/12, every common roof covering is above its code minimum, and asphalt shingles need only single underlayment.

Load this example in the calculator

Roof pitch to degrees: 1/12 to 12/12

These values are computed from the formulas above, not typed in. For pitches up to 24/12, plus hip and valley factors, use the printable roof pitch chart.

Pitch	Angle	Slope	Rafter multiplier
1/12	4.76°	8.3%	1.003
2/12	9.46°	16.7%	1.014
3/12	14.04°	25%	1.031
4/12	18.43°	33.3%	1.054
5/12	22.62°	41.7%	1.083
6/12	26.57°	50%	1.118
7/12	30.26°	58.3%	1.158
8/12	33.69°	66.7%	1.202
9/12	36.87°	75%	1.25
10/12	39.81°	83.3%	1.302
11/12	42.51°	91.7%	1.357
12/12	45°	100%	1.414

Which roofing works at your pitch

The International Residential Code sets a minimum slope for each roof covering. Under the 2021 IRC, asphalt shingles need at least 2/12, with double underlayment below 4/12. Clay and concrete tile need 2½/12, wood shingles and shakes 3/12, and slate 4/12. Standing-seam metal and membrane roofs can go down to ¼/12. The calculator checks your pitch against these minimums. Theminimum roof pitch guide lists every covering with its code section. Local codes and manufacturers can be stricter, so treat these as the floor.

Common mistakes

Measuring along the slope. The 12 inches must be level. Measuring 12 inches along the roof surface gives a pitch that's too low, and the error grows on steeper roofs.
Confusing slope percent with angle. 50% is 26.57°, not 45°, and 100% is 45°.
Applying the multiplier to the full span. On a gable, each rafter covers half the span. Multiply the run (half span) plus the overhang, not the building width.
Rounding too early. A roof that measures 6½/12 isn't 6/12. The difference is about 2% more area and over 1° of angle, enough to matter when you order materials or cut rafters. Keep the decimal and round only at the end.
Skipping the ridge allowance. Rafter lengths from a multiplier run to the centre of the ridge. With a ridge board, take half its thickness off each rafter. See the rafter length calculator.

Need the roof's area next? The roofing squares calculator uses the same pitch to turn a footprint into squares and bundles.

Frequently asked questions

How do I measure roof pitch?

Hold a level against the underside of a rafter in the attic (or on the roof surface), mark 12 inches along the level, then measure straight up from that mark to the rafter or roof deck. That vertical measurement is the rise per 12, so 6 inches means a 6/12 pitch. Our guide to measuring roof pitch covers the attic, roof and phone-app methods.

How many degrees is a 4/12 or 6/12 roof pitch?

A 4/12 pitch is 18.43° and a 6/12 pitch is 26.57°. Angle = arctan(rise ÷ 12). The full table above lists 1/12 to 12/12, and the printable roof pitch chart goes to 24/12.

Can you put shingles on a 3/12 roof?

The 2021 International Residential Code (R905.2.2) allows asphalt shingles on slopes of 2/12 or more, but requires double underlayment from 2/12 up to 4/12. So a 3/12 roof can be shingled with two layers of underlayment. Check the shingle maker's instructions and your local code too — they can be stricter.

What is the difference between roof pitch, slope and angle?

They describe the same steepness three ways. Pitch is rise per 12 units of run (6/12). Slope percent is rise ÷ run × 100 (50%). Angle is the angle from horizontal in degrees (26.57°). A 100% slope is 45°, not 90°.

What is a rafter multiplier?

It is how much longer the sloped rafter is than its level run: √(rise² + 12²) ÷ 12. For 6/12 it is 1.118, so a rafter that covers 10 ft of level run is 11.18 ft long before the overhang and ridge allowance. The rafter length calculator does the full cut length.

Roofing allowed at this pitch (2021 IRC minimums)

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