Roof Pitch Calculator

A roof pitch calculator finds the steepness of a roof from two measurements: rise and run. It reports the pitch as a ratio (such as 6:12), the roof angle in degrees, and the slope length of the roof surface. Builders, roofers, and homeowners use roof pitch to choose materials, order the right amount of them, and plan drainage.

What is roof pitch?

Roof pitch is a measure of how steep a roof is. It compares rise, the vertical height a roof gains, to run, the horizontal distance it covers. In North America, pitch is usually written as X:12, meaning the roof rises X inches for every 12 inches of run. A 6:12 roof rises 6 inches for every 12 inches it runs horizontally.

How to calculate roof pitch

Pitch formula

$\text{Pitch} = \frac{\text{Rise}}{\text{Run}} \times 12$

Divide the rise by the run, then multiply by 12. The result is written as a ratio out of 12.

Angle formula

$\text{Angle} = \tan^{-1}\left(\frac{\text{Rise}}{\text{Run}}\right)$

The angle in degrees is the arctangent (inverse tangent) of rise divided by run.

Slope length formula

$\text{Slope Length} = \sqrt{\text{Rise}^2 + \text{Run}^2}$

Slope length, also called rafter length, is the distance along the roof surface from eave to ridge. It comes from the Pythagorean theorem, since rise and run form the two short sides of a right triangle and the slope is the long side.

Special cases

A flat roof has a rise of 0. Its pitch is 0:12, its angle is 0 degrees, and its slope length equals the run. A vertical wall has a run of 0. Its pitch is written as ∞:12 (infinite), its angle is 90 degrees, and its slope length equals the rise.

Example: calculating a 4:12 roof

A roof rises 4 inches for every 12 inches of run.

Pitch: (4 ÷ 12) × 12 = 4:12
Angle: arctan(4 ÷ 12) = 18.4°
Slope length: √(4² + 12²) = √160 = 12.6 inches of slope for every 12 inches of run

Example: calculating a 9:12 roof

A steeper roof rises 9 inches for every 12 inches of run.

Pitch: (9 ÷ 12) × 12 = 9:12
Angle: arctan(9 ÷ 12) = 36.9°
Slope length: √(9² + 12²) = √225 = 15 inches of slope for every 12 inches of run

Common roof pitch ratios

Pitch	Angle	Description
2:12	9.5°	Low slope; common on porches and modern homes
4:12	18.4°	Low-to-moderate slope; many ranch homes
6:12	26.6°	Common on houses in temperate climates
9:12	36.9°	Steep; sheds snow and rain well
12:12	45.0°	Very steep, a 45-degree angle

Roof pitch and roofing materials

Roofing materials have minimum pitch requirements. Installing a material below its minimum can cause leaks and void its warranty.

Flat roofing membranes (EPDM, TPO): work on pitches as low as roughly 0.5:12 to 2:12
Metal roofing: many products allow pitches as low as 2:12 to 3:12
Asphalt shingles: usually need at least 4:12
Clay or concrete tile: usually need at least 4:12
Slate: usually needs at least 6:12

How to measure a roof's pitch

The rise and run of a roof can be measured in a few ways.

From inside the attic: measure the vertical distance from the top of a ceiling joist to the underside of a rafter, then measure the horizontal distance across the same span.
With a level and tape measure: hold a level flat against the roof surface, mark a point 12 inches out from the wall, then measure straight down from that point to the roof.
From building plans: roof plans often list the pitch directly as X:12.

Measuring a roof from a ladder or by walking on it is dangerous. A professional roofer can measure a roof safely when attic access is not available.

Other ways to express roof slope

Percentage slope is rise divided by run, multiplied by 100. A 4:12 pitch equals a 33.3% slope. Percentage slope is common for very low-slope commercial roofs. Degree angle, calculated the same way as above, is common in architectural drawings and outside North America. A 6:12 pitch equals a 26.6-degree angle.

Frequently asked questions

What is roof pitch?

Roof pitch is the steepness of a roof, expressed as the ratio of vertical rise to horizontal run. In the United States it is usually written as X:12, such as 6:12.

What is a "standard" roof pitch for a house?

Most houses in the United States have a pitch between 4:12 and 9:12. A 6:12 pitch is common on houses in temperate climates, but the right pitch depends on climate, architectural style, and local building codes.

What is the difference between roof pitch and roof slope?

The terms are often used interchangeably. Roof pitch usually refers to the X:12 ratio, while roof slope can also be expressed as a percentage or as a degree angle. All three describe the same steepness in different units.

How is rafter length different from roof pitch?

Rafter length, also called slope length, is the physical distance along the roof surface from the eave to the ridge. It depends on both the pitch and the size of the roof, and is found using the Pythagorean theorem.

What roof pitch works best in heavy snow?

A pitch of 6:12 or steeper is often recommended in regions with heavy snowfall, because steeper roofs shed snow more easily and carry less structural load from accumulated snow.

Can a roof's pitch be changed during a renovation?

Yes, but it changes the roof's structure and usually requires an engineer's review, a building permit, and possibly new framing. It is not a do-it-yourself project.

Roof Pitch Calculator - Slope, Angle & Rafter Length