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Rise / RunPitch · Angle · RafterFree

Roof Pitch
Calculator

Roof pitch is the rise over a 12-unit run. Enter the rise and run to get the pitch as x:12, the angle in degrees, percent slope, the roof-area multiplier, and optional rafter length.

Who it's for: architects, builders, roofers, and homeowners who need a quick pitch read — the angle, slope, and how much extra roof area the slope adds — before ordering materials at the pre-construction stage or sizing rafters.

Pitch = rise : run
Pitch (x:12) = (rise / run) × 12. Angle = arctan(rise / run). Slope multiplier = √((rise/run)² + 1) — multiply plan (footprint) area by this to get true sloped roof area. Rafter length = horizontal run × slope multiplier.
Common pitches
PitchAngleMultiplier
3:1214.0°1.031
4:1218.4°1.054
6:1226.6°1.118
9:1236.9°1.250
12:1245.0°1.414
Pitch Calculator
Pitch · angle · slope · rafter

How to use this calculator

1
Enter the rise
The vertical height the roof gains, in any unit. For a roof that climbs 6 inches, enter 6.
2
Enter the run
The horizontal distance over which that rise occurs, in the same unit as the rise. Use 12 to read the pitch directly in x:12 notation.
3
Add a horizontal run for rafter (optional)
Type the horizontal span a rafter covers to get its sloped length. Leave blank if you only need the pitch.
4
Read the pitch, angle, and slope
See the pitch as x:12, the roof angle in degrees, the percent slope, and the Low slope / Standard / Steep label.
5
Use the slope multiplier for area
Multiply the building footprint area by the slope multiplier to get the true sloped roof area for a materials takeoff.

The formula

Roof pitch relates a vertical rise to a fixed 12-unit horizontal run; from it flow four companion values used in design and materials ordering.

Pitch (x:12) = (rise ÷ run) × 12
Angle = arctan(rise ÷ run), in degrees
Percent slope = (rise ÷ run) × 100
Slope multiplier = √((rise ÷ run)² + 1)
Rafter length = horizontal run × slope multiplier

rise = vertical height gained (any unit)
run = horizontal distance over which that rise occurs (same unit as rise)
The slope multiplier converts a plan (footprint) area to the actual sloped roof surface area.

Worked example

Example
With a 6-unit rise over a 12-unit run, the pitch is 6 : 12: a roof angle of 26.6°, a 50% slope, and a slope multiplier of 1.1180 (labeled Standard). Over a 5,000 mm horizontal run the rafter length is 5,590.2 mm (5,000 × 1.1180). Multiply the footprint area by 1.1180 to get the true sloped roof area for materials.

When this estimate will be off

  • Assumes a simple gable or shed roof — hip, gambrel, and mansard roofs have multiple pitch sections that each need a separate calculation.
  • Rise and run must be in the same unit. Mixing feet and inches without converting first gives a wrong pitch and wrong rafter length.
  • The rafter result is the straight-line length along the slope only. It does not include overhangs, fascia extension, or ridge board offset — add those before ordering lumber.
  • Curved or barrel-vault roofs have no constant pitch. Measure at several points and use the steepest section when sizing waterproofing or ordering materials.

Frequently asked questions

A common mistake: Assumes a simple gable or shed roof — hip, gambrel, and mansard roofs have multiple pitch sections that each need a separate calculation.

Roof pitch is the steepness of a roof, written as rise over run: the vertical rise for every 12 units of horizontal run. A 6:12 pitch climbs 6 inches for every 12 inches across. Rise and run must use the same unit. Pitch drives drainage, material choice, and how much roof area a footprint actually covers.

Take the arctangent of rise divided by run, then read it in degrees. For a 6:12 pitch, arctan(6 / 12) = arctan(0.5) = 26.6°. A 12:12 pitch equals exactly 45°, and 4:12 works out to about 18.4°. This calculator runs that conversion automatically once you enter the rise and run.

The x:12 notation fixes the run at 12 and reports the rise over that span. A 4:12 roof rises 4 units for every 12 units of horizontal travel, and 9:12 rises 9. Twelve is the convention because it matches inches per foot, so framers can read pitch straight off a framing square.

Low-slope roofs sit below about 18°, around 3:12 or shallower, and usually need membrane or sealed systems because shingles can leak at shallow angles. Standard pitched roofs run roughly 18° to 45° (about 4:12 to 12:12). Anything steeper than 45°, above 12:12, is a steep slope. This calculator labels each range.

Sources

  • IRC 2021 R905 — minimum slope requirements by roofing material type (e.g. asphalt shingles: 2:12 minimum; low-slope membrane: below 2:12)

This free Roof Pitch Calculator is built and maintained by DataDrivenAEC, using the relevant codes and standards. It does not substitute for professional judgment.