Roof Pitch Calculator

Enter a rise and run and get the pitch in x-in-12, the angle in degrees, the grade percent, the slope factor, and the rafter length — drawn to scale, in both unit systems.

Inputs
in
in
Results update as you type — no submit
ResultsLIVE
Roof pitch
6/12
= 26.6° · 50% grade · slope factor 1.118
Angle26.6°
Grade50%
Slope factor1.118
Rafter (over this run)13.4 in (34.1 cm)
Formula
pitch = 6 ÷ 12 × 12 = 6/12
angle = arctan(6 ÷ 12) = 26.6° · grade = 50%
slope = √(6² + 12²) ÷ 12 = 1.118 · rafter = 13.4 in
Diagram — roof triangleNTS
26.6°12 in6 in6/12 · RAFTER 13.4 INRISE / RUN · ROOF TRIANGLE

Roof pitch is just the steepness of the slope, written as rise over run. The run is fixed at `12` — think of it as `12` inches of horizontal travel — and the rise is how many inches the roof climbs over that run. A roof that goes up `6` inches for every `12` inches across is a `6/12` pitch. That single ratio is all you need; every other way of describing the slope comes straight out of it with basic trigonometry.

The angle in degrees is the arctangent of rise divided by run. The grade, the same percentage a road sign uses, is rise divided by run times `100`. The slope factor — the multiplier that turns flat footprint area into real roof area — is the length of the sloped face per unit of run, or the square root of rise squared plus run squared, divided by run. The rafter length is the hypotenuse of that same triangle: the straight-line distance from the top of the wall to the ridge over the run you entered.

To measure your own pitch, hold a level horizontally against the roof or a rafter, mark `12` inches along it, and measure straight down from that mark to the roof surface. That vertical drop in inches is your rise. Enter it with a run of `12` and the calculator does the rest. If you are working from a known half-span and total rise instead, enter those directly — the ratio comes out the same.

Worked example
Rise `6 in` · run `12 in`
pitch = `6 ÷ 12 × 12` = `6/12`
angle = `arctan(6 ÷ 12)` = `26.6°`
grade = `6 ÷ 12 × 100` = `50%`
slope factor = `√(6² + 12²) ÷ 12` = `1.118`
rafter over this run = `√(6² + 12²)` = `13.4 in`
Measure it with a level and a tape. Hold the level flat against the underside of a rafter or on top of the roof, mark 12 inches, and measure down to the surface at that mark. If the drop is 6 inches, you have a 6/12 roof. Most houses land between 4/12 and 9/12.
SOURCESRight-triangle trigonometry · published roof pitch / angle / slope-factor chart
Estimates for planning only — verify before purchase