Roof Pitch Calculator
Enter rise and run, a known angle, or a pitch with the building span to get the roof pitch as an x:12 ratio, the slope angle in degrees, the grade as a percentage, the slope factor and the rafter length. Switch between imperial and metric units, and turn on the cost estimate to size and price the roof area.
Formula
Worked example
Rise 4 in over run 12 in: slope = 4 ÷ 12 = 0.333, so pitch = 4:12. Angle = atan(0.333) = 18.43°, grade = 33.3%, rafter = √(4² + 12²) = 12.65 in per 12 of run, and slope factor = √(0.333² + 1) = 1.0541, so 1,500 sq ft of footprint becomes about 1,581 sq ft of roof.
What roof pitch means
Roof pitch describes how steep a roof is. It is most often written as a ratio of vertical rise to a fixed horizontal run of 12, for example 4:12, which reads as four units of rise for every twelve units of run. The same steepness can be stated three other ways: the slope angle in degrees between the roof surface and the horizontal, the grade as a percentage (rise divided by run times 100), and the slope as a plain decimal. This calculator reports all of them, plus the rafter length, so you can match whatever a building plan, shingle warranty or framing square uses.
Four ways to enter the roof
Pick the mode that matches what you can measure. Rise and run is the classic field method: hold a level against the roof and measure the drop over a known horizontal distance. Roof angle lets you enter degrees directly, useful when you have a digital inclinometer or a plan that gives the angle. Pitch and building span is a reverse-solve mode: enter the x:12 pitch and the full width of the building, and the calculator takes the run as half the span (for a symmetric gable) and works out the rise, angle and rafter length for you. Imperial and metric unit switches keep inches or centimetres consistent across the rise, run and span.
Rafter length and the slope factor
A sloped roof always has more surface than the flat footprint it sits over, so ordering materials from the footprint alone leaves you short. The rafter length is the straight sloped distance from the wall to the ridge, found with the Pythagorean theorem as the square root of rise squared plus run squared. The slope factor, also called the roof pitch multiplier, is the rafter length divided by the run, or the square root of the slope squared plus one. Multiply the building footprint area by the slope factor to get the true roof area for shingles, underlayment or sheathing. A 4:12 roof has a factor of about 1.054, so it needs roughly five percent more material than the footprint suggests, while a steep 12:12 roof needs about 41 percent more.
Estimating roof area and cost
Turn on the area and cost estimate to size and price the job. Enter the roof footprint (the flat ground area the roof covers, length times width of the plan), a waste allowance for cuts, hips, valleys and overlap, and an installed price per square foot. The calculator multiplies the footprint by the slope factor to get the true roof area, adds the waste, and multiplies by your price for a planning total. Roofing material is often sold in squares of 100 square feet (asphalt shingle bundles cover about a third of a square each), so divide the area to order by 100 to count squares. The total is an estimate only: local prices, roof complexity and tear-off all move the real figure, so confirm against supplier quotes.
How to measure rise and run
The simplest field method uses a level and a tape. Hold a 12-inch level horizontally against the underside of a rafter or against the roof surface, level it, then measure straight down from the 12-inch mark to the roof. That vertical distance is the rise for a run of 12, so it is already the x in x:12. You can measure over any run as long as the rise is measured over the same horizontal distance; the calculator normalizes whatever you enter to the standard per-12 form. For safety, you can also measure the pitch from inside the attic against a rafter rather than on the roof itself.
Common roof pitches
| Pitch (x:12) | Angle | Grade | Slope factor |
|---|---|---|---|
| 1:12 | 4.76° | 8.3% | 1.0035 |
| 3:12 | 14.04° | 25.0% | 1.0308 |
| 4:12 | 18.43° | 33.3% | 1.0541 |
| 6:12 | 26.57° | 50.0% | 1.1180 |
| 9:12 | 36.87° | 75.0% | 1.2500 |
| 12:12 | 45.00° | 100.0% | 1.4142 |
Slope angle, grade and slope factor for standard pitches.
Frequently asked questions
What is a good roof pitch?
Most homes use a conventional pitch between 4:12 and 9:12, which sheds water and snow well and accepts standard asphalt shingles. Below about 2:12 a roof is considered low-slope and generally needs a membrane system instead of shingles, while pitches above 9:12 are steep and harder and costlier to work on.
How do I convert roof pitch to degrees?
Divide the rise by the run to get the slope, then take the arctangent (inverse tangent) of that slope. For a 6:12 pitch the slope is 6 ÷ 12 = 0.5, and atan(0.5) is about 26.57 degrees. This calculator does the conversion automatically in both directions.
How do I find the rafter length?
The rafter (line) length is the straight sloped distance from the wall to the ridge. By the Pythagorean theorem it equals the square root of the rise squared plus the run squared. Enter rise and run, or a pitch and the building span, and the calculator returns the rafter length along with the pitch and angle. This is the line length, not including overhang, ridge board thickness or the birdsmouth cut.
What is the slope factor used for?
The slope factor, or roof pitch multiplier, converts the flat footprint area of a building into the actual sloped roof area. Multiply your footprint (length times width) by the slope factor to size shingles, underlayment and decking. It equals the square root of the slope squared plus one, which is the same as the rafter length divided by the run.
How do I estimate roofing material cost?
Turn on the area and cost estimate, enter your roof footprint, a waste allowance (10 to 15% is typical) and an installed price per square foot. The calculator multiplies the footprint by the slope factor for true roof area, adds the waste, and multiplies by your price. It is a planning figure: local prices, roof complexity and tear-off costs vary, so confirm with quotes.