Roof Pitch Calculator
How do I calculate roof pitch?
A roof pitch calculator converts the rise and run of a roof into the numbers you need to order material and cut rafters. Enter the rise and the run and you get the pitch in x/12, the angle in degrees, the slope as a percentage, the rafter length and the pitch multiplier. Add the footprint of the house and the overhang and the calculator also gives the sloped roof area and the number of roofing squares to order. The run is the horizontal distance, never the distance along the sloping roof, so measure it level.
Calculate roof pitch
Enter a rise greater than 0.
Enter a run greater than 0.
Enter a footprint length greater than 0.
Enter a footprint width greater than 0.
Enter an overhang of 0 or more.
Enter your dimensions and click Calculate.
No result yet. Enter your dimensions and click Calculate.
The rafter length is the line length, not the end-to-end cut length. The overhang makes the finished rafter longer.
The calculator has three modes. Rise and Run is the default: enter the rise and the run and it works out the pitch, angle, slope, rafter length and multiplier. Pitch and Run takes a pitch in x/12, for example 6, and a run. Angle and Run takes an angle in degrees and a run. Every dimension has its own unit selector (in, ft, yd, cm, m). The optional roof area section takes the footprint length, footprint width and overhang (1 ft by default). When the footprint is entered, the calculator shows the sloped roof area and the roofing squares, rounded up to whole squares. When the footprint is blank, no area is shown. The formula used is shown directly under the result, so you can check the number.
What is roof pitch?
Roof pitch is the vertical rise of a roof for every 12 units of horizontal run, written as x/12. A 6/12 pitch rises 6 inches for every 12 inches of horizontal run. A 12/12 pitch rises 12 inches for every 12 inches of run, which is a 45 degree angle.
Strictly speaking, pitch is rise over span and slope is rise over run. The roofing industry uses the two words interchangeably, and this page follows that use, with pitch always written as x/12. The run is the horizontal distance from the outside of the wall to the centre of the ridge. For a symmetrical gable roof, the run is half the span. It is never the distance along the sloping roof surface. A common mistake is to measure the sloped rafter length and use it as the run, which gives a wrong pitch.
The rafter length this calculator gives is the line length, measured from the inside of the birdsmouth, parallel to the rafter edge. It is not the end-to-end cut length. The overhang makes the finished rafter longer, and rafters are commonly installed long and cut later. When you measure from the centre of the ridge beam, subtract half the ridge beam thickness, for example 3/4 in for a 1 1/2 in beam.
Building codes set minimum pitches for roofing materials. Under IRC R905.2.2, asphalt shingles may be used only on roof slopes of 2:12 or steeper, and on slopes from 2:12 up to 4:12 a double underlayment is required. Check local building codes for the minimum pitch for your roofing material and your area, since adopted codes and local amendments can differ.
How to calculate roof pitch
- Measure the run. Measure horizontally from the outside of the wall to the centre of the ridge. For a symmetrical gable, the run is half the span. Do not use the sloped rafter length. A simple way to measure on the roof is to hold a level horizontally, mark 12 in along it, and measure the vertical rise at that mark.
- Measure the rise. Measure vertically from the eave level to the ridge, in the same units as the run.
- Work out the pitch. Divide the rise by the run and multiply by 12. Pitch (x/12) = (rise / run) x 12.
- Work out the angle. Angle = arctan(rise / run). A 6/12 pitch is 26.57 degrees.
- Work out the rafter length. Rafter length = the square root of (rise squared + run squared). This is the line length, not the cut length.
- Work out the multiplier and the roof area. Pitch multiplier = the square root of (1 + (rise / run) squared). Multiply the footprint area, including the overhang, by the multiplier to get the sloped roof area. Divide by 100 to get roofing squares, and round up to whole squares.
Common roof pitches:
| Pitch | Angle | Slope | Pitch multiplier | Unit rafter length (per 12 in run) | Category |
|---|---|---|---|---|---|
| 3/12 | 14.04 deg | 25.0% | 1.031 | 12.37 in | Low pitch |
| 4/12 | 18.43 deg | 33.3% | 1.054 | 12.65 in | Conventional, lower end |
| 6/12 | 26.57 deg | 50.0% | 1.118 | 13.42 in | Conventional, most common US residential |
| 8/12 | 33.69 deg | 66.7% | 1.202 | 14.42 in | Conventional, upper end |
| 12/12 | 45.00 deg | 100.0% | 1.414 | 16.97 in | Steep |
A pitch of 6/12 or less is easily walkable. Above 7/12 a roof is considered non-walkable and needs extra equipment. In snow regions the minimum pitch is typically 6/12 or 7/12. The minimum pitch for any roof is 0.5/12, since even a flat roof needs that much slope for water to run off.
Roof pitch formula and worked example
Pitch (x/12): Pitch (x/12) = (rise / run) x 12.
Slope %: Slope % = (rise / run) x 100.
Angle: Angle = arctan(rise / run).
Rafter length: Rafter length = the square root of (rise squared + run squared).
Pitch multiplier: Pitch multiplier = the square root of (1 + (rise / run) squared), which is the same as rafter length divided by run.
Unit rafter length (per 12 in run): Unit rafter length = the square root of (144 + x squared) inches, where x is the pitch number.
Sloped roof area: Sloped roof area = footprint area including overhang x pitch multiplier.
Roofing squares: Roofing squares = sloped roof area / 100, rounded up to whole squares (1 square = 100 sq ft).
Worked Example
A 6/12 pitch, 12 ft run, house 40 x 30 ft with 1 ft overhang on all sides:
Pitch is 6/12. Rise = 12 x 0.5 = 6 ft. Angle = arctan(0.5) = 26.57 degrees. Slope = 50%.
Rafter length = sqrt(144 + 36) = sqrt(180) = 13.42 ft
This is the line length, before the overhang, not the cut length.
Pitch multiplier = the square root of 1.25 = 1.118. Check: 12 x 1.118 = 13.42 ft.
Footprint with overhang = 42 x 32 = 1,344 sq ft.
Sloped roof area = 1,344 x 1.118 = 1,503 sq ft
Roofing squares = 1,503 / 100 = 15.03 squares. Order 16 squares, rounded up to whole squares. No waste allowance is added in this arithmetic. Allow extra for cuts and waste and confirm the allowance with your supplier before ordering.
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Frequently asked questions
What is roof pitch?
Roof pitch is the vertical rise of a roof for every 12 inches of horizontal run, written as x/12. A 6/12 pitch rises 6 inches for every 12 inches of horizontal run.
How do you calculate roof pitch?
Measure the rise and the run in the same units. Pitch = rise divided by run, multiplied by 12. Angle = arctan(rise divided by run). Rafter length = the square root of rise squared plus run squared. For example, a rise of 6 inches and a run of 12 inches gives a 6/12 pitch, an angle of 26.57 degrees, and a rafter length of 13.42 inches per 12 inches of run.
What is the standard pitch for a roof?
There is no single standard pitch. US residential roofs are typically 4/12 to 9/12, and 6/12 is the most common pitch.
What is a 4/12 roof pitch?
A 4/12 pitch rises 4 inches for every 12 inches of horizontal run. Its angle is 18.43 degrees, its slope is 33.3 percent, and its pitch multiplier is 1.054.
What is the minimum roof pitch for snow?
In snow regions the minimum pitch is typically 6/12 or 7/12. Check local building codes for the minimum pitch in your area.
What roof pitch is walkable?
A pitch of 6/12 or less is easily walkable. Above 7/12 a roof is considered non-walkable and needs extra equipment.