What Is the Roof Pitch Calculator?
The Roof Pitch Calculator converts two simple measurements, rise and run, into every common way of describing a roof’s slope. It gives the pitch in the x/12 format used by North American builders, the angle in degrees, the slope as a percentage, and the multiplier that converts a roof’s footprint into its true surface area.
Pitch affects more than appearance. It decides which roofing materials are allowed, how quickly water and snow shed, how much attic space sits under the roof, and how much material the roof needs. It also affects labor cost, because steep roofs require more safety equipment and take longer to work on.
How the Calculator Works
Pitch is a ratio. It compares how far the roof rises vertically to how far it runs horizontally. The calculator divides the rise by the run to get that ratio, then expresses it in several forms.
To get the standard pitch, it scales the ratio so that the run equals 12 inches. A rise of 3 inches over a run of 6 inches is the same slope as 6 inches over 12, so both are a 6/12 pitch.
The angle is the arctangent of the ratio. The percentage is the ratio multiplied by 100. The area multiplier is the length of the sloped side of the triangle formed by the rise and run when the run is 1.
The Roof Pitch Formula
Pitch = (Rise ÷ Run) × 12, written as x/12
Angle = arctan(Rise ÷ Run)
Slope % = (Rise ÷ Run) × 100
Area multiplier = √(1 + (Rise ÷ Run)²)
Pitch and slope are not quite the same word
In everyday use, pitch and slope are interchangeable. Strictly, slope is rise over run, and pitch is rise over the full span of the roof. A 6/12 slope on a symmetrical gable is a 1/4 pitch in the older definition. Almost everyone now says pitch and means the x/12 figure, and that is what this calculator reports.
Step-by-Step Explanation
- Measure a horizontal distance along a level. Twelve inches is convenient.
- Measure the vertical distance from the end of that level line up to the roof surface or the underside of the rafter.
- Divide the rise by the run.
- Multiply by 12 to express the result as rise per 12 inches.
- For the angle, take the arctangent of the rise divided by the run.
- For the area multiplier, square the ratio, add 1, and take the square root.
Worked Example
In the attic, you hold a 24 inch level against the underside of a rafter so that it is horizontal. From the far end of the level, the rafter is 12 inches above it.
- Ratio: 12 ÷ 24 = 0.5.
- Pitch: 0.5 × 12 = 6, so the roof is 6/12.
- Angle: arctan(0.5) = 26.57 degrees.
- Slope: 50 percent.
- Multiplier: √(1 + 0.25) = 1.118.
If this roof covers a 1,500 square foot footprint, its surface is 1,500 × 1.118 = 1,677 square feet. The Roofing Calculator performs that step and converts the area to squares.
How to Use the Calculator
- Measure the run. Any length works, as long as it is level.
- Measure the rise at right angles to the run.
- Enter both values. They can be in inches, centimeters, millimeters or feet, and they do not need to be in the same unit.
- Press Calculate.
- Read the pitch, angle, slope and multiplier.
You can also work from full roof dimensions. Enter the height of the ridge above the wall plate as the rise and half the building width as the run. Once you have the pitch, the Roof Shingle Calculator estimates bundles and accessories from the roof area. For framing, rafter stock can be priced with the Lumber Calculator. The same rise and run geometry applies to stairs, which have their own rules in the Stair Calculator, and the footprint itself comes from the Square Footage Calculator.
Practical Tips
- Measure from inside the attic when possible. Rafters give a clean straight edge and you stay off the roof.
- If you must measure on the roof surface, place the level on a straight board to bridge shingle texture.
- A smartphone level app held against a rafter gives the angle directly. Enter a run of 12 and adjust the rise until the angle matches.
- Measure in more than one place. Old roofs sag, and additions often have a different pitch from the main house.
- Record the pitch of every roof plane. Porches and dormers are commonly lower in slope.
- Check the minimum slope for your chosen roofing material in the manufacturer’s installation instructions.
Common Mistakes
Measuring along the slope instead of horizontally. The run must be level. Measuring 12 inches along the rafter gives a wrong, lower pitch.
Confusing degrees with pitch. A 12/12 roof is 45 degrees, not 12 degrees. A 6/12 roof is 26.6 degrees, not half of 45.
Using the full span as the run. For a symmetrical gable, the run is half the span, from the wall to the point below the ridge.
Assuming one pitch for the whole house. Many houses combine pitches, especially where additions have been built.
Rounding to the nearest whole pitch too early. A measured 5.4/12 should be treated as such when calculating area. Round only when describing the roof.
Pitch Categories and Materials
Roofs below 2/12 are treated as flat. They need a continuous membrane such as modified bitumen, EPDM or TPO, because water drains slowly and can back up under overlapping materials.
Between 2/12 and 4/12 is low slope. Asphalt shingles are generally allowed with a double layer of underlayment or a full ice and water membrane. Standing seam metal performs well here.
From 4/12 to 9/12 is the conventional range, where almost every roofing material can be used and roofers can usually walk the surface.
Above 9/12 is steep. Roof jacks, harnesses and staging are needed, shingles may need extra fasteners, and labor prices rise.
Pitch to Degrees Reference
- 2/12 = 9.46°
- 3/12 = 14.04°
- 4/12 = 18.43°
- 5/12 = 22.62°
- 6/12 = 26.57°
- 7/12 = 30.26°
- 8/12 = 33.69°
- 9/12 = 36.87°
- 10/12 = 39.81°
- 12/12 = 45.00°
Why Pitch Matters for Snow and Rain
Steeper roofs shed water and snow faster, which reduces the chance of leaks and ice dams. In heavy snow regions, pitches of 6/12 and above are common. In hot, dry regions, low slopes are widespread because shedding is less critical and low roofs are cheaper to build. Local building codes set snow load requirements, and the roof framing must be designed to match.
Pitch and Attic Space
The pitch also sets the height at the ridge. A 30 foot wide house with a 4/12 roof has a ridge 5 feet above the wall plate. At 12/12 the ridge is 15 feet up, which is enough for a habitable attic. If you are planning a loft conversion, calculate the ridge height by multiplying half the building width in feet by the pitch and dividing by 12.
Rafter Length From Pitch
The calculator shows the rafter length per foot of run. Multiply it by the run in feet to get the rafter length from the wall plate to the ridge, before adding the overhang. For a 15 foot run at 6/12, the figure is 13.42 inches per foot, so the rafter is about 201 inches, or 16 feet 9 inches, plus the tail. Subtract half the ridge board thickness for an exact cut length.
Using Pitch When Reading a Quote
Roofers often add a steep-slope charge once the pitch passes a threshold, commonly 7/12 or 8/12, because the crew needs roof jacks, harnesses and more time per square. Knowing your pitch tells you whether that charge should apply. Pitch also affects which warranty terms apply, since some shingle warranties change below 4/12. If a quote lists a pitch that is different from the one you measured, raise it. An error of even one unit of pitch changes the roof area by a few percent, and the cost follows. Keep the measurement with your house records so it is to hand for future repairs, solar panel layouts or gutter sizing.