Roof Pitch Calculator
Enter what you know, rise and run, a pitch like 6/12, an angle in degrees or a percent slope, and get the other three, plus the multiplier that turns floor area into roof area.
Pitch is the rise in inches for every 12 inches of run: pitch = rise ÷ run × 12. Angle = arctan(rise ÷ run). Percent slope = rise ÷ run × 100. The roof area multiplier is √(1 + (rise ÷ run)²).
Example: 6 in of rise over 12 in of run is a 6/12 pitch. That is 26.57°, a 50% slope and a multiplier of 1.118.
Method
How this calculator works
This is pure geometry, so no data source is needed. Every form of slope comes from one number: the tangent, which is rise divided by run.
Slope from what you know
Rise and run must use the same unit, and run is measured level, not along the slope. A pitch is rise per 12 in of run, a percent slope is rise per 100, and an angle is converted with the tangent. All four reduce to one ratio. Stairs use the same rise and run geometry, with the angle taken from riser and tread: see the Stair Calculator.
Slope = Rise ÷ RunSlope = Pitch ÷ 12 = Percent ÷ 100 = tan(Angle)Pitch, angle and percent
From the slope, the other forms follow. A 100% slope is 45°, which is a 12/12 pitch.
Pitch = Slope × 12Angle = arctan(Slope)Percent = Slope × 100Roof area multiplier
A sloped roof is longer than the level distance under it. The multiplier is the surface length per unit of run, so multiplying a flat footprint by it gives the roof area. The roofing calculator uses the same value.
Multiplier = √(1 + Slope²)Roof area = Footprint × MultiplierSloped length per foot of run
The same multiplier gives the length along the slope for each foot of level run. It is a geometry result, not a rafter design: it ignores overhang, ridge board, birdsmouth cuts and member size.
Slope length per 1 ft of run (in) = Multiplier × 12Worked example: 6 in of rise over 12 in of run
Arithmetic checked| Step | Math | Result |
|---|---|---|
| Slope (rise ÷ run) | 6 ÷ 12 | 0.5 |
| Pitch (rise per 12 in of run) | 0.5 × 12 | 6/12 |
| Angle | arctan(0.5) | 26.57° |
| Percent slope | 0.5 × 100 | 50% |
| Roof area multiplier | √(1 + 0.5²) = √1.25 | 1.1180 |
| Sloped length per 1 ft of run | 1.1180 × 12 | 13.42 in |
| Pitch | 6/12, or 26.57° | |
Going the other way, a 30° roof has a slope of tan(30°) = 0.5774, which is a pitch of 6.93/12 and a multiplier of 1.1547.
| Pitch | Angle | Slope | Area multiplier |
|---|---|---|---|
| 2/12 | 9.46° | 16.7% | 1.0138 |
| 3/12 | 14.04° | 25.0% | 1.0308 |
| 4/12 | 18.43° | 33.3% | 1.0541 |
| 5/12 | 22.62° | 41.7% | 1.0833 |
| 6/12 | 26.57° | 50.0% | 1.1180 |
| 7/12 | 30.26° | 58.3% | 1.1577 |
| 8/12 | 33.69° | 66.7% | 1.2019 |
| 9/12 | 36.87° | 75.0% | 1.2500 |
| 10/12 | 39.81° | 83.3% | 1.3017 |
| 12/12 | 45.00° | 100.0% | 1.4142 |
Disclaimer
Results are planning estimates based on the dimensions and assumptions you enter. They are not engineering, structural or building-code advice. Product yields, densities and coverage vary by manufacturer, batch and site conditions. Check product labels, your supplier and your local building department before you order materials or start work. Read the full calculation disclaimer.
Accuracy
What affects your reading
The formulas are exact. A pitch is only as accurate as the measurement that goes into it.
Measure run level
Run is the horizontal distance, not the distance along the rafter. With a level held flat, measure 12 in out and read the rise straight up from the end of the level to the roof.
Same unit for rise and run
The ratio only works if both numbers use the same unit. 6 in over 1 ft is 6 over 12, not 6 over 1.
Pitch is not roof area
A pitch tells you how steep. To turn a footprint into area, apply the multiplier, which the roofing calculator does for you. Add overhangs to the footprint first.
Materials set the limits
The lowest and steepest slope a roofing material allows comes from the maker’s installation instructions and local code, not from this calculator. Check them before you choose a product.
This tool converts slope. It does not size rafters, trusses or sheathing or check snow and wind loads. Those need a designer or engineer. Roofs are a fall hazard, so measure from the ground, from plans or from the attic when you can.
Common mistakes
Measuring along the slope instead of level
Run is the level distance. Measuring along the roof surface gives a longer number and a pitch that is too gentle.
Mixing pitch and degrees
A 6/12 pitch is 26.57°, not 6°. Check which form a plan or a product sheet uses before you enter it.
Forgetting that percent is not degrees
A 100% slope is 45°, not 100°. Percent is rise per 100 of run, so it climbs past 100% on steep roofs.
Questions people ask
How do you calculate roof pitch?
Divide the rise by the run and multiply by 12. If a roof rises 4 in over 12 in of level run, the pitch is 4/12. With rise and run in any single unit, 4 ft over 12 ft is also 4/12. The guide on how to calculate roof pitch shows three safe ways to measure it and a pitch chart.
What does a 2:12 roof pitch look like?
It rises 2 in for every 12 in of run, which is 9.46° or a 16.7% slope. It is a gentle slope. Whether a given roofing material suits it depends on the maker’s minimum slope.
Is a 10 degree roof pitch OK?
Ten degrees is about a 2.12/12 pitch (tan 10° × 12). Whether it works depends on the roofing material and local code, so check the manufacturer’s minimum slope for the product you plan to use.
How do I convert degrees to pitch?
Take the tangent of the angle and multiply by 12. For 30°, tan 30° is 0.5774, so the pitch is 6.93/12. The calculator does this when you choose angle.
What is the roof area multiplier?
The factor that turns the level footprint into the sloped roof area: √(1 + slope²). For 6/12 it is 1.118, so 1,200 ft² of footprint becomes 1,341.64 ft² of roof.
Related calculators and guides
Sources
Where the numbers come from
These formulas are pure trigonometry (rise, run, tangent and the Pythagorean theorem), so no outside data is used. Minimum and maximum slopes for a roofing product are in the installation instructions for that product.