Inputs
Tip: The pitch uses a 12-unit horizontal base (e.g., "X in 12").
Results
Slope (rise / run)
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Simplified ratio shown below.
Percent grade (%)
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Angle (degrees)
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Angle (radians)
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Gradient (1 in n)
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Roof pitch (rise per 12 run)
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Hypotenuse length
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Simplified ratio
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Example Data Table
Common roof/stair slopes with computed grades and angles. Click a row to load values.
| Rise | Run | Units | Slope (rise/run) | Percent Grade (%) | Angle (°) | Pitch (rise in 12) |
|---|
Formulas Used
Given rise
R and run H (horizontal):1) Slope:
m = R / H2) Percent grade:
%grade = (R / H) × 1003) Angle (radians):
θ = arctan(R / H)4) Angle (degrees):
θ° = arctan(R / H) × 180 / π5) Gradient form:
1 in n where n = H / R (if R > 0)6) Roof pitch (rise per 12 run):
pitch = 12 × (R / H)7) Hypotenuse length:
L = √(R² + H²)8) Simplified ratio: divide
R and H by their greatest common divisor.How to Use This Calculator
- Enter the rise and run values, then pick your units.
- Choose a rounding preference to control decimal places.
- Click Calculate to update slope, grade, angle, pitch, and more.
- Use Download CSV or Download PDF to save results.
- Click any row in the Example Data table to preload inputs.
- Share your exact setup with the Copy Shareable URL button.
All slope measures are unitless; only lengths (e.g., hypotenuse) carry units.
How to calculate slope from rise and run
Follow these quick steps to convert rise and run into common slope measures.
- Identify the vertical change (rise) and horizontal distance (run).
- Compute slope:
m = rise / run. This value is unitless. - Percent grade:
%grade = m × 100. Example: 0.25 → 25% grade. - Angle in degrees:
θ° = arctan(m) × 180 / π. - Gradient form: write as
1 in n, wheren = run / rise. - Roof pitch: express as “rise in 12” using
pitch = 12 × m.
Worked example
Given rise = 4 and run = 12:
1) Slope:
m = 4 / 12 = 0.33332) Percent grade:
33.33%3) Angle:
arctan(0.3333) ≈ 18.435°4) Gradient:
1 in 3 (since 12 / 4 = 3)5) Roof pitch:
4 in 12Rise/Run Quick Reference (Common Slopes)
Handy conversions for frequently used roof, ramp, and stair slopes.
| Rise | Run | Slope (R/H) | Percent Grade (%) | Angle (°) | Pitch (rise in 12) |
|---|---|---|---|---|---|
| 1 | 20 | 0.0500 | 5.00 | 2.86 | 0.60 in 12 |
| 1 | 12 | 0.0833 | 8.33 | 4.76 | 1.00 in 12 |
| 2 | 12 | 0.1667 | 16.67 | 9.46 | 2.00 in 12 |
| 3 | 12 | 0.2500 | 25.00 | 14.04 | 3.00 in 12 |
| 4 | 12 | 0.3333 | 33.33 | 18.43 | 4.00 in 12 |
| 6 | 12 | 0.5000 | 50.00 | 26.57 | 6.00 in 12 |
| 8 | 12 | 0.6667 | 66.67 | 33.69 | 8.00 in 12 |
| 12 | 12 | 1.0000 | 100.00 | 45.00 | 12.00 in 12 |
Values are approximate; verify against your project specifications and codes.
Reverse Calculations (Given Grade or Angle)
A) Given grade and run
Grade = 7.5%, Run = 10.00 ft
Rise = Run × (grade/100) = 10.00 × 0.075 = 0.750 ft (9.00 in)
B) Given angle and run
Angle = 30°, Run = 12 in
Rise = tan(angle) × Run = tan(30°) × 12 ≈ 6.928 in
C) Given roof pitch (rise in 12)
Pitch = 5 in 12 ⇒ slope = 0.4167
Percent grade = 41.67%, Angle ≈ 22.62°