Inputs
Enter any two independent values. The calculator will derive the rest.
Results
Rise: —
Run: —
Diagonal: —
Angle: —
Slope %: —
Pitch: — in 12
Rise:Run ratio: —
History / Example Data
Use Add to Table to build scenarios. Some starter rows included.
| # | Rise | Run | Diagonal | Angle (deg) | Slope % | Pitch (x-in-12) | Units |
|---|---|---|---|---|---|---|---|
| 1 | 0.150 | 0.600 | 0.618 | 14.036 | 25.000 | 3.000 | m |
| 2 | 6.000 | 12.000 | 13.416 | 26.565 | 50.000 | 6.000 | in |
| 3 | 0.300 | 0.800 | 0.854 | 20.556 | 37.500 | 4.500 | m |
Formulas Used
d = √(rise² + run²)θ = atan(rise / run)(radians)θ° = θ × 180 / πslope% = 100 × rise / runpitch12 = 12 × rise / run- Given
θand one length:- with run:
rise = run × tan θ,d = run / cos θ - with rise:
run = rise / tan θ,d = rise / sin θ - with d:
run = d × cos θ,rise = d × sin θ
- with run:
How to Use
- Choose units and desired precision.
- Enter any two independent values: lengths, angle, slope percent, or pitch.
- Click Calculate to derive all remaining fields.
- Optionally click Add to Table to log the scenario.
- Export the table to CSV or PDF for records and sharing.
Tip: If you enter angle plus percent or pitch, only one is needed; the others are derived automatically.
Reference: Common Roof Pitches (x-in-12), Angle, and Grade
| Pitch (x-in-12) | Angle (deg) | Slope % |
|---|---|---|
| 3 | 14.036 | 25.000 |
| 4 | 18.435 | 33.333 |
| 5 | 22.620 | 41.667 |
| 6 | 26.565 | 50.000 |
| 8 | 33.690 | 66.667 |
| 12 | 45.000 | 100.000 |
Use this chart to estimate angle and grade from roof pitch.
Stair Examples: Rise, Run, Angle, Diagonal, and Grade
| Rise | Run | Angle (deg) | Diagonal | Slope % | Units |
|---|---|---|---|---|---|
| 7.000 | 11.000 | 32.471 | 13.038 | 63.636 | in |
| 7.500 | 10.000 | 36.870 | 12.500 | 75.000 | in |
| 6.500 | 12.000 | 28.443 | 13.647 | 54.167 | in |
| 6.000 | 10.500 | 29.745 | 12.093 | 57.143 | in |
Values are illustrative; verify local building requirements for compliance.
Angle ↔ Grade ↔ Pitch Quick Table
| Angle (deg) | Slope % | Pitch (x-in-12) |
|---|---|---|
| 5 | 8.749 | 1.050 |
| 10 | 17.633 | 2.116 |
| 12 | 21.256 | 2.551 |
| 15 | 26.795 | 3.215 |
| 20 | 36.397 | 4.368 |
| 25 | 46.631 | 5.596 |
| 30 | 57.735 | 6.928 |
| 35 | 70.021 | 8.402 |
| 40 | 83.910 | 10.069 |
| 45 | 100.000 | 12.000 |
Pitch column expresses rise per 12 units of run.
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