Calculator
Live results update as you typeAngle (degrees)
34.99°
Slope (%)
70.00%
Ratio (1 : n)
1 : 1.43
Angle (radians)
0.61
Typical interior stair pitch is often around 30–37 degrees depending on jurisdiction. Always verify with local building codes before installation.
Effective run used
250.00 mm
Pitch-line per step
305.94 mm
Total flight (approx)
Rise 2100 mm · Run 3000 mm · Pitch 3667 mm
Example Data
Use these rows or add your own| # | Rise | Run | Nosing | Ref | Angle (°) | Slope (%) | Ratio (1:n) | Pitch (mm) | Note |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 170 mm | 260 mm | 15 mm | toNose | 33.0 | 65.4 | 1:1.53 | 310.1 | Comfortable |
| 2 | 180 mm | 240 mm | 0 mm | toRiser | 36.9 | 75.0 | 1:1.33 | 300.0 | Upper typical |
| 3 | 190 mm | 220 mm | 10 mm | toNose | 40.1 | 86.4 | 1:1.26 | 292.4 | Steep |
Formula used
Angle (degrees): θ = arctan( rise / run ) × 180 / π
Slope (%): S = ( rise / run ) × 100
Ratio: 1 : n where n = run / rise
Pitch-line (per step): hyp = √( rise² + run² )
Effective run (measurement to nosing): runeff = run + nosing
Slope (%): S = ( rise / run ) × 100
Ratio: 1 : n where n = run / rise
Pitch-line (per step): hyp = √( rise² + run² )
Effective run (measurement to nosing): runeff = run + nosing
If you measure the going to the tread nosing, the effective horizontal increases by the projection amount, lowering the angle slightly. When measured to the riser face, ignore the nosing value.
How to use this calculator
- Enter the rise and run for a typical step. Choose your preferred units.
- Optionally enter a nosing projection and select whether your run is referenced to the riser or to the nosing.
- Press Calculate to see the angle in degrees and radians, the slope percentage, and the grade ratio.
- Provide the number of steps if you want total flight estimates for rise, horizontal run, and pitch-line length.
- Click Add to Example Table to append your scenario for later export.
- Use Download CSV or Download PDF to export results and example table rows.
Note: Typical interior stairs are often in the ~30–37° range, but requirements vary. Always consult your local building authority and project specifications.
FAQs
Angle is the geometric pitch measured in degrees via arctangent of rise divided by run. Slope percent expresses the same gradient as a percentage: rise divided by run times one hundred.
It can. If you measure the going to the nosing tip, effective run increases by the projection, which reduces the angle slightly. If you measure to the riser face, ignore the nosing value.
Many guidelines consider around 30–37° typical for interior stairs, but acceptable values vary by region and building type. Always follow the specific requirements of local codes and project documents.
You can enter rise, run, and nosing in millimeters, centimeters, or inches. Results are computed consistently after converting everything internally to millimeters.
The pitch angle depends on the ratio between rise and run for a typical step. Scaling the number of steps changes totals but not the per-step ratio, so the angle remains the same.
Treat the outputs as planning aids. For compliance and safety, consult local building codes and have measurements verified by a qualified professional before installation.