Steps of a staircase
Number of steps, a comfortable riser and tread by Blondel's rule, and the staircase's length.
How it is calculated
Number of steps = height to climb (in cm) ÷ desired riser, rounded to the nearest whole number (minimum 1). Actual riser = height ÷ number of steps: it always comes out a little different from the desired one, because the number of steps has to be a whole number.
The tread (depth of each step) is calculated with Blondel's rule: 2 × riser + tread = 63 cm, a classic compromise between the length of a stride while climbing (about 60-64 cm) and comfort. Risers between 15 and 19 cm give comfortable, safe stairs for daily use; below that they are very flat steps (easy to trip on), and above it, very steep.
The horizontal length taken up is the tread multiplied by the number of treads, which is one step fewer than the number of steps (the last step lands on the arrival floor, which does not need a tread of its own): length = tread × (number of steps − 1). The angle is the arctangent of (height ÷ horizontal length). The stringer (the sloped beam that carries the steps) is the hypotenuse: √(height² + horizontal length²).
Example with the default values: height 3 m (300 cm), desired riser 17.5 cm. Number of steps = round(300/17.5) = round(17.14) = 17. Actual riser = 300/17 = 17.65 cm. Tread = 63 − 2×17.65 = 27.71 cm. Horizontal length = 27.71 × 16 / 100 = 4.43 m. Angle = arctan(3/4.43) ≈ 34.1°. Stringer = √(3² + 4.43²) ≈ 5.35 m.
Keep in mind
- Blondel's rule is a comfort guideline, not a structural safety standard: for stairs in public use, also check the accessibility and fire-safety regulations in force at the time (minimum widths, handrails, a landing every so many steps).
- With more than 12-16 steps in a row, it is a good idea to add a rest landing; this calculator does not account for that.
- If the angle comes out over 45°, consider a spiral staircase, extending the available opening, or, as a last resort, a fixed ladder-type stair.