Stair Riser: Calculating Rise and Tread from Floor Height

From the floor height and the number of steps, finds the riser and a guideline tread depth (2 × riser + tread = 60 cm). Japanese building law requires a riser of 23 cm or less and a tread of 15 cm or more in homes.

Explanation

The riser is the height of one step; the tread is its depth. Divide the floor-to-floor height by the number of steps and you have the riser.

\text{riser} = \dfrac{\text{floor height}}{\text{steps}}

The tread comes from a long-standing rule of thumb.

2 \times \text{riser} + \text{tread} = 60\ \text{cm}

It is drawn from the human stride: the taller each step, the shallower its tread can be, and the shorter the step, the deeper it should be. It is a guideline, not a legal formula.

Example

Take the defaults, a floor height of 280 cm over 14 steps.

\text{riser} = \dfrac{280}{14} = 20\ \text{cm}

\text{tread} = 60 - 2 \times 20 = 20\ \text{cm}

That gives a riser of 20 cm with a suggested tread of 20 cm. Add one step and 280 ÷ 15 = 18.67 cm, a gentler climb over the same floor height.

Notes

Japanese building law lets a house, excluding the shared stairs of an apartment block, go as far as a 23 cm riser with a 15 cm tread. That is a legal floor, not a comfortable stair, and it permits something considerably steeper than most readers outside Japan will have met. Real houses usually settle around 18 to 20 cm. Anything that is not a house, shared apartment stairs included, is held to a stricter standard.
Steps here means risers, the number of level changes. The upper floor forms the last one, so a flight has one fewer tread than it has steps.
Floor height means finished floor to finished floor, not ceiling height. Confusing the two leaves the top step the wrong size.
Enter a whole number of steps, at least 1. A riser of 30 cm or more is not a stair, and the calculator will not compute it.
The 60 cm rule is sometimes written as 60 to 65 cm. If the suggested tread comes out uncomfortably shallow, add steps to bring the riser down.