Why is there one fewer tread than riser?

Because the top riser lands on the upper floor, which is not a tread. A flight of sixteen risers has fifteen treads.

What is the Blondel rule?

Twice the riser plus the tread should be about 600 to 650mm, which reflects the natural stride. Stairs outside that range feel awkward regardless of whether they pass code.

Construction & Homestructural

Staircase Design Calculator

Staircase geometry from the floor-to-floor height. Risers must be equal, so the height decides the count and the count decides the riser, not the other way round.

Also called: stair calculator, riser and tread.

Number of risers

17 risers of 176.5mm and 16 treads of 280mm, needing 4,480mm of horizontal run. Within the maximum riser and the comfortable Blondel range.

Actual riser height (mm)

176.5

Number of treads

Horizontal run needed (mm)

4,480

Angle (degrees)

33.81

Blondel value (2R + T)

632.9

Comfort and compliance

Within the maximum riser and the comfortable Blondel range.

How this is calculated

Method and background

How this is calculated

Divide the total rise by a preferred riser and round to a whole number, then divide the height by that count to get the actual riser. Every riser in a flight must be identical, which is why the preferred height is only a starting point. There is always one fewer tread than riser, since the top landing is not a tread. The Blondel rule checks comfort: twice the riser plus the tread should land around 600 to 650mm, and stairs outside that feel wrong to walk even when they meet code.

the riser count is the height divided by a preferred riser, rounded; Blondel rule checks the result is comfortable

H: Total rise (mm)
R: Riser height (mm)
T: Tread depth (mm)

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a three metre floor height

Floor to floor height (mm): 3,000
Preferred riser height (mm): 175
Tread depth (mm): 280
Maximum riser allowed (mm): 190

Number of risers17

3000 / 175 rounds to 17, then 3000 / 17

Open this example

the tread count is always one fewer

Floor to floor height (mm): 2,800
Preferred riser height (mm): 175
Tread depth (mm): 280
Maximum riser allowed (mm): 190

Number of risers16

boundary: the off-by-one people get wrong

Open this example

Method and limits

What it assumes

A straight flight with no winders or landings.

What it deliberately does not model

Building codes set maximum risers and minimum treads that vary by jurisdiction and occupancy.
Headroom, nosing and handrail requirements are separate checks.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why is there one fewer tread than riser?: Because the top riser lands on the upper floor, which is not a tread. A flight of sixteen risers has fifteen treads.
What is the Blondel rule?: Twice the riser plus the tread should be about 600 to 650mm, which reflects the natural stride. Stairs outside that range feel awkward regardless of whether they pass code.