Stair geometry
Riser count from a specified maximum
- where
- risers
- total finished rise (mm)
- specified maximum rise (mm)
- actual rise (mm)
Explain this equation
Finds the fewest risers needed to climb a height without any rise exceeding a set maximum, and the resulting equal rise.
H is the total finished rise in millimetres. rmax is the largest rise allowed. N is the number of risers, and r the actual rise of each.
Dividing the height by the maximum and rounding up with ⌈ ⌉ gives the least number of steps that keeps every rise within the limit. The height is then shared equally between them.
2600 mm with a 220 mm limit needs 12 risers of about 216.7 mm. Lowering the limit to 200 mm needs 13 risers of exactly 200 mm.
Watch out: the maximum rise is your project input, not a legal value. Also check the minimum rise, going and pitch.
Find a whole riser count not exceeding a supplied maximum rise.
Enter your values to see the result.
Good to know
The maximum is a project input, not an automatic legal recommendation. Also check minimum rise, going, pitch and all other stair provisions.
Limits
Stair going is measured horizontally between nosing lines. Building guidance differs across UK nations. Stair geometry must be checked against the applicable nation, building use and project requirements.
Sources
This is a calculation aid, not a structural design or compliance certificate. Every default is an example, not a specification for your project.