Stair geometry
Straight stair: rise, going & pitch
- where
- rise per step (mm)
- floor-to-floor height (mm)
- risers
- goings
- total run (mm)
- going (mm)
- pitch (°)
- step relationship 2r + g (mm)
Explain this equation
Works out the geometry of a straight flight from the floor-to-floor height, the number of risers and the going.
H is the finished floor-to-floor height in millimetres. N is the number of risers, and r the rise of each step. n is the number of goings, and g the going of each tread. L is the total horizontal run. θ is the pitch, and S the 2r + g relationship.
Every riser shares the height equally. There is one fewer going than risers, because the top floor acts as the last tread. The pitch is the angle of the triangle formed by one rise and one going. 2r + g is a long-standing check that steps suit a normal stride.
2600 mm over 13 risers is 200 mm each. With 12 goings of 250 mm the run is 3000 mm, the pitch about 38.7° and 2r + g = 650 mm.
Watch out: this is geometry only. Check every limit in your national regulations.
Calculate a uniform straight flight with the upper floor acting as the last landing.
Enter your values to see the result.
Good to know
Geometry only, not a compliance pass. Landings, headroom, nosings, winders, guarding, accessibility and local national rules must also be checked. One flight, no intermediate landing.
Limits
Stair going is measured horizontally between nosing lines. The straight-flight tool assumes the upper floor forms the last landing, so goings equal risers minus one. 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.