Stair geometry
Vertical clearance to a level soffit
- where
- pitch-line height (mm)
- pitch-line datum height (mm)
- horizontal distance (mm)
- rise (mm)
- going (mm)
- headroom clearance (mm)
- soffit level (mm)
Explain this equation
Checks the vertical clearance between a stair's pitch line and a level ceiling or beam above it, at any point along the flight.
h0 is the height of the pitch line at a known starting point. x is the horizontal distance from there. r and g are the rise and going. hp is the pitch-line height at that point. zs is the level of the soffit above, and hc the vertical clearance. All are in millimetres on one datum.
The pitch line climbs r for every g travelled horizontally, so at distance x it has risen x × r/g. Subtracting that line's height from the soffit level gives the clearance.
Starting at 0 with a 200 mm rise and 250 mm going, the line is 800 mm up after 1000 mm. A soffit at 3000 mm leaves 2200 mm clear.
Watch out: all heights must share one datum. This is not a full headroom or regulations check.
Calculate vertical clearance above a straight pitch line at a specified horizontal station.
Enter your values to see the result.
Good to know
All levels share one datum; distance is horizontal from a stated pitch-line point. Geometry only, not a complete headroom or building-regulations check.
Limits
Building guidance differs across UK nations. Stair geometry must be checked against the applicable nation, building use and project requirements.
Sources
- Geometry / arithmetic
This is a calculation aid, not a structural design or compliance certificate. Every default is an example, not a specification for your project.