Stair geometry
Stair pitch-line segment
- where
- one interval length (mm)
- rise per step (mm)
- going per step (mm)
- pitch-line length (mm)
- going intervals
Explain this equation
Gives the length along the pitch line of a stair for a set number of steps, useful when marking out a string.
r is the rise and g the going of one step, in millimetres. s is the sloping length of one step along the pitch line. n is the number of going intervals. L is the total pitch-line length.
One rise and one going make a right-angled triangle whose hypotenuse lies on the pitch line, so s = √(r² + g²) by Pythagoras. Identical steps simply repeat that length n times.
A 200 mm rise and 250 mm going gives about 320 mm per step. Twelve steps give about 3842 mm.
Watch out: this is not the full string length. Extensions at top and bottom, housings and joints are extra.
Calculate a pitch-line segment spanning a known number of identical going intervals.
Enter your values to see the result.
Good to know
Intervals are explicit. This is not a full string blank length; top/bottom extensions, housings, joints and landings are separate.
Limits
Stair going is measured horizontally between nosing lines. The pitch-line segment tool uses an explicit number of going intervals; it does not silently equate a full floor-height diagonal with a string blank. 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.