Stair Calculator — Rise, Run and Stringer
Works out a straight flight from the floor-to-floor rise: how many steps, how high each riser, how long the run and the stringer, and whether it meets the riser, going and comfort rules you enter.
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The formula
risers = ceiling(total rise ÷ max riser) riser = total rise ÷ risers treads = risers − 1; run = treads × going angle = arctan(rise ÷ run); stringer = √(rise² + run²)
The riser count is rounded up so no riser exceeds the maximum, then the rise is divided exactly so every riser matches. There is one fewer tread than risers because the top floor is the last tread. The stringer is the hypotenuse of the whole flight.
What to watch out for
What makes a stair right rather than merely built:
- Equal risers. Measure the total rise on site, divide by the count, and cut every riser to that. A 10 mm odd step at the top or bottom is a trip hazard that codes specifically prohibit.
- 2R + G between 550 and 700 mm. The old rule that matches a normal stride. Around 600–650 is best; outside the range the stair feels wrong even when it is legal.
- The limits are code. Maximum riser and minimum going differ — UK domestic allows 220 mm risers and 220 mm goings; the US IRC allows 7¾ in risers and wants 10 in goings. Enter the ones that apply to you.
- Headroom of 2 m measured vertically over the pitch line is not checked here and is often the thing that forces a redesign.
Frequently Asked Questions
How many steps for a 2.7 m rise?
With a 220 mm maximum riser, 2,700 ÷ 220 rounds up to 13 risers of 207.7 mm, and 12 treads. At a 250 mm going that is a 3 m run and a 42° stair — right at the domestic limit, so a 260–280 mm going would be more comfortable.
What is the ideal riser height and tread depth?
Around 180–190 mm riser and 260–280 mm going for a domestic stair, giving 2R + G of about 620–650 mm. Public stairs are shallower still. The maximums in most codes are a ceiling, not a target.
How do I calculate stringer length?
Pythagoras on the whole flight: √(total rise² + total run²). A 2,700 mm rise over a 3,000 mm run needs a 4,036 mm stringer, so a 4.2 m board with a little spare for the cuts.
Why is the bottom riser cut shorter on a stringer?
Because the tread thickness adds to every step except the first. Cutting the bottom riser short by one tread thickness means that once the treads are fitted, every step — including the first off the floor — rises by the same amount.