Stair stringer calculator
Stair geometry is constrained: total rise divided into equal risers, with the tread following from a comfort rule.
Riser height
180.00mm
- Number of risers
- 15
- Number of treads
- 14
- Total run
- 3500
- Stringer length
- 4420
- Stair angle
- 37.65 degrees Normal domestic
- Two risers plus a tread The comfort rule: aim for 600 to 640 mm.
- 610
- Effective going
- 225
Show the working
- Total rise, floor to floor = 2700
- Preferred riser height = 180
- Tread depth = 250
- Nosing overhang = 25
- Number of risers = round(2700 / 180) = 15
- Riser height = 15 > 0 ? 2700 / 15 : 0 = 180
- Number of treads = 15 - 1 = 14
- Total run = 14 * 250 = 3500
- Stringer length = hypot(2700, 3500) = 4420.41
- Stair angle = 3500 > 0 ? deg(atan(2700 / 3500)) : 0 = 37.6476
- Two risers plus a tread = 2 * 180 + 250 = 610
- Effective going = 250 - 25 = 225
- headroom_run = 3500 * (2000 / 2700) = 2592.59
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- risers = round(total rise / preferred riser)
- riser height = total rise / risers
- stringer = sqrt(total rise^2 + total run^2)
- comfort rule: 2 x riser + tread should be 600 to 640 mm
Every riser in a flight must be the same height to within a few millimetres. Uneven risers are the single most common cause of stair falls.
Building codes set limits on riser height, going and headroom. Check the local ones before cutting anything.