How to use the stair calculator
- Measure the total rise: the vertical distance from the finished surface of the lower floor to the finished surface of the upper floor. Include flooring that is not installed yet.
- Enter the maximum riser height you are allowed or want. In the US, the International Residential Code (IRC) limits risers to 7¾ in.
- Enter the tread depth, the horizontal distance from one riser to the next. The IRC minimum is 10 in.
- Read the number of risers, the exact riser height, the total run and the stringer length.
The formulas
Risers = total rise ÷ maximum riser height (rounded up) Riser height = total rise ÷ risers Treads = risers − 1 Total run = treads × tread depth Stringer length = √(total rise² + total run²) Stair angle = arctan(total rise ÷ total run)There is one fewer tread than risers because the top "step" is the upper floor itself. The stringer length here is the diagonal from the bottom to the top of the flight. Buy stringer stock a little longer to allow for the top and bottom cuts.
US residential code limits (IRC R311.7)
| Item | Requirement |
|---|---|
| Riser height | 7¾ in maximum |
| Tread depth | 10 in minimum |
| Variation within a flight | ⅜ in maximum between the largest and smallest riser or tread |
| Nosing | ¾ in to 1¼ in where the tread is less than 11 in deep |
| Headroom | 6 ft 8 in minimum |
| Width | 36 in minimum |
| Handrail | Required on at least one side of a flight with four or more risers, 34–38 in high |
| Height of one flight | 151 in maximum between floors or landings |
Many US jurisdictions adopt the IRC with local amendments, so check with your building department. Commercial stairs under the IBC are stricter, with a 7 in maximum riser and an 11 in minimum tread.
Metric stairs and the 2R + G rule
In metric mode, enter the rise, riser and going in millimetres. A widely used comfort rule is that twice the rise plus the going (2R + G) should fall between 550 mm and 700 mm. England's Approved Document K, for example, allows private stairs a rise of 150–220 mm, a going of 220–300 mm and a maximum pitch of 42°. Rules differ by country, so check your local regulations.
Worked example
A total rise of 108 in, a 7¾ in maximum riser and 10 in treads:
- Risers: 108 ÷ 7.75 = 13.9, so 14 risers of 108 ÷ 14 = 7.71 in (about 7 11/16 in).
- Treads: 14 − 1 = 13 treads, for a total run of 13 × 10 = 130 in (10 ft 10 in).
- Stringer: √(108² + 130²) ≈ 169 in (14 ft 1 in), at an angle of about 39.7°.
Tips
- Keep every riser in a flight the same height. Uneven steps are a common cause of trips and falls.
- A deeper tread with a slightly lower riser makes a gentler, more comfortable stair, but it needs more floor space.
- Cut one stringer, test-fit it, and use it as the template for the others.
Frequently asked questions
What is the maximum riser height for stairs?
For homes in the US, the International Residential Code allows a maximum riser height of 7¾ in and a minimum tread depth of 10 in. Commercial buildings under the IBC are limited to a 7 in riser and an 11 in tread.
How many stairs do I need for a 9 ft rise?
A 9 ft (108 in) total rise with a 7¾ in maximum riser needs 14 risers of about 7.71 in each, and 13 treads.
Why is there one less tread than risers?
The last riser takes you onto the upper floor, which acts as the final tread. A straight flight with 14 risers therefore has 13 treads.
How long should a stair stringer be?
The diagonal length is √(rise² + run²). For a 108 in rise and a 130 in run that is about 169 in. Buy boards a little longer to allow for the plumb and level cuts at each end.