How to Calculate Stairs: Rise, Run, Number of Steps and Stringer
To lay out stairs, divide the total rise by a riser height of about 7 inches to get a whole number of risers, and then divide the rise by that number to find the exact riser. A 108 inch rise (9 ft) takes 15 risers of 7.20 inches and 14 treads, which with 10 inch treads makes a run of 11.7 ft and a stringer 14.7 ft long. The stair calculator does it for your own height and checks the result against the usual code limits.
Stairs for common heights
With a target riser of about 7¼ inches and 10 inch treads:
| Floor to floor | Risers | Riser height | Treads | Total run | Stringer | Angle |
|---|---|---|---|---|---|---|
| 8 ft (96 in) | 13 | 7.38 in | 12 | 10.0 ft | 12.8 ft | 38.7° |
| 8.5 ft (102 in) | 14 | 7.29 in | 13 | 10.8 ft | 13.8 ft | 38.1° |
| 9 ft (108 in) | 15 | 7.20 in | 14 | 11.7 ft | 14.7 ft | 37.6° |
| 9.5 ft (114 in) | 16 | 7.13 in | 15 | 12.5 ft | 15.7 ft | 37.2° |
| 10 ft (120 in) | 17 | 7.06 in | 16 | 13.3 ft | 16.7 ft | 36.9° |
| 11 ft (132 in) | 18 | 7.33 in | 17 | 14.2 ft | 17.9 ft | 37.8° |
| 12 ft (144 in) | 20 | 7.20 in | 19 | 15.8 ft | 19.9 ft | 37.2° |
The number of treads is one fewer than the number of risers, because the top riser lands on the upper floor.
The formula
- Measure the total rise from the finished floor below to the finished floor above.
- Divide it by about 7 to 7¼ inches and round to the nearest whole number to get the risers.
- Divide the rise by the number of risers to get the exact riser, and check that it is not more than 7¾ inches.
- The treads are one fewer than the risers. Use a tread of 10 inches or more (10 to 11 is typical).
- Check the comfort rule: twice the riser plus the tread should be about 24 to 25 inches.
The code limits for stairs (IRC)
- Riser: 7¾ inches at most.
- Tread: 10 inches at least, measured from nosing to nosing.
- Uniformity: the largest riser or tread in a flight must not be more than 3/8 inch bigger than the smallest.
- Headroom: 6 feet 8 inches at least.
- Width: 36 inches at least (clear of the handrail).
- Handrail: 34 to 38 inches high, on at least one side of a flight of four or more risers.
- Guards: required at open sides over 30 inches above the floor, 36 inches high, with openings that a 4 inch sphere cannot pass.
Local codes differ, so check with your building department. Stairs are a safety item: get a permit and an inspection.
Cutting the stringers
- Use a framing square with stair gauges set to the riser and the tread, and mark the steps along a 2×12 stringer.
- Cut the first and last steps so that all the risers end up the same height once the thickness of the tread is allowed for: drop the bottom of the stringer by the tread thickness.
- Use at least three stringers for a 36 inch stair. Trim one of them to check the fit before you cut the rest.
- See the slope and grade calculator for ramps and the ramp guide.
Frequently asked questions
How do you calculate the number of stair steps?
Divide the total rise (the height from floor to floor, in inches) by a target riser height of about 7 inches, and round to a whole number of risers. A 108 inch rise gives 15 risers of 7.20 inches.
How many steps for a 9 foot ceiling?
With a floor to floor height of about 9 feet (108 inches) you need 15 risers, each 7.20 inches high, and 14 treads. For 8 feet (96 inches) it is 13 risers of 7.38 inches.
What are the maximum rise and minimum run for stairs?
In the International Residential Code a riser can be at most 7¾ inches high and a tread at least 10 inches deep. The heights must be uniform within 3/8 inch in a flight.
How long is a stair stringer?
The stringer is the hypotenuse of the stairs: 14.7 ft for a 108 inch rise with 14 treads of 10 inches. Buy the next standard board length, 16 ft here.
How much headroom do stairs need?
At least 6 feet 8 inches measured from the sloped line through the front edges of the treads (the nosing line) to the ceiling, under the code. Stairs are also at least 36 inches wide.
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Estimates only. Quantities depend on your materials, site and supplier. Confirm important numbers before you order, and follow local building codes for anything structural.