How the stair calculation works
Every riser in a flight must be the same height, so the total rise decides everything. Divide it by the riser height you would like, round up to a whole number of risers, then divide the total rise by that number to get the exact riser height.
- Risers. risers = total rise ÷ preferred riser height, rounded up. Rounding up keeps each step at or below your target.
- Actual riser height. total rise ÷ risers.
- Treads. One fewer than the risers, because you step off onto the upper floor.
- Total run. treads × tread depth. This is the floor space the stair needs, measured horizontally.
- Stringer length. The diagonal: √(rise² + run²).
risers = ⌈total rise ÷ preferred riser⌉ · riser = total rise ÷ risers · run = (risers − 1) × tread
Worked example
The total rise is 108 in (9 ft), you want about 7½ in risers, and treads 10 in deep. 108 ÷ 7.5 = 14.4, so round up to 15 risers. Each riser is 108 ÷ 15 = 7.2 in, about 7 3/16 in. There are 14 treads, so the total run is 140 in, or 11 ft 8 in. The stringer line is 14 ft 8 13/16 in long and the stair angle is 35.8°, so cut the stringers from 16 ft stock. In metric, a 2,700 mm rise with 180 mm risers and 260 mm treads gives 15 risers, 14 treads, a 3,640 mm run and a 4,532 mm stringer line at 34.7°.
Common US code limits for home stairs
These figures come from the International Residential Code (IRC), which most US states and cities adopt, sometimes with changes. Canada and Australia have their own national codes with different numbers. Treat this table as a starting point and check local code before you cut.
| Item | Common IRC limit |
|---|---|
| Riser height | 7¾ in maximum |
| Tread depth (nose to nose) | 10 in minimum |
| Difference between largest and smallest riser or tread | ⅜ in maximum |
| Nosing, when treads are under 11 in deep | ¾ to 1¼ in |
| Headroom | 6 ft 8 in minimum |
| Stair width | 36 in minimum |
| Handrail height above nosings | 34 to 38 in, required with 4 or more risers |
Comfort check: 2 risers plus 1 tread
A long-standing rule of thumb says two riser heights plus one tread depth should come to about 24 to 25 inches, which matches a normal stride. The example above gives 2 × 7.2 + 10 = 24.4 in. If your result is well outside that range, change the preferred riser or the tread depth and compare.
Measuring the total rise
- Measure from the finished surface of the lower floor to the finished surface of the upper floor. If flooring is not installed yet, add its thickness at the top and bottom, or the first and last steps will differ from the rest.
- Measure at the spot where the stair will land, not across the room. Floors are rarely perfectly level.
- For deck stairs, measure from the deck surface down to the landing pad or grade where the bottom step will sit.
Building tips and safety
- Lay out stringers with a framing square and stair gauges set to the riser and tread. Cut one, test it in place, then use it as a pattern.
- Cut the bottom of the stringer short by one tread thickness, so the first riser comes out the same height as the rest once treads are on.
- Stringers are usually cut from 2×12 lumber. Keep a solid band of wood below the notches; for cut deck stringers, 5 in is a widely used minimum.
- A 36 in wide stair usually gets three stringers. Wider stairs or thin tread material need more.
- Guards are required on open sides more than 30 in above the floor or grade in the IRC. Stairs are structural and a fall hazard, so get a permit and inspection where required.
Frequently asked questions
How many steps do I need for a 9 ft rise?
A 108 in rise needs 15 risers of 7.2 in each if you aim for 7½ in steps, or 14 risers of about 7.71 in if you allow up to 7¾ in. The flight has one fewer tread than risers.
What is the maximum stair riser height?
The US IRC allows up to 7¾ in for home stairs, with treads at least 10 in deep. Commercial stairs and other countries use different limits, so check local code.
How long should a stair stringer be?
Find the diagonal: square the total rise and the total run, add them and take the square root. For a 108 in rise and 140 in run that is about 14 ft 9 in, so buy 16 ft boards.
Does the top tread count?
No. The upper floor acts as the last step, so a stair with 15 risers has 14 treads.