How to use the stair calculator
- Measure the total rise. From the top of the finished lower floor (or ground pad) to the top of the finished upper floor or deck. Include flooring you haven't installed yet.
- Set a maximum riser height. 7¾″ is the IRC limit for homes; 7–7½″ feels more comfortable. The calculator picks the fewest steps that stay under it and makes every riser equal.
- Set the tread run. This is the horizontal depth of each step, not counting the nosing. Two 2×6 boards give about 11″; a single 2×12 gives 11¼″.
- Read the layout. You get the exact riser height, number of treads, total run (how far the stairs reach out), stringer length and the stair angle.
Stair formulas
Riser height = Total rise ÷ Risers
Treads = Risers − 1
Total run = Treads × Tread run
Stringer length = √(Total rise² + Total run²)
Stair angle = arctan(Riser height ÷ Tread run)
There is one fewer tread than risers because the upper floor acts as the last step. The comfort rule most carpenters use is 2 × riser + tread = 24″ to 25½″.
IRC stair requirements (residential)
| Rule | Requirement |
|---|---|
| Maximum riser height | 7¾″ (197 mm) |
| Minimum tread depth | 10″ (254 mm), nosing to nosing |
| Riser and tread variation | Max ⅜″ between the largest and smallest |
| Nosing | ¾″ to 1¼″ when tread depth is under 11″ |
| Minimum width | 36″ (914 mm) clear above the handrail |
| Headroom | 6′ 8″ (2,032 mm) minimum |
| Handrail | Required on at least one side with 4 or more risers |
Local codes can differ, and commercial stairs follow the stricter IBC rules (7″ max riser, 11″ min tread). Check with your building department before you build.
How to lay out a stair stringer
- Clamp stair gauges to a framing square: the riser height on the tongue (short arm) and the tread run on the blade (long arm).
- Starting at one end of a 2×12, trace the first step, then slide the square along and repeat for every step.
- Cut the bottom of the stringer short by one tread thickness so the first step comes out the same height as the rest. This is called "dropping the stringer".
- Cut one stringer, test it in place, then use it as a template for the others.
Worked examples
Total rise 105″ (8′ 9″), max riser 7½″: 105 ÷ 7.5 = 14 risers of exactly 7½″ and 13 treads. At a 10½″ run the stairs reach out 136½″ (11′ 4½″). Stringer = √(105² + 136.5²) = 14′ 4¼″, so use 16 ft 2×12s. Angle 35.5°.
Deck surface 30″ above the patio, max riser 7½″: 4 risers of 7½″ and 3 treads. With 11″ treads (two 2×6s), the run is 33″ and each stringer is 3′ 8⅝″.
Frequently asked questions
How many steps do I need for an 8 ft ceiling?
A typical floor-to-floor height with an 8 ft ceiling is about 105″ once you add the floor framing. At a 7½″ riser that's 14 risers and 13 treads. Always measure your actual rise, as joist depth and flooring change it.
How many stringers does a stair need?
Space stringers no more than about 16″ to 18″ apart. A 36″ wide stair normally uses three. Composite treads usually need closer spacing; check the manufacturer's span rating.
What size lumber do I use for stringers?
2×12 is standard because it leaves enough wood (the throat) behind the notches. Most codes want at least 3½″ to 5″ of solid wood remaining below the cuts.
Does the stringer length include the nosing?
No. The nosing overhangs the riser below and doesn't change the stringer. It does add to the overall depth of each finished tread.