Stair Calculator
Design a straight staircase from the floor-to-floor height. Enter the total rise and a target riser height (or a fixed number of steps), pick a tread depth, and this calculator returns the actual riser height, number of steps, total run, stringer length, and angle — and warns you if it breaks common IRC code limits.
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A staircase is a balance between three numbers: the total rise you have to climb, the height of each step (riser), and the depth of each tread (run). Building codes bound how steep a step can be so stairs stay safe and comfortable. The design process starts by dividing the total rise into a whole number of equal risers, because you cannot have a fractional step. That fixes the riser height; multiplying the tread depth by the number of treads gives the horizontal run; and the diagonal stringer that carries the steps is simply the hypotenuse of the rise and run.
How it’s calculated
Number of risers = round(total rise ÷ target riser). Actual riser = total rise ÷ number of risers. Treads = risers − 1 (the top landing is not a tread), so total run = treads × tread depth. Stringer length = √(total rise² + total run²). Stair angle = arctangent(total rise ÷ total run). The code check compares the riser to the IRC maximum of 7.75 in and the tread to the IRC minimum of 10 in (R311.7.5).
A straight-run stair without winders or landings, measured in inches. Add material at the stringer ends for connections, and always verify against your local building code — requirements vary by jurisdiction.
IRC stair limits
| Element | IRC limit |
|---|---|
| Maximum riser height | 7.75 in (197 mm) |
| Minimum tread depth | 10 in (254 mm) |
| Minimum headroom | 6 ft 8 in (2032 mm) |
| Minimum stair width | 36 in (914 mm) |
| Max riser variation | 3/8 in between tallest & shortest |
International Residential Code R311.7. Local codes may be stricter; confirm before building.
Worked example
A floor-to-floor rise of 108 in (9 ft) with a target riser of 7.5 in needs 108 ÷ 7.5 = 14.4, rounded to 14 risers. The actual riser is 108 ÷ 14 = 7.71 in — just under the 7.75 in limit. With 13 treads at 10 in, the total run is 130 in (10.83 ft). The stringer is √(108² + 130²) ≈ 169 in, and the stair angle is arctan(108/130) ≈ 39.7°.
Common mistakes
- Counting treads instead of risers — the number of steps is set by the risers, and there is always one fewer tread.
- Measuring rise from the subfloor and forgetting the finished floor thickness at top and bottom.
- Letting the riser creep over 7.75 in or the tread under 10 in, which fails IRC.
- Ignoring headroom — a steep stair under a low opening can violate the 6 ft 8 in minimum.
Where it is used
- Framing interior stairs between floors.
- Building deck, porch, and basement stairs.
- Cutting stringers for a shed or loft.
- Checking an existing stair against current code.
Frequently asked questions
How do you calculate the number of stair steps?
Divide the total rise (floor-to-floor height) by your target riser height and round to a whole number of risers. Then divide the total rise by that number of risers to get the actual riser height. For example, 108 inches of rise ÷ 7.5 target = 14.4, rounded to 14 risers, giving a 7.71-inch riser.
What is the maximum riser height by code?
The International Residential Code (IRC R311.7.5) sets a maximum riser height of 7.75 inches and a minimum tread depth of 10 inches for residential stairs. The calculator flags a warning if your riser exceeds 7.75 inches or your tread is under 10 inches. Local codes can differ, so confirm with your building department.
What is the difference between rise, run, and stringer?
Rise is the vertical height of one step (riser); total rise is floor-to-floor. Run is the horizontal depth of one tread; total run is the whole horizontal distance. The stringer is the diagonal board that supports the steps — its length is the hypotenuse of the total rise and total run.
How long should a stair stringer be?
The stringer length equals the square root of (total rise squared + total run squared). For a stair with 108 inches of rise and 130 inches of run, the stringer is √(108² + 130²) ≈ 169 inches. Add extra length for the top and bottom connections when cutting.
What is a comfortable stair angle?
Residential stairs are typically between about 30 and 37 degrees, with 30–35 degrees considered most comfortable. Steeper stairs (approaching the code limits of a 7.75-inch riser and 10-inch tread, about 38 degrees) are legal but feel steep. The calculator reports the angle so you can judge.