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Stair Calculator: Risers, Treads and Stringer Length
Enter the floor-to-floor rise, a target riser height and your tread depth. The calculator finds how many equal risers fit, the exact riser height, the total run, the slope angle, the stringer length and the 2R+T comfort check.
How the stair layout is worked out
A stair is a set of equal risers climbing a fixed total rise. Dividing the total rise by the target riser height and rounding gives the whole number of risers, and dividing the total rise by that number gives the exact riser height. Every riser in a flight should be the same, because people rely on a steady rhythm and a variation of even a few millimeters can cause a trip.
A straight flight has one fewer tread than risers, because the upper floor takes the place of the last tread. Total run is the number of treads multiplied by the tread depth. The stringer, measured along the nosing line, is the hypotenuse √(rise² + run²), and the slope angle is atan(riser ÷ tread).
The 2R+T comfort guide
Designers have long used simple rules to judge whether a stair feels natural to climb. One common guide is that twice the riser plus the tread should land around 24 to 25 inches, or about 610 to 635 millimeters. A steeper stair has a tall riser and a short tread, which pushes the figure up or down away from that range. The rule is a guide to comfort and not a legal test, and it is only one of several formulas people quote.
| Riser | Tread | 2R+T | Feel |
|---|---|---|---|
| 7 in | 11 in | 25 in | Typical |
| 6 in | 12 in | 24 in | Gentle |
| 8 in | 9 in | 25 in | Steep |
The last row shows why the figure alone is not enough: a short tread can fit the sum and still feel cramped.
Common mistakes
- Measuring to the wrong surface. Use finished floor to finished floor. Flooring added later to the top or bottom changes the first or last riser.
- Counting treads as risers. There is always one more riser than tread in a flight with a landing at the top.
- Ignoring headroom and landing space. The run must fit the available space, and the clear height above the steps must be adequate.
- Forgetting the thickness of the tread material. The first riser is shortened or lengthened to compensate, so the cut stringer must account for it.
Limits and safety
This tool is for estimating and learning. Stairs are a leading source of household falls, and requirements for riser height, tread depth, headroom, handrails, guards, winders and landings vary by country, region and building type. Local building codes and a qualified builder, carpenter or structural professional decide what is allowed and safe for your project. Do not cut stringers from these numbers alone. Measure the actual opening, confirm the dimensions with a qualified person and check that the structure can carry the load before construction starts.
Worked example
A floor-to-floor rise of 105 inches, aiming for 7 inch risers and using 11 inch treads.
Inputs
| Units | Imperial (inches) |
|---|---|
| Total rise, finished floor to finished floor (inches or mm) | 105 |
| Target riser height (inches or mm) | 7 |
| Tread depth, nosing to nosing (inches or mm) | 11 |
Result
14 treads of 11.00 in give a total run of 154.0 in.
| Number of risers | 15 |
|---|---|
| Number of treads | 14 (the top floor acts as the last tread) |
| Exact riser height | 7.000 in |
| Total run | 154.0 in |
| Slope angle | 32.5° |
| Stringer length (nose line) | 186.4 in |
| 2 × riser + tread | 25.0 in (guide 24 to 25 in) |
- Riser and tread limits are set by local codes and differ between places. Check the rules that apply to your project.
Estimating note: Quantities and ratings here are estimates for planning and learning. Products, local codes and site conditions differ, so check manufacturer data and local regulations, and use a qualified professional for electrical, structural or safety-critical work.
Frequently asked questions
How do I calculate the number of steps in a staircase?
Divide the total rise by the riser height you want and round to the nearest whole number. The result is the number of risers, and treads number one fewer.
What is the 2R+T rule for stairs?
It adds twice the riser height to the tread depth. A total of roughly 24 to 25 inches, or 610 to 635 millimeters, is often quoted as a comfortable proportion.
Why are there fewer treads than risers?
The top riser meets the upper floor, which serves as the last tread. A straight flight therefore has one more riser than it has treads.
Can the risers in one flight be different heights?
They should be equal. Uneven risers surprise a person climbing in a rhythm, and building codes generally set a strict limit on variation between risers in one flight.
What is the stringer length used for?
It is the length of the sloping board along the nosing line, so it tells you the minimum length of lumber you need before allowing for the cuts at both ends.
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References and sources
- Local building codes and the national residential code that applies in your region set the legal riser, tread, headroom and handrail limits; consult the authority that issues permits.