Stair Calculator: Steps, Rise, Run & Stringer Length

Every straight staircase is a right triangle: the total rise is the vertical side, the total run is the horizontal side, and the stringer is the hypotenuse. Six formulas turn your three inputs into a full cut plan.

• Number of steps: round(total rise ÷ desired riser), minimum 2. Steps have to be whole and equal, so the calculator rounds to the nearest whole step count.
• Actual riser height: total rise ÷ steps. Because of the rounding above, this is almost never exactly the riser height you typed — but it is always the same on every step.
• Number of treads: steps − 1. The top "tread" is the upper floor or landing itself, so you always build one fewer tread than there are risers.
• Total run: tread depth × (steps − 1) — the horizontal footprint the staircase will occupy on the floor.
• Stringer length: √(total rise² + total run²) — the hypotenuse of the stair triangle, and the length to lay out on your stringer board.
• Stair angle: arctan(total rise ÷ total run) × (180 ÷ π), shown in degrees. Most comfortable home stairs sit between 30° and 37°.

Sources: 2021 International Residential Code (IRC) Section R311.7 — Stairways; The Spruce — stair code requirements; calculator.net — stair calculator reference.

Take a total rise of 36 inches, a desired riser height of 7.5 inches, and a tread depth of 10 inches.

1. Steps: 36 ÷ 7.5 = 4.8, which rounds to 5 steps.
2. Actual riser: 36 ÷ 5 = 7.20 inches on every step.
3. Treads: 5 − 1 = 4 treads. Total run: 4 × 10 = 40 inches (3 ft 4 in).
4. Stringer: √(36² + 40²) = √2896 = 53.81 inches (4 ft 5.81 in).
5. Stair angle: arctan(36 ÷ 40) ≈ 42.0° — a touch steep, but fine for a short flight.

Code check: the 7.20 in riser is under the 7.75 in residential maximum, and the 10 in tread meets the minimum. Comfort check: 7.2 + 10 = 17.2 in, inside the classic 17–18 in range.

Three measurements in, one cut plan out. The most important one is the total rise — get that right and everything downstream follows.

Step by step

1. Measure the total rise. Hook your tape on the finished lower floor and measure straight up to the finished upper floor. Include flooring thickness at both ends — a tile floor that goes in later changes every riser.
2. Enter your desired riser height. The default is 7.5 in, a comfortable residential target. The calculator will round to whole, equal steps, so think of this as a preference, not a promise.
3. Enter the tread depth. The default is 10 in, the code minimum with nosing. Measure nosing to nosing — the nosing overhang beyond the riser does not count toward the run.
4. Press Calculate. Read your step count, actual riser, total run, stringer length and stair angle underneath.
5. Check the notes. The calculator flags risers outside the 4–7.75 in comfort-and-code band and tells you when rise plus run drifts outside the classic comfort range.

Builders use precise words for stair parts, and mixing them up is the fastest way to miscut a stringer. The total rise is the full vertical climb. Each riser is one vertical step face — your foot lifts exactly one riser per step. Each tread is the flat part you stand on, and its depth is also called the unit run. The total run is the whole horizontal footprint. The stringer is the notched board running diagonally underneath that carries the treads, and its length is the hypotenuse of the rise-and-run triangle.

Two facts surprise first-time stair builders. First, there is always one fewer tread than risers, because the upper floor does the job of the top tread. Second, the stringer is pure Pythagoras — it is simply the hypotenuse of the right triangle your rise and run describe.

Code-compliant and comfortable are not the same thing, and a good staircase is both. In the US, the International Residential Code (IRC) Section R311.7 sets the geometric envelope for residential stairs:

The 3/8 in variation rule is the one most DIY stairs fail: every riser in a flight must be nearly identical, because your feet climb on rhythm and one tall step trips people. Always confirm the edition your local building department has adopted — The Spruce has a plain-English rundown of the IRC stair requirements if you want the full picture before you cut.

The comfort rules

Code keeps stairs legal; the old carpenter rules keep them pleasant. The 7-11 rule says riser + tread should total 17–18 in — a 7 in riser with an 11 in tread is the classic pairing. The older 2R + T rule says twice the riser plus the tread should land near 24–25 in. Both describe the same idea: a taller step wants a shallower tread, and a short step wants a deeper one.

This stair calculator checks both for you. If your riser plus tread falls outside 17–18 in, it says so under the results — and if you want to see exactly how steep your design is, run the rise and run through our slope calculator to get the pitch angle.

Most miscut stringers trace back to one of five mistakes. Avoid them and the calculator's numbers will land on the wood exactly.

• Measuring to the subfloor. Measure finished floor to finished floor. A 3/4 in hardwood floor added later shifts every riser by 3/4 in — the bottom one grows, the top one shrinks.
• Unequal risers. Mark every riser from the same layout, and check the 3/8 in variation rule with a tape before you cut. Your feet expect rhythm; give it to them.
• Forgetting the bottom riser sits on the floor. The first riser includes the tread thickness of the tread you stand on, and the top riser meets the upper floor. Account for tread thickness at both ends of the layout.
• Counting nosing as run. Nosing overhangs the riser for toe room, but it adds nothing to the run. The run is nosing to nosing — this is also why the unit run input defaults to 10 in.
• Skipping the dry fit. Cut one stringer, test-fit it, and use it as the pattern for the rest. Stringers usually come in pairs or triples on 2×12 stock, and one bad layout multiplied is an expensive lesson.

When you lay out the stringer, double-check every number against the calculator's breakdown before the saw touches wood. If your tape measure and your lumber list are in different units, convert first with our length converter. For a deeper walkthrough of code-compliant stair framing, this stairs building guide covers IRC limits and stringer span tables in detail.