How to Calculate Stairs: Risers, Treads and Stringer Length

To build stairs you need the number of steps, the height of each riser, the depth of each tread, and the length of the stringer, the sloped board the treads sit on. It all starts from the total rise, measured floor to floor.

For learning and planning practice. Check your local building codes and the manufacturer’s numbers before you build: the code numbers here are typical values, not the law where you live.

Try it with your own problem ↓

The steps

Measure the total rise in inches, from finished floor to finished floor.
Divide by the tallest riser allowed (7 3/4" is typical in US house codes) and round up. That is the number of risers.
Riser height = total rise ÷ number of risers.
There is one tread fewer than risers. Total run = treads × tread depth (at least 10" is typical).
Stringer length = √(rise² + run²), by the Pythagorean theorem.

A worked example

The total rise is 112 inches. With risers at most 7 3/4" and 10" treads, find the risers, the treads, the total run and the stringer length.

Risers: 112 ÷ 7.75 ≈ 14.45, so round up to 15 risers.
Each riser: 112 ÷ 15 ≈ 7.467", about 7 7/16".
Treads: 15 − 1 = 14. Total run: 14 × 10 = 140" = 11' 8".
Stringer: √(112² + 140²) = √32,144 ≈ 179.29", about 14' 11 5/16".
Comfort check: 2 × riser + tread = 2 × 7.467 + 10 ≈ 24.93", inside the usual 24" to 25".

15 risers of about 7 7/16", 14 treads, a total run of 11' 8", and a stringer about 14' 11 5/16" long.

Why it works

Every step must be the same height or people trip, so the rise is shared out equally among the risers. Rounding the count up makes sure each share is no taller than the limit. The stairs make a right triangle with the floor and the wall: the rise and the run are its legs and the stringer is the hypotenuse, which is why the Pythagorean theorem gives its length.

Try it with your own problem

Open The Framing Square (free) with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: total rise 112 inchesOpens The Framing Square with this example

Or try these

More carpentry math, every step written out: open The Framing Square.

Common mistakes

Rounding the riser count down. 14 risers would be 8" each, taller than allowed. Always round up.
Counting as many treads as risers. The top step is the upper floor, so there is one tread fewer.
Measuring to the subfloor. Measure finished floor to finished floor, or the first or last step comes out a different height.
Rounding every step. 15 × 7 7/16" = 111 9/16", not 112". Lay out with the exact 7.467" if you can.

Questions people ask

How many steps for a 104 inch rise?

104 ÷ 7.75 ≈ 13.42, so 14 risers of 104 ÷ 14 ≈ 7 7/16" each, and 13 treads.

What is the 2R + T rule?

Two risers plus one tread should come to about 24" to 25", one comfortable stride. Here 2 × 7.467 + 10 ≈ 24.9".

How steep are these stairs?

tan⁻¹(riser ÷ tread) = tan⁻¹(7.467 ÷ 10) ≈ 36.7°.

Keep learning

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