Stair calculator: rise, run and stringer length

Every stair starts with one number: the total rise, measured from finished floor to finished floor. Divide it into equal risers and you know how many steps you need. The calculator lists the step count closest to your target riser height plus two options on each side, so you can trade comfort against floor space.

For each option you get:

• riser height and tread depth (run per step)
• number of treads (one fewer than risers, because the top floor is the last step)
• total run, stair angle and stringer length along the nosing line
• the comfort values 2R + T, R + T and T − R
• a pass/fail check against IRC R311.7 and UK Approved Document K
• the length of the floor opening needed for your headroom

By default the tread comes from the classic comfort formula 2R + T = 63 cm (about 24.8 in). If your run is fixed, enter it and the calculator divides it evenly instead. A dimensioned section drawing shows the steps, the floor above and the headroom line. Everything runs in your browser, no sign-up, and the PDF and Excel export is free.

In the US, residential stairs follow the International Residential Code as adopted, and sometimes amended, by your state or city. In England, Approved Document K gives the guidance for private stairs in dwellings.

Rule	2021 IRC R311.7	Approved Document K, private stair
Riser height	max 7-3/4 in	150–220 mm
Tread depth (going)	min 10 in	220–300 mm
Stair angle	not set directly	max 42°
2R + going	not set	550–700 mm
Headroom	min 6 ft 8 in	min 2 m (reduced for loft conversions)
Width	min 36 in clear	not covered here

The IRC also limits variation: the tallest riser and the deepest tread in a flight may not exceed the smallest by more than 3/8 in. A single flight may rise at most 12 ft 7 in between floors or landings. Always confirm the edition and amendments your building department uses.

Example: total rise 108 in (9 ft) from finished floor to finished floor, target riser 7.5 in, tread from 2R + T = 24.8 in.

Risers	Riser	Tread	Total run	Angle	IRC
13	8.31 in	8.19 in	98.3 in	45.4°	fails
14	7.71 in	9.38 in	121.9 in	39.5°	tread too short
15	7.20 in	10.40 in	145.6 in	34.7°	passes
16	6.75 in	11.30 in	169.6 in	30.8°	passes

The 15-riser option works:

1. Riser: 108 / 15 = 7.2 in (just under 7-1/4 in)
2. Tread: 24.8 − 2 × 7.2 = 10.4 in (about 10-3/8 in)
3. Treads: 15 − 1 = 14; total run 14 × 10.4 = 145.6 in, about 12 ft 1-5/8 in
4. Angle: arctan(7.2 / 10.4) = 34.7°
5. Stringer line: √(108² + 145.6²) = 181.3 in, about 15 ft 1-5/16 in

It also meets the UK private-stair limits: 183 mm rise, 264 mm going, 34.7° pitch, 2R + G = 630 mm.

Short on space? Keep 14 risers and fix the tread at 10.5 in: total run 136.5 in, angle 36.3°, 2R + T = 25.9 in. That passes the IRC numbers but is a bit steeper to climb.

Walking up, your head passes under the floor above, so the opening must be long enough to keep clear headroom over every nosing. The calculator finds where the floor may still overhang the stair and measures the opening from there to the top landing.

Continuing the 15-riser example with an 11 in floor assembly (joists, subfloor and ceiling) and 6 ft 8 in (80 in) headroom: the floor may extend 14.2 in over the bottom of the run, so the opening is 131.5 in, about 10 ft 11-1/2 in long.

Include the whole floor assembly in the thickness, including the ceiling finish below.

• Measure finished to finished. If flooring is not installed yet, add its thickness at the bottom and the top, or the first or last riser will be off.
• Keep every step the same. The 3/8 in IRC tolerance is tight; feet notice an odd step.
• Treads = risers − 1. Planning 15 treads for 15 risers adds a full tread to the run.
• Tread depth is nosing to nosing. A nosing makes the board deeper than the tread depth used in the math.
• Stringer length is not board length. Buy stock longer than the stringer line to cover the top and bottom cuts; 2×12 is common for cut stringers.
• Get the structure checked. Stringer spans, guards and handrails have their own rules; ask your building department or a pro.

Pouring concrete steps? The concrete calculator has a steps mode. For angles and right triangles, use the triangle calculator.