Rise and run in one sentence
Rise is the vertical height of one step and run is its horizontal depth; the stair's overall slope is total rise over total run. A rise and run calculator works the overall numbers back into steps. Because the treads are one fewer than the risers, a change of one riser changes the tread depth of every step.
If only the height is fixed and you can choose the tread, the stair calculator is quicker. If neither count works, the climb is too steep for the space; a landing with a turn folds the run into two shorter legs.
Standard stair rise and run
The standard stair rise and run for a US house is a riser of at most 7-3/4 in and a tread of at least 10 in under the IRC[1]. These are limits, not targets. Most builders aim near a 7 to 7-1/2 in riser and a 10-1/2 to 11 in tread.
| Code | Riser (rise) | Tread (run / going) |
|---|---|---|
| IRC (US homes)[1] | ≤ 7-3/4 in | ≥ 10 in |
| IBC (US commercial)[2] | 4 to 7 in | ≥ 11 in |
| England, private stair[3] | 150 to 220 mm | 220 to 300 mm |
| Canada, private stair[4] | 125 to 200 mm | 255 to 355 mm |
| Australia[5] | 115 to 190 mm | 240 to 355 mm |
How many steps for a given height
The number of steps is the total rise divided by 7-3/4 in, rounded up. This table uses the IRC maximum and shows the riser you end up with; the run assumes 10-1/2 in treads.
| Total rise | Risers | Riser height | Treads | Total run |
|---|---|---|---|---|
| 2′ 0″ (610 mm) | 4 | 6″ | 3 | 2′ 7-1/2″ |
| 3′ 0″ (914 mm) | 5 | 7-3/16″ | 4 | 3′ 6″ |
| 4′ 0″ (1219 mm) | 7 | 6-7/8″ | 6 | 5′ 3″ |
| 5′ 0″ (1524 mm) | 8 | 7-1/2″ | 7 | 6′ 1-1/2″ |
| 6′ 0″ (1829 mm) | 10 | 7-3/16″ | 9 | 7′ 10-1/2″ |
| 7′ 0″ (2134 mm) | 11 | 7-5/8″ | 10 | 8′ 9″ |
| 8′ 0″ (2438 mm) | 13 | 7-3/8″ | 12 | 10′ 6″ |
| 8′ 6″ (2591 mm) | 14 | 7-5/16″ | 13 | 11′ 4-1/2″ |
| 9′ 0″ (2743 mm) | 14 | 7-11/16″ | 13 | 11′ 4-1/2″ |
| 9′ 6″ (2896 mm) | 15 | 7-5/8″ | 14 | 12′ 3″ |
| 10′ 0″ (3048 mm) | 16 | 7-1/2″ | 15 | 13′ 1-1/2″ |
| 10′ 6″ (3200 mm) | 17 | 7-7/16″ | 16 | 14′ 0″ |
| 11′ 0″ (3353 mm) | 18 | 7-5/16″ | 17 | 14′ 10-1/2″ |
Stair angle calculator: slope and comfort
The stair angle is the arctangent of riser ÷ tread, and the table above shows it for every riser count; the IRC limits (7-3/4 over 10) allow up to 37.8°. The NBS stair-safety guidelines cite 2R + T = 63 cm (about 25 in) and a 25–30° energy-optimal slope from the research literature[6]. England caps a private stair at 42°[3]. In the results table, the angle column lets you trade a slightly taller riser for a deeper, safer tread.
- Rise and run calculator for ramps or roofs: the same ratio is a roof pitch when quoted per 12 in of run.
- For outdoor steps the tread is often set by deck boards; see the deck stair calculator, or the concrete stair calculator for poured steps.
Frequently asked questions
What does a standard stair rise and run calculator use?
The IRC limits for homes: a riser of at most 7-3/4 in and a tread of at least 10 in. Commercial stairs under the IBC use 4 to 7 in risers and 11 in treads. This calculator also checks the UK, Canadian and Australian rules.
How many steps for 8 feet?
A 96 in rise needs 13 risers of 7-3/8″ under the IRC, with 12 treads.
What is a good rise and run for stairs?
About 7 to 7-1/2 in of rise with 10-1/2 to 11 in of run. That keeps 2R + T near 25 in, which stair research describes as comfortable.
How do I calculate rise and run?
Divide the total rise by the number of risers for the rise, and the total run by the number of treads (risers minus one) for the run.
How do I calculate stair angle?
Take the arctangent of riser ÷ tread. A 7-1/2 in riser over a 10 in tread is 36.9°; 7 over 11 is 32.5°.
Sources
- 2021 International Residential Code, Chapter 3: Building Planning (R301.5, R311.7 stairways, R312 guards)
- 2021 International Building Code, Chapter 10: Means of Egress (1011.5.2, 1015.3)
- Approved Document K: Protection from falling, collision and impact (2013 edition, for use in England)
- National Building Code of Canada 2020, Division B, Part 9, Section 9.8 Stairs, ramps, handrails and guards
- ABCB Housing Provisions, Part 11.2 Stairway and ramp construction (NCC 2022)
- Guidelines for Stair Safety, Building Science Series 120 (Archea, Collins, Stahl)