Published August 16, 2026 · Updated August 23, 2026 · By Tupep
Where the number comes from
Ask why stairs are built around a 7 in riser and an 11 in tread and you get “because code says so.” Code says something close, but code did not invent it. The number comes from how a person walks, and once we see the reasoning we can tell whether an unusual stair will feel wrong before building it.
Start with a flat walk. An adult stride on level ground covers roughly 24 to 25 in per step. Stairs interrupt that stride, and the leg has to move forward and lift at once. Lifting costs more per inch than moving forward, and the old carpentry approximation is about twice as much, so a step that trades vertical for horizontal at 2 to 1 keeps effort per step roughly constant.
The three rules of thumb
That reasoning produces the oldest formula in stair building.
- 2R + T = 24 to 25 in. Two rises plus one tread. This is the effort-equivalence rule and the most useful of the three.
- R + T = 17 to 18 in. A quick sanity check on proportion.
- R x T = 72 to 75. An older comfort check that keeps extremes from passing the first two.
Run 7 and 11 through all three: 25, 18, and 77. It passes the first two cleanly and sits just above the third, which is why 7 and 11 is a target rather than a magic number. Run 7.5 and 10 and you get 25, 17.5 and 75, which passes all three and is the other combination you see constantly in real houses.
| Rise | Tread | 2R + T | R + T | R x T | How it feels |
|---|---|---|---|---|---|
| 4 in | 17 in | 25 | 21 | 68 | Garden step, deliberate slow pace |
| 5 in | 15 in | 25 | 20 | 75 | Monumental steps, works outdoors |
| 6 in | 13 in | 25 | 19 | 78 | Gentle, eats floor space |
| 7 in | 11 in | 25 | 18 | 77 | The classic, comfortable up and down |
| 7.5 in | 10 in | 25 | 17.5 | 75 | Typical house stair, still fine |
| 8 in | 9 in | 25 | 17 | 72 | Passes the formula, feels like a ladder |
| 7 in | 9 in | 23 | 16 | 63 | Cramped, heel overhangs on the way down |
The last two rows are the interesting ones. The 8 and 9 combination satisfies 2R + T perfectly and is still a bad stair, so the formula is necessary but not sufficient. The reason is the foot. An adult shoe is about 11 to 12 in long, and a 9 in tread leaves the heel hanging in space on the way down, which is where people fall. That is the real argument for 11 in of tread: it is a foot-length number, not a stride-length number.
Why the rule breaks at the ends
Garden steps at 4 in of rise and 17 in of tread satisfy 2R + T and feel fine, because at that angle you are walking a ramp with interruptions and your stride adapts. At the steep end the formula stops protecting you, because the limit becomes knee and hip flexion rather than energy per step. A tall riser demands a range of motion many people do not have, which is why codes cap riser height with a hard number.
Consistency beats geometry
Here is the part that matters more than the arithmetic. After a step or two, people stop looking at the stair. The foot learns the rhythm from the first couple of treads and then runs open loop, especially going down and especially while carrying something. The nervous system predicts where the next tread is rather than measuring it.
So the most dangerous thing in a stair is not a riser slightly too tall. It is one riser different from the others. A 3/8 in discrepancy catches a toe or drops a heel through empty air, at the moment nobody is looking. That is why codes commonly limit the difference between the tallest and shortest riser in a flight. The allowable variation, along with maximum riser, minimum tread, nosing projection and handrail requirements, is jurisdiction dependent, so verify all of it with your building department.
Why the division has to come out even
Total rise is 96 in and you want a 7.5 in riser. 96 / 7.5 = 12.8, and you cannot build 12.8 risers. Cut twelve at 7.5 in and that is 90 in, leaving 6 in at the bottom as a riser 1.5 in shorter than the rest. That is a guaranteed fall and a correction notice.
Instead pick the riser count and let the height fall out. 96 / 13 = 7.385 in, thirteen equal risers. Total rise divided by riser count is the riser height, with no leftover to place anywhere. We do this before touching a framing square, and if it produces an ugly fraction, that fraction is the answer.
Using the rule to size a stair
Solve 2R + T = 25 for the tread once you know the riser and you get a footprint to check against the space you have. For a 110 in total rise:
| Risers | Riser height | Tread from 2R + T = 25 | Treads | Total run |
|---|---|---|---|---|
| 14 | 7.857 in | 9.29 in | 13 | 120.7 in |
| 15 | 7.333 in | 10.33 in | 14 | 144.7 in |
| 16 | 6.875 in | 11.25 in | 15 | 168.8 in |
Fourteen risers gives a compact stair with a 9.29 in tread, which the formula likes and your heel will not, plus a riser probably over your local limit. Sixteen gives a comfortable stair that eats 14 feet of floor. Fifteen is the compromise most houses land on.
One last practical note
The nosing is free run. A 3/4 to 1-1/4 in nosing adds tread depth for the foot without adding an inch to the footprint, which is why almost every stair has one and why codes commonly require one when the run is shallow. If you are short on total run, look at the nosing before stealing from riser height.
Related guides
- Stair Riser and Tread Count for an 8 ft Basement Drop
- Deck Stair Stringer Layout: Rise, Run, and Code
- Deck Framing Lumber List for a 10×12 Deck
- Door and Window Casing for a Full Remodel
Sources and Further Reading
Run your own numbers with the Stair Calculator, or browse every tool on the calculators index. Coverage figures and material constants are cross-checked against manufacturer technical data sheets before publication. See our Methodology page for how figures are selected and verified.
Planning estimate only. Results assume standard conditions and are intended for material planning. Verify against your product’s technical data sheet and your local building code before purchasing. Structural, electrical, and gas work should be specified by a licensed professional.
Last updated: August 23, 2026
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