Stair calculator

Enter the floor-to-floor height to get the number of steps, riser height, tread depth and stringer length, with a check against the residential building code.

By the Calcist team · Checked against known answers · Updated October 27, 2026

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How the stairs are worked out

Start with the total rise: the height from the finished floor at the bottom to the finished floor at the top. Divide it into equal risers that are no taller than the code allows. There's always one fewer tread than risers, because the top floor is the last step.

Risers = total rise ÷ 7.75 in, rounded up
Riser height = total rise ÷ risers
Treads = risers − 1
Total run = treads × tread depth
Stringer length = √(total rise² + total run²)
Angle = arctan(riser ÷ tread)

Worked example

A total rise of 105 inches: 105 ÷ 7.75 = 13.5, so round up to 14 risers of 105 ÷ 14 = 7.5 inches. That gives 13 treads. At 10 inches deep, the total run is 130 inches. The stringer is √(105² + 130²) = 167.1 inches (13 ft 11.1 in) along the line of the nosings, and the stairs climb at arctan(7.5 ÷ 10) = 36.9°. The comfort check: 2 × 7.5 + 10 = 25 inches.

What the building code says

Most US homes are built to the International Residential Code (IRC). Section R311.7 sets these limits for a residential stairway (your city or county may amend them, so check locally):

Rule	IRC limit
Riser height (R311.7.5.1)	7¾ in maximum; risers in a flight may differ by no more than ⅜ in
Tread depth (R311.7.5.2)	10 in minimum, nosing to nosing; treads may differ by no more than ⅜ in
Headroom (R311.7.2)	6 ft 8 in minimum
Width (R311.7.1)	36 in minimum
Height of one flight (R311.7.3)	151 in maximum between floors or landings

The 2R + T comfort rule

A long-standing design rule of thumb says two risers plus one tread should come to about 24 to 25 inches, which matches a normal walking stride. It isn't in the IRC, but stairs well outside that range feel too steep or too shallow.

Limitations

It's for straight stairs. Winders, spirals and landings follow extra rules.
Measure the rise between finished floors. Adding flooring later changes the first and last riser.
The stringer length is the diagonal along the steps. Buy a longer board to allow for the cuts at the top and bottom.
Commercial buildings follow the IBC, which has stricter limits (7 in max riser, 11 in min tread).

Sources

ICC: 2021 International Residential Code, Chapter 3, Section R311.7 Stairways

How we checked this

Before every update, this calculator is run in a real browser with these known answers, and it must match all of them:

105 in rise, 10 in treads: 14 risers of 7.5 in ✓
Same: stringer 167.11 in, angle 36.87°, 2R + T = 25 ✓
108 in rise into a 132 in run: 13 treads of 10.154 in ✓
Forcing 10 risers on 105 in gives 10.5 in risers, which fails IRC R311.7.5.1 ✓
160 in rise passes riser and tread limits but needs a landing (R311.7.3, 151 in) ✓
8 in rise: 2 risers and 1 tread (singular) ✓

Last checked October 26, 2026. Spotted something wrong? The math is done in your browser with the formula shown on this page, so you can check any result by hand.

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Questions people ask

How many steps do I need for a 9-foot rise?

A 9-foot (108 in) rise needs at least 14 risers of about 7.71 inches, since 13 risers would be 8.3 inches, over the IRC limit of 7¾ in. That's 13 treads.

What is the maximum riser height for stairs?

7¾ inches under IRC R311.7.5.1 for homes. Commercial buildings under the IBC are limited to 7 inches.

What is the minimum tread depth?

10 inches for homes under IRC R311.7.5.2, measured nosing to nosing. The IBC requires 11 inches in commercial buildings.

How long should a stair stringer be?

Use the Pythagorean theorem: √(total rise² + total run²). For a 105 in rise and 130 in run, that's 167.1 inches. Buy a longer board to allow for cuts.

What is a comfortable stair angle?

Most home stairs are between about 30° and 37°. The IRC limits (7¾ in risers, 10 in treads) allow up to about 37.8°.

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