Stair Calculator
A 42 inch rise, a 7 inch target riser, and a 10 inch tread is 6 risers, 5 treads, a 7.00 inch actual riser, a 50.00 inch run, and a 65.30 inch stringer.
Last updated . Total rise starts at 42 in, which is 3 ft 6 in. The target riser starts at 7 in. Tread depth starts at 10 in. Nosing starts at 1 in.
A stair calculator for the riser count, the tread count, the actual riser, the total run, the stringer length, and the angle. The flag compares the result with the common 2021 IRC residential limits.
Concrete volume for solid steps: concrete steps calculator. Deck boards: deck calculator. A level guard between posts: baluster spacing calculator. A sloping walk from a rise: ramp calculator.
Stair risers and stringer
Tread depth is the going, measured nosing to nosing, which is the 2021 IRC R311.7.5.2 measurement. Total run uses that going. The nosing is the projection past the riser and does not lengthen the run. The tread board depth is the going plus the nosing. The stringer is the straight diagonal of the total rise and total run, with no tail past the bottom and no extra at the top. Concrete volume for solid steps is a different page.
Results
How the risers and the stringer are counted
The riser count rounds the total rise divided by the target riser. The actual riser is the total rise divided by that count, so the risers in one flight match. Treads are one fewer than the risers. Total run is treads × tread depth. For 42 in, a 7 in target, and a 10 in tread, that is 6 risers, a 7.00 in riser, 5 treads, and a 50.00 in run.
Stringer length is sqrt(total rise² + total run²). The angle is atan(total rise ÷ total run). Nosing is not part of the run. The tread board depth is the going plus the nosing, 11.00 in at the default. Equal risers meet the code’s 3/8 in uniformity rule by the math. The finished stair still has to be measured.
The limits used for the flag are the 2021 International Residential Code. R311.7.5.1: riser height not more than 7 3/4 in (196 mm). R311.7.5.2: tread depth not less than 10 in (254 mm), measured nosing to nosing. R311.7.5.3: a nosing projection of 3/4 in to 1 1/4 in, not required where the tread depth is at least 11 in. Those sections are quoted in the City of Boise IRC stair handout and the riser and tread limits are in ICC’s 2021 IRC plan-review slides. Stairs that do not serve a building, porch, or deck can fall outside R311.7. This page does not check width, headroom, landings, or handrails, and it is not a permit determination.
Target riser on a 42 inch rise
Tread depth stays 10 in and the nosing stays 1 in. Only the target changes.
| Target | Risers | Actual riser | Treads | Run | Stringer | IRC flag |
|---|---|---|---|---|---|---|
| 6.5 in | 6 | 7.00 in | 5 | 50.00 in | 65.30 in | Within |
| 7 in | 6 | 7.00 in | 5 | 50.00 in | 65.30 in | Within |
| 7.5 in | 6 | 7.00 in | 5 | 50.00 in | 65.30 in | Within |
| 8 in | 5 | 8.40 in | 4 | 40.00 in | 58.00 in | Riser over 7.75 in |
Worked example
Enter 42 in of total rise, a 7 in target, a 10 in tread, and a 1 in nosing. Risers read 6. Treads read 5. Actual riser reads 7.00 in · 177.80 mm. Total run reads 50.00 in · 4.17 ft · 1.27 m. Stringer length reads 65.30 in · 5.44 ft · 1.66 m. Angle reads 40.03°. Tread board reads 11.00 in. The flag says the result is within 2021 IRC R311.7.5.
Stair questions
How many risers are in a 42 inch rise?
Leave the total rise at 42 in and the target at 7 in. Risers read 6. The actual riser reads 7.00 in · 177.80 mm. 42 ÷ 7 is 6, so the actual riser matches the target.
How many treads, and how long is the run?
Treads read 5, one fewer than the risers, because the top of the flight is the landing. Leave the tread at 10 in. Total run reads 50.00 in · 4.17 ft · 1.27 m. That is 5 × 10 in.
How long is the stringer?
Stringer length reads 65.30 in · 5.44 ft · 1.66 m. The angle reads 40.03°. The length is sqrt(42² + 50²) = sqrt(4,264). It is the diagonal of the rise and the run, with no extra tail at the bottom.
What are the IRC riser and tread limits?
The 2021 IRC R311.7.5.1 maximum riser is 7.75 in (7 3/4 in). R311.7.5.2 minimum tread depth is 10 in. R311.7.5.3 calls for a nosing of 0.75 in to 1.25 in unless the tread is at least 11 in. The default flag reads: Within 2021 IRC R311.7.5: riser 7.00 in is not over 7.75 in, tread 10.00 in is at least 10 in, and nosing 1.00 in is from 0.75 in to 1.25 in. Local amendments can differ. This is not a permit review.
What if the target riser is 8 inches?
Set the target to 8 in and leave the total rise at 42 in. Risers read 5. The actual riser reads 8.40 in · 213.36 mm. Treads read 4. Total run reads 40.00 in · 3.33 ft · 1.02 m. Stringer length reads 58.00 in · 4.83 ft · 1.47 m. The angle reads 46.40°. The flag reads: Outside 2021 IRC R311.7.5: riser 8.40 in is over the 7.75 in maximum.
What does the nosing change?
The nosing does not change the run. Tread depth is the going from nosing to nosing. At the default, the tread board reads 11.00 in, which is the 10 in going plus the 1 in nosing. Set the nosing to 0 and leave the tread at 10 in. The run stays 50.00 in. The flag reads: Outside 2021 IRC R311.7.5: nosing 0.00 in is outside 0.75 in to 1.25 in.
What if the tread is 11 inches and the nosing is 0?
Set the tread to 11 in and the nosing to 0. Risers stay 6 and the actual riser stays 7.00 in. Treads stay 5. Total run reads 55.00 in · 4.58 ft · 1.40 m. Stringer length reads 69.20 in · 5.77 ft · 1.76 m. The angle reads 37.37°. The tread board reads 11.00 in. The flag reads: Within 2021 IRC R311.7.5: riser 7.00 in is not over 7.75 in, tread 11.00 in is at least 11 in, so a nosing is not required.
Is this the concrete steps calculator?
No. This page counts risers, treads, the stringer, and the angle for a stair or a deck stair. It does not calculate concrete volume. Solid steps from grade, plus a landing, are the concrete steps calculator. Deck boards and joists are the deck calculator.