Number of steps, riser height, tread depth, stringer length and stair angle from total rise and run, checked against IRC riser and tread limits.
By AdminDrafted with AI writing toolsUpdated Checked examples: 5
15 risers of 7.2 in (183 mm) and 14 treads of 10 in (254 mm) climb 108 in (2,743 mm) at a pitch of 35.8°. Both dimensions are within the IRC limits.
Rounded up so no riser is taller than the target.
The top floor serves as the last step, so there is one tread fewer than risers.
The slope of the line through the tread nosings.
From the foot of the first riser to the top nosing; buy a board long enough to add the bottom and top cuts.
Blondel's rule of thumb: 24–25 in (about 63 cm) feels natural.
Table 1.1 limits: rise 150–220 mm, going 220–300 mm, pitch at most 42°, 2R + G between 550 and 700 mm. This stair meets all four.
The number of risers is the floor-to-floor rise divided by the tallest riser you will accept, rounded up, so every riser is the same height and none exceeds your limit. The run is divided by one fewer than the risers to give the tread depth, because the upper floor forms the top step. The pitch is arctan(riser ÷ tread), the slope of the line through the nosings, and the stringer length is √(rise² + run²).
The default stair, 108 in (9 ft) floor to floor over 140 in of run, gives 15 risers of 7.2 in and 14 treads of 10 in at a pitch of 35.8°. That meets the US residential limits of a 7¾ in maximum riser and 10 in minimum tread (2021 IRC R311.7.5; 2024 IRC R318.7.5).
Measure the rise between finished floor surfaces. Tread depth here is the going, nosing to nosing. The check covers risers and treads only; stair width, headroom, handrails and local amendments need checking separately.
For a straight flight, round the floor-to-floor rise ÷ your tallest acceptable riser up to a whole number of risers, then share the run among one fewer treads. A 105 in rise with a 7.5 in limit takes 14 risers of 7.5 in, and 140 in of run gives 13 treads of 10.77 in.
Tread depth here is the going: the horizontal distance from one nosing to the next. With an overhanging nosing, the tread board itself is deeper than the going.
US homes are limited to risers of at most 7¾ in and treads of at least 10 in (2021 IRC R311.7.5.1 and R311.7.5.2, renumbered R318.7.5 in the 2024 IRC). The City of Boise stair handout sets out both limits.
Those limits make the steepest code stair arctan(7.75 ÷ 10) = 37.78°. A flight that meets them needs at least 10 in of run per tread: 15 risers and 14 treads need 140 in.
The IRC also sets stair width, headroom, handrail height and a 3/8 in limit on how much risers or treads may vary within one flight. Check those separately for your layout.
England's Approved Document K allows private stairs with a rise of 150–220 mm, a going of 220–300 mm, a pitch of at most 42°, and twice the rise plus the going between 550 and 700 mm.
A 2,800 mm rise over 3,600 mm of run with a 180 mm limit gives 16 risers of 175 mm and 15 goings of 240 mm. Twice the rise plus the going is 590 mm and the pitch is 36.10°, inside all four ranges.
The same flight fails the IRC tread minimum, because 240 mm is less than 10 in (254 mm). Check the rules where the stair will be built.
Pitch follows the line through the tread nosings, so it comes from one riser and one going. Approved Document K defines pitch on that line.
The stringer estimate is the diagonal of the whole flight, √(rise² + run²): 176.82 in, or 14.73 ft, for 108 in over 140 in. Its slope is steeper than the pitch, 37.65° against 35.75°, because the flight has 15 risers but only 14 goings.
Actual stringer stock depends on how the stringer bears at the top and bottom and how it is notched, so allow for those details on top of the diagonal.
"Default" is the 108 in rise over 140 in of run with a 7.5 in limit. "Exact target count" is the 105 in rise above. "Short tread" is a 100 in rise over 100 in of run with a 7.75 in limit.
"Metric flight" is the 2,800 mm stair, shown in inches. "Exact IRC boundaries" is a 100.75 in rise over 120 in of run with a 7.75 in limit, which lands exactly on both IRC limits.
| Scenario | Risers | Riser height, in | Tread going, in | Pitch, degrees |
|---|---|---|---|---|
| Default | 15.000000 | 7.200000 | 10.000000 | 35.753887 |
| Exact target count | 14.000000 | 7.500000 | 10.769231 | 34.854456 |
| Short tread | 13.000000 | 7.692308 | 8.333333 | 42.709390 |
| Metric flight | 16.000000 | 6.889764 | 9.448819 | 36.098284 |
| Exact IRC boundaries | 13.000000 | 7.750000 | 10.000000 | 37.775684 |
The short-tread flight fails the 10 in minimum with 8.33 in treads. Its 12 treads need 120 in of run to pass.
For concrete steps, work out the volume with the concrete calculator. For an attached deck, count boards and joists with the deck calculator.
Checked against: ⌈108/7.5⌉ = 15; 108/15 = 7.2 in; 140/14 = 10 in; √(108² + 140²) = 176.816 in; pitch atan(7.2/10) = 35.754°, pitch being the slope of the line through the nosings (Approved Document K, 2013, Appendix A)
Checked against: Hand calculation: 105/7.5 = 14 exactly; 140/13 = 10.769 in; 105:140:175 is a 3-4-5 triangle
Checked against: ⌈100/7.75⌉ = 13; 100/12 = 8.33 in < 10 in (2021 IRC R311.7.5.2); pitch atan(7.6923/8.3333) = 42.709°
Checked against: Hand calculation: ⌈2800/180⌉ = 16; 2800/16 = 175 mm; 3600/15 = 240 mm < 254 mm
In US homes it is 7¾ in, with treads at least 10 in deep and no more than 3/8 in difference between the tallest and shortest riser in a flight (2021 IRC R311.7.5.1–R311.7.5.2; 2024 IRC R318.7.5). Buildings under the 2021 IBC (§1011.5.2) need risers of 4 to 7 in and treads of at least 11 in, except R-3 buildings and stairs inside R-2 dwelling units, which may use 7¾ in and 10 in.
At least 14 risers. Divide the rise by the maximum riser and round up: 108 in ÷ 7.75 in = 13.9, so 14 risers of 7.71 in; a 7.5 in target gives 15 risers of 7.2 in. There is one tread fewer than risers (13 or 14), because the upper floor acts as the last step. Measure from finished floor to finished floor, including flooring.
This calculator estimates the total rise/run diagonal as √(rise² + run²). For 108 in of rise over 140 in of run, that is 176.8 in, or 14.73 ft. This diagonal is distinct from the line through the tread nosings, because there is one fewer tread than risers. Actual stringer stock and cuts depend on the bearing and connection details; the diagonal alone does not determine a finished board length.
For US homes, the IRC's 7¾ in riser over a 10 in tread gives a maximum of arctan(7.75/10) ≈ 37.8°. IBC stairs, at 7 in over 11 in (2021 IBC §1011.5.2), top out near 32.5°. England's Approved Document K, Table 1.1, allows 42° for a private stair, with rises of 150–220 mm, goings of 220–300 mm and twice the rise plus the going between 550 and 700 mm.
The IRC stairway section (2021 R311.7; 2024 R318.7) requires a clear width of at least 36 in and headroom of 6 ft 8 in. Handrails go 34 to 38 in above the tread nosings (2021 IRC R311.7.8; 2024 IRC R320). Riser heights and tread depths may differ by at most 3/8 in within one flight, so cut every step from the same layout.
This calculator includes 5 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.