How the calculator works it out
Stairs are laid out from two measurements: the total rise (how far up) and the total run (how far along). The calculator picks the fewest risers that keep each one at or under the code maximum, divides the rise equally between them, and divides the run between the treads. There is one fewer tread than risers, because the last step up lands on the upper floor.
Risers = total rise ÷ 7.75, rounded up · Riser height = total rise ÷ risers
Treads = risers − 1 · Tread depth = total run ÷ treads
Stringer length = √(total rise² + total run²)
Throat = board depth − riser × tread ÷ √(riser² + tread²)
Worked example: a 9 ft basement stair
The floors are 108 inches apart and there are 135 inches of floor for the stair to land on. 108 ÷ 7.75 = 13.9, so 14 risers of 7.714 inches (just over 7 11/16). That leaves 13 treads of 135 ÷ 13 = 10.385 inches (about 10 3/8), above the 10 inch minimum. The stringer runs √(108² + 135²) = 172.9 inches, 14 ft 5 in, so cut it from a 16 ft 2×12. Each notch removes 7.714 × 10.385 ÷ 12.94 = 6.19 inches of depth, leaving a 5.06 inch throat in the 11¼ inch board: just over the 5 inch minimum. The stair is 36 inches wide, which needs three cut stringers at 18 inches apart. With 14 risers it needs a handrail, and with treads under 11 inches each needs a nosing. The 135 inch run is longer than the 6 ft that AWC DCA 6 allows a cut stringer to span unsupported, so the calculator marks the span as one to check: outdoors you would add a post or a landing, and indoors the stringers are usually fastened to a wall or framing along their length. This stair is loaded when the page opens.
The rules it checks
| Rule | Limit | Source |
|---|---|---|
| Riser height | 7¾ in maximum | IRC R311.7.5.1 |
| Tread depth | 10 in minimum | IRC R311.7.5.2 |
| Riser or tread variation in a flight | 3/8 in maximum | IRC R311.7.5.1, R311.7.5.2 |
| Rise of one flight | 12 ft 7 in (151 in) maximum between floors or landings | IRC R311.7.3 |
| Headroom | 6 ft 8 in (80 in) minimum | IRC R311.7.2 |
| Width | 36 in minimum, above handrail height | IRC R311.7.1 |
| Nosing | ¾–1¼ in where treads are under 11 in | IRC R311.7.5.3 |
| Handrail | One side, 34–38 in high, at 4 or more risers | IRC R311.7.8, R311.7.8.1 |
| Cut stringer throat | 5 in minimum, 2×12 minimum | AWC DCA 6 (deck stairs) |
| Cut stringer span | 6 ft horizontal maximum without a support post | AWC DCA 6 (deck stairs) |
| Cut stringer spacing | 18 in maximum | AWC DCA 6 (deck stairs) |
The span and spacing limits come from the American Wood Council's prescriptive deck guide and are written for exterior deck stairs. Interior stairs are often built differently, for example with a stringer fixed to a wall along its length, so treat a span warning indoors as a prompt to check how the stringer is supported rather than a code failure.
What the numbers are based on
- IRC stair limits. The 2021 IRC text of section R311.7, as reproduced with the International Code Council's permission in the Stairway Manufacturers' Association's Visual Interpretation of the 2021 IRC stair code. The same limits appear in city stair handouts such as Grinnell, Iowa's (based on the 2015 IRC). Older handouts based on the 2012 or earlier codes may show different numbers, so note the edition.
- Stringers. The American Wood Council's DCA 6 prescriptive residential wood deck construction guide, Figures 28 and 29: cut stringers 2×12 minimum with at least 5 inches of throat, a 6 ft maximum span and 18 inches maximum spacing.
- Stock lengths. The suggested board adds 12 inches to the stringer length for the top and bottom cuts and rounds up to an even length from 8 to 20 ft.
Before you cut
- Measure the rise to the finished floors. If the bottom floor will get tile or the top gets carpet pad later, allow for it or the first or last riser will be off by more than 3/8 inch.
- The bottom of a cut stringer is trimmed by one tread thickness so the first riser comes out the same height as the others once the treads are on.
- Cut one stringer, test it in place, then use it as the pattern for the rest.
Questions people ask
How do I work out the number of steps?
Measure the total rise from finished floor to finished floor, then divide by the tallest riser allowed, 7¾ inches under the 2021 IRC, and round up. A 108 inch rise is 108 ÷ 7.75 = 13.9, so 14 risers of 108 ÷ 14 = 7.71 inches (7 11/16). There is always one fewer tread than risers, because the top "step" is the upper floor: 13 treads.
What are the IRC rules for stair risers and treads?
Under the 2021 International Residential Code, a riser can be at most 7¾ inches (R311.7.5.1) and a tread at least 10 inches deep (R311.7.5.2). In one flight, the largest riser or tread may not exceed the smallest by more than 3/8 inch. Headroom must be at least 6 ft 8 in (R311.7.2), the stair at least 36 inches wide (R311.7.1), and one flight can rise at most 12 ft 7 in between floors or landings (R311.7.3). Your city or state may amend any of these, so check the code it has adopted.
How long should a stair stringer be?
The sloped length is the diagonal of the total rise and the total run: √(rise² + run²). For 108 inches of rise and 135 inches of run that is 172.9 inches, about 14 ft 5 in. You also need extra for the plumb cut at the top and the level cut at the bottom, so the calculator adds a foot and suggests the shortest stock board that fits: a 16 ft 2×12.
What is the throat of a stringer and how much do I need?
The throat is the solid wood left between the inside corner of each notch and the bottom edge of the board. Notching removes rise × tread ÷ √(rise² + tread²) of depth. A 2×12 is 11¼ inches deep, so a 7.71 × 10.38 inch step leaves about 5.1 inches. The American Wood Council's deck guide (DCA 6) asks for at least 5 inches on cut stringers, 2×12 at minimum, spaced no more than 18 inches apart and spanning no more than 6 ft without support.
When is a handrail required?
The IRC (R311.7.8) requires a handrail on at least one side of any flight with four or more risers, set 34 to 38 inches above the tread nosings (R311.7.8.1). Open sides more than 30 inches above the floor or ground also need a guard.
Do I need a nosing on the treads?
Under R311.7.5.3, treads less than 11 inches deep need a nosing that projects ¾ to 1¼ inches past the riser below. With treads of 11 inches or more, no nosing is required. The calculator tells you which case your stair falls into.