Stair calculator (risers, treads, stringer and headroom)
Total rise → number of steps, riser height, tread run, stringer length, opening and code check.
- Instant
- Free
- Private (processed locally)
- No sign-up
Work out a straight staircase in seconds
Before you buy stringers, cut a stairwell or order a kit, you need the number of risers, the riser height, the tread run and the total run the stair will take up. This stair calculator starts from the total rise and applies the stride rule (2R + T ≈ 25 in, Blondel’s formula) to suggest the most comfortable stair, then checks every dimension against the code you pick: IRC, UK Part K, DIN 18065 or French rules.
It also gives what many stair calculators leave out: the minimum stairwell opening for safe headroom, the stringer length, the pitch angle and a stringer layout with the position of every nosing. A variants table compares 14, 15 or 16 risers in one click, and every length is shown in decimal inches and in fractions to the nearest 1/16 in.
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Measure the total rise
Measure from the finished lower floor to the finished upper floor, including flooring still to be installed. It is the key input: a ¾ in error spreads across every riser.
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Enter the total run if space is tight
Leave it empty for a free calculation based on the stride rule. If the stair must fit a given length, enter it and the tool picks the number of risers that comes closest to the target stride.
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Set headroom and floor thickness
Headroom is the clear height above the nosings (80 in under the IRC, 2.0 m in the UK and Germany). Together with the upper floor thickness, it sets the stairwell opening length.
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Pick a code and compare
Each dimension is checked and marked compliant, to check or not compliant. Click any row of the variants table to try another number of risers, then copy the summary for your plans.
Stair formulas used by the calculator
- Number of risers:
n = round(total rise ÷ target riser), then actual riserR = rise ÷ n. Example: 108 ÷ 7.25 = 14.9 → 15 risers of 7.2 in. - Number of treads:
n − 1, because the upper floor is the last step. - Tread run from the stride rule:
T = stride − 2R= 25 − 14.4 = 10.6 in. With a fixed total run:T = run ÷ (n − 1). - Total run:
(n − 1) × T= 14 × 10.6 = 148.4 in (12 ft 4⅜ in). - Pitch angle:
arctan(R ÷ T)= arctan(7.2 ÷ 10.6) ≈ 34.2°. - Stringer length:
√(rise² + run²)= √(108² + 148.4²) ≈ 183.5 in, before end cuts. - Minimum opening:
(headroom + floor thickness) × T ÷ R= 90 × 10.6 ÷ 7.2 = 132.5 in.
The stringer length is the hypotenuse of a right triangle whose legs are the total rise and the total run, so you can double-check it with the Pythagorean theorem calculator. For a concrete stair, estimate the volume of the waist slab and steps with the concrete volume calculator.
Stair calculation examples
| Total rise | Risers × R | Tread run | Pitch | Total run | Min. opening |
|---|---|---|---|---|---|
| 108 in (9 ft) | 15 × 7.2 in | 10.6 in | 34.2° | 148.4 in | 132.5 in |
| 118 in (9 ft ceiling + floor) | 16 × 7.375 in (7⅜) | 10.25 in | 35.7° | 153.75 in | 125.1 in |
| 270 cm | 15 × 18 cm | 27 cm | 33.7° | 378 cm | 330 cm |
| 280 cm | 16 × 17.5 cm | 28 cm | 32.0° | 420 cm | 352 cm |
| 270 cm, run limited to 300 cm | 14 × 19.3 cm | 23.1 cm | 39.9° | 300 cm | 263.3 cm |
Imperial rows: stride 25 in, headroom 80 in, floor 10 in. Metric rows: stride 63 cm, headroom 200 cm, floor 20 cm.
One riser more or less changes the footprint a lot: for a 270 cm rise, 16 risers instead of 15 give 16.9 cm risers, a 29.3 cm run and a gentler 30° pitch, but the stair grows from 378 cm to 438.8 cm long.
Comfort guidelines and building codes
| Code | Riser height | Tread run | Stride 2R + T | Other |
|---|---|---|---|---|
| Comfort (guidelines) | 16-18 cm (6.3-7.1 in) | 25-32 cm (9.8-12.6 in) | 60-64 cm (23.6-25.2 in) | pitch ≤ 37°, headroom ≥ 1.90 m |
| US, IRC R311.7 | ≤ 7¾ in | ≥ 10 in | - | headroom ≥ 6 ft 8 in |
| UK, Approved Document K (private stair) | 150-220 mm | 220-300 mm | 550-700 mm | pitch ≤ 42°, headroom ≥ 2.0 m |
| Germany, DIN 18065 (house, ≤ 2 dwellings) | 14-20 cm | 23-37 cm | 59-65 cm recommended | headroom ≥ 2.0 m |
| France, apartment buildings (common areas) | ≤ 17 cm | ≥ 28 cm | - | decree of 24 Dec 2015 |
| France, public buildings (accessible) | ≤ 16 cm | ≥ 28 cm | - | decree of 20 Apr 2017 |
Codes change and local amendments apply: the IRC also sets a 36 in minimum width, a ⅜ in maximum variation between risers and handrail rules. Treat this calculator as a planning aid and confirm with your building department or inspector.
Stair terms explained
- Rise / riser: the vertical height of one step; the vertical board is the riser.
- Run / tread: the horizontal distance from one nosing to the next. The tread board is deeper by the nosing overhang (¾ to 1¼ in).
- Total run: the floor length taken by the flight, from the first riser to the top landing.
- Headroom: the clear height measured vertically from the line of nosings to the ceiling or the edge of the opening.
- Stringer: the sloped board that carries the treads, cut with a saw tooth profile from the layout table.
Common mistakes
- Measuring the rise on the bare subfloor and forgetting the finished flooring: the first or last step ends up a different height, which is a classic trip hazard.
- Counting as many treads as risers: a 15 riser stair has only 14 treads to cut.
- Framing a stairwell that is too short: headroom is measured plumb from the nosing line at the edge of the opening.
- Adding risers for a gentler stair without checking the total run: every extra riser makes the stair one tread longer.
Frequently asked questions
How do I calculate the number of stairs?
Divide the total rise (finished floor to finished floor) by your target riser height and round: 108 in ÷ 7.25 in = 14.9, so 15 risers. Each riser is then 108 ÷ 15 = 7.2 in. Because the upper floor acts as the last step, a straight stair with 15 risers has only 14 treads.
How many steps do I need for a 9 ft ceiling?
Add the upper floor structure to the ceiling height to get the total rise: 9 ft (108 in) plus about 10 in of joists and subfloor gives roughly 118 in. At about 7¼ in per riser that is 16 risers of 7⅜ in and 15 treads; with a 10¼ in run the stair is 153¾ in (12 ft 9¾ in) long. Measure your actual rise before ordering stringers.
What is the 2R + T stair rule?
Known as Blondel’s formula, it says that two risers plus one tread should equal a natural stride, about 24 to 25 in (60 to 64 cm). With a 7.2 in riser, the tread run is 25 − 14.4 = 10.6 in. The UK Approved Document K expresses the same idea as 2R + G between 550 and 700 mm.
What does the IRC require for residential stairs?
The International Residential Code (R311.7) limits riser height to 7¾ in, requires a tread depth of at least 10 in measured nosing to nosing, and at least 6 ft 8 in (80 in) of headroom measured vertically from the line of the nosings. Select “United States: IRC” to check every dimension; local amendments may be stricter.
How long should the stairwell opening be?
The minimum opening length is (headroom + floor thickness) × tread run ÷ riser height. With 80 in of headroom, a 10 in floor, a 10.6 in run and 7.2 in risers: 90 × 10.6 ÷ 7.2 = 132.5 in, about 11 ft. A shorter opening means people would hit their head on the edge of the floor above.