Stair Calculator
Enter the height from floor to floor to get the number of steps, riser height, tread depth, total run, stringer length and angle, the headroom you need, and a check against your country’s building code.
Finished floor to finished floor. You can type 8' 9" or 2 m 67 cm.
Figures to check with your local building office.
Typical 7 in (about 175–180 mm). Rounded to a whole number of risers.
Floor space the stair can take, measured flat, from the bottom nosing to the upper floor’s edge.
Nosing to nosing, without the overhang. Typical 10–11 in (250–280 mm).
How far each tread sticks out past the riser below. 0 if none.
Usual: one fewer tread than risers. Some deck stairs put a tread level with the deck.
Joists, floor and ceiling together. Typical 10–12 in (250–300 mm).
The hole in the floor above, measured back from the top of the stair.
Leave blank for the code figure.
Typical: 2×12 is 11¼ in, 2×10 is 9¼ in; 225–300 mm in metric.
Cut this off the bottom of the stringer so the first step isn’t taller.
Typical 16–18 in (400–450 mm). Check your tread maker’s span.
Side view, to scale
Stringer cut layout
How your stairs are worked out
Total rise ÷ risers = riser height, treads × going = run, and each step along the slope is √(rise² + going²).
- 1
Count the risers
105 ÷ 7 = 1515 risers
- 2
Riser height
105 in ÷ 15= 7 in each
- 3
Total run
14 treads × 10 in= 140 in
- 4
Angle and stringer
atan(7/10) = 34.99°14 × √(7² + 10²)= 170 7/8 in
Read more: the formulas, a worked example, comfort rules and the code figures by country
A stair splits the height from floor to floor into equal risers, so every step is the same. The number of treads is one fewer than the risers when the last riser steps onto the upper floor. The run is the treads times the going, and the stringer is the sloping board that carries the treads: each step along it is the long side of a right triangle with the riser and the going as the short sides.
The formula
risers = total rise ÷ riser height wanted, rounded to a whole number (more if the code's maximum riser is broken)
riser height = total rise ÷ risers
treads = risers − 1 (or = risers if the top tread is level with the floor)
total run = treads × going · floor space = total run + nosing
angle = arctan(riser ÷ going)
one step along the slope = √(riser² + going²) · stringer length = treads × √(riser² + going²)
throat = board width − riser × going ÷ √(riser² + going²)
comfort: 2 × riser + going ≈ 600–650 mm (24–25.5 in); UK and Australian codes: 550–700 mm
headroom at the opening edge = (total rise − floor thickness) − (riser + (distance from the first riser + nosing) × riser ÷ going)
shortest opening = total run − ((total rise − floor thickness − riser − headroom needed) × going ÷ riser − nosing)
Worked example
The floors are 105 in apart (8 ft 9 in) and you would like 7 in risers. 105 ÷ 7 = 15, so you need 15 risers of 105 ÷ 15 = 7 in. The last riser steps onto the upper floor, so there are 15 − 1 = 14 treads. With a 10 in going the total run is 14 × 10 = 140 in (11 ft 8 in), and with a 1 in nosing the stair takes 141 in of floor. The angle is arctan(7 ÷ 10) = arctan(0.7) = 34.99°. Each step along the slope is √(7² + 10²) = √149 = 12.2066 in, so the stringer is 14 × 12.2066 = 170.89 in (about 14 ft 2 7/8 in): buy 16 ft boards. On a 2×12 (11¼ in wide) the throat is 11.25 − 7 × 10 ÷ 12.2066 = 11.25 − 5.73 = 5.52 in. The comfort check is 2 × 7 + 10 = 24 in (609.6 mm), inside 600–650 mm. For 6 ft 8 in (80 in) of headroom under a 10 in thick floor, the ceiling is 105 − 10 = 95 in up, so the opening must start where the nosing line is 95 − 80 = 15 in high: (95 − 7 − 80) × 10 ÷ 7 − 1 = 10.43 in from the first riser. The opening must be at least 140 − 10.43 = 129.57 in long (about 10 ft 9 9/16 in).
Building code figures by country
| Country | Riser | Going | Pitch | Headroom | Also |
|---|---|---|---|---|---|
| US (2018 IRC R311.7) | 7¾ in max (R311.7.5.1) | 10 in min (R311.7.5.2) | — | 6 ft 8 in (R311.7.2) | Nosing ¾–1¼ in with solid risers, not needed if treads are 11 in or more (R311.7.5.3); winders 10 in at 12 in from the narrow side, 6 in minimum; handrail 34–38 in high (R311.7.8); 36 in width; 151 in max per flight |
| UK (Approved Document K 2013, private stair) | 150–220 mm | 220–300 mm | 42° max | 2.0 m (loft conversions: 1.9 m at the centre may be accepted) | 2R + G 550–700 mm (the code range; 600–650 mm is the comfort sweet spot) |
| Australia (NCC housing) | 115–190 mm | 240–355 mm | — | 2.0 m | 2R + G 550–700 mm; 2 to 18 risers per flight |
| Canada (NBC, private) | 125–200 mm | 255–355 mm | — | 1.95 m | 860 mm width; 3.7 m max per flight |
These are the usual house (private stair) figures, summarised. Rules change, local areas add their own, and there are exceptions (loft conversions, spiral and winder stairs, decks). Always check with your local building office before you build. The main US figures (riser, tread, width, headroom, handrail) were checked on 11 October 2026 against a city building department handout based on the IRC; the UK, Australia and Canada figures are not yet checked against the official pages.
Comfort rules of thumb
- 2 × riser + going between about 600 and 650 mm (24–25.5 in). François Blondel’s 17th-century rule puts the ideal at about 630 mm, one easy stride.
- Riser + going about 17–18 in (430–460 mm), and riser × going about 70–75 in².
- An angle between about 30° and 37° feels easy. Steeper stairs save space but are harder on knees.
Marking out a stringer
Set a framing square on the board with the riser height on the tongue and the going on the blade, both touching the top edge. Draw the triangle, slide the square along to where the last one ended, and repeat once for each tread. Each mark is one step along the slope apart. Cut the bottom level, then take the tread thickness off the bottom (the drop) so the first riser comes out the same as the rest once the treads are on. Keep at least about 3.5 in (89 mm) of solid board under the notches (the throat); this is a typical figure, check your timber and local rules.
Common questions
How do I work out how many steps I need?
Measure the total rise from the finished lower floor to the finished upper floor, then divide it by the riser height you want and round to a whole number. For a 105 in rise and 7 in risers that is 105 ÷ 7 = 15 risers. With the usual top, where the last riser steps onto the upper floor, you have one fewer tread: 14.
How do I find the length of a stair stringer?
Each step along the slope is √(rise² + going²). With 7 in risers and 10 in treads that is √149 = 12.21 in. Multiply by the number of treads: 14 × 12.21 = 170.89 in, about 14 ft 3 in. Buy the next common board length, here 16 ft, so there is room for the cuts.
What is the 2R + G rule for stairs?
Twice the riser height plus the going (tread depth) should land between about 600 and 650 mm, or about 24 to 25.5 in. That matches a normal walking stride, so the stair feels easy. A stair with 7 in risers and 10 in treads gives 2 × 7 + 10 = 24 in. The UK and Australian codes ask for 550 to 700 mm.
What is the steepest stair allowed?
It depends on the country. The US code (IRC) allows risers up to 7¾ in with treads at least 10 in. The UK private stair rule (Approved Document K) allows a rise up to 220 mm, a going of at least 220 mm and a pitch of no more than 42°. Check with your local building office before you build.
How much headroom do stairs need?
Headroom is measured straight up from the line of the nosings to the ceiling or the edge of the floor above. The US code asks for 6 ft 8 in, the UK and Australia 2.0 m, and Canada 1.95 m for houses. The calculator shows the shortest floor opening that gives you that headroom.
What is the difference between a riser, a tread and the going?
The riser is the height of one step. The tread is the board you stand on. The going is the flat distance from one nosing to the next, which is the tread depth without the nosing overhang. A 10 in going with a 1 in nosing needs an 11 in deep tread board.
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Made by Zulu Calculator, part of AlphaZulu LLC. Formulas are shown in full and rule figures are checked against official sources; see how we build calculators.