5 equal risers of 7 3/16″ (7.2″) and 4 treads of 10″, covering 3′ 4″ along the floor. Meets the IRC limits.
Pitch line. Buy a 6 ft board, 4 stringers.
Target was 7 1/2″. Every riser is equal, so variation is 0.
4 treads at 10″.
First plumb cut 6 3/16″ (6.2″) after dropping the tread thickness.
Measure the total rise, floor to floor, and type it in. This online stair calculator, also called a staircase calculator, hands back equal risers, tread depth, total run, stringer length and an IRC pass or fail, before you cut a single 2×12. Tall stair or a turn? Switch on a landing.
Quick answer A 36 in (914 mm) rise works out to 5 equal risers of 7 3/16″ (7.2″) with 4 treads of 10 in (254 mm). The stringer line is 4′ 5 13/16″, so buy a 6 ft 2×12 and cut 4 stringers. The IRC (R311.7.5) wants risers no taller than 7¾ in and treads at least 10 in deep.
How to calculate stairs comes down to one division. Take the total rise, finished floor to finished floor, and divide it by the riser height you like (7½ in is a comfortable target). Round to a whole number of risers. If that leaves any riser taller than 7¾ in, add one and divide again. Every riser comes out identical, which is what keeps you inside the IRC's ⅜ in variation limit. Uneven risers are the classic trip hazard, and the one a building inspector measures first.
The upper floor counts as the last step, so a stair has one fewer tread than risers. Total run is treads times tread depth. The stringer line is the straight distance from the bottom plumb cut to the top plumb cut: the hypotenuse of total rise and total run. The board you buy has to be longer than that line, because the cuts at each end eat wood, so the calculator adds one board depth and rounds up to the next stock length. The rest of the calculations for stairs are plain geometry. Cut the first stringer, test-fit it, then trace it for the rest. A bad cut copied four times is four ruined 2×12s.
Rise over 12 ft 7 in, or a stair that has to turn? Switch Landing on. The calculator splits the stair at the whole riser nearest the middle (or at the landing height you enter) and gives each flight its own risers, run and stringer. It then checks the landing: at least 36 in deep on a straight stair, and at least as deep as the stair is wide on a 90° turn, which is how an L-shaped staircase works. The plan diagram shows how much floor the whole stair takes, so you can find out it does not fit before the lumber arrives.
The stair angle is arctan(riser ÷ tread). A 7½ in riser with a 10 in tread comes to about 37°. Taller risers or shorter treads steepen it, which is why the code caps both.
Every stair has two ends. The deck calculator sizes the platform at the top, and the baluster calculator spaces the guard along the open side. The same rise-over-run idea sets a roof slope in the roof pitch calculator.
L = stringer pitch line, H = total rise, t = number of treads, d = tread depth.
risers = round(total rise / target riser) then add 1 while riser > 7.75 in
riser height = total rise / risers
treads = risers − 1 upper floor is the top step (standard)
= risers top tread is a separate step
total run = treads × tread depth
stringer line = √(total rise² + total run²)
angle = arctan(riser height / tread depth)
first cut = riser height − tread thickness
board to buy = next stock length ≥ stringer line + one board depth
stringers = ceil(width / max spacing) + 1
landing at = riser nearest risers / 2, or landing height / riser height
flight 1 = (landing at) risers, one tread fewer than risers
flight 2 = risers − (landing at) risers, one tread fewer than risers (floor on top)
footprint = straight: run 1 + landing depth + run 2 by width
= 90° turn: (run 1 + landing depth) by (width + run 2)Total rise 36 in (914 mm), target 7½ in. round(36 ÷ 7.5) = 5 risers of 7.2 in. 4 treads of 10 in (254 mm) make a 40 in (1.02 m) run. The stringer line is √(36² + 40²) = √2896 ≈ 53.8 in. With a 2×12 that needs a 6 ft board. A 36 in wide stair with 5/4 decking treads takes 4 stringers. First cut is 7.2 − 1 = 6.2 in.
Total rise 9′ (2.74 m), target 7¼ in. That rounds to 15 risers of 7.2 in and 14 treads, so the run is 11′ 8″ (3.56 m). The pitch line is √(108² + 140²) ≈ 176.8 in (14′ 8 13/16″). Adding a 2×12 depth for the end cuts needs about 15.7 ft, so buy 16 ft stock. The 7 ft headroom entered clears the 6 ft 8 in minimum.
Total rise 10′ (3.05 m), straight landing. That is 16 risers of 7.5 in, split 8 and 8 with the landing 60 in (1.52 m) above the floor. Each flight has 7 treads, a 70 in (1.78 m) run and a 7′ 8 3/16″ stringer, so buy 10 ft boards. A 36 in landing makes the stair 14′ 8″ long and 3 ft wide. As a 90° turn it takes 8′ 10″ by 8′ 10″ instead.
Total rise 13′ 4″ (4.06 m). One flight of 21 risers would rise 13′ 4″, over the 151 in (12 ft 7 in) limit, so the flight check fails. With a landing the stair is 21 risers in two flights of 11 and 10, rising 6′ 11 13/16″ and 6′ 4 3/16″. Both are under the limit and the check passes.
Total rise 2600 mm, 225 mm going. 15 risers of 173.3 mm, so 2R + G = 572 mm (limit 550–700 mm). The pitch is 37.61° against the 42° limit. Every England private-stair check passes. The 225 mm going is under the IRC 10 in minimum tread, so the same stair would not meet the US code.
Find your rise in the first table and you have a ballpark before you even open the calculator. Every row assumes a 7½ in target riser, 10 in treads, the upper floor as the top step and an 11¼ in stringer board. Your floors will not be exactly these heights, so run your real number above. The second table settles how many stringers a stair needs, and the third shows a stair with a landing, split at the middle riser.
| Total rise | Risers | Riser height | Treads | Total run | Stringer length |
|---|---|---|---|---|---|
| 2′ | 4 | 6 in | 3 | 2′ 6″ | 3′ 2 7/16″ |
| 2′ 6″ | 4 | 7.5 in | 3 | 2′ 6″ | 3′ 6 7/16″ |
| 3′ | 5 | 7.2 in | 4 | 3′ 4″ | 4′ 5 13/16″ |
| 3′ 6″ | 6 | 7 in | 5 | 4′ 2″ | 5′ 5 5/16″ |
| 4′ | 7 | 6.857 in | 6 | 5′ | 6′ 4 13/16″ |
| 4′ 6″ | 7 | 7.714 in | 6 | 5′ | 6′ 8 3/4″ |
| 5′ | 8 | 7.5 in | 7 | 5′ 10″ | 7′ 8 3/16″ |
| 6′ | 10 | 7.2 in | 9 | 7′ 6″ | 9′ 7 1/4″ |
| 7′ | 11 | 7.636 in | 10 | 8′ 4″ | 10′ 10 5/8″ |
| 8′ | 13 | 7.385 in | 12 | 10′ | 12′ 9 11/16″ |
| Stair width | At 16 in spacing | At 24 in spacing |
|---|---|---|
| 32 in | 3 | 3 |
| 36 in | 4 | 3 |
| 42 in | 4 | 3 |
| 48 in | 4 | 3 |
| 60 in | 5 | 4 |
| Total rise | Risers | Risers per flight | Longest stringer | Straight footprint | 90° turn footprint |
|---|---|---|---|---|---|
| 8′ | 13 | 7 + 6 | 6′ 7 3/16″ | 12′ 2″ × 3′ | 8′ × 7′ 2″ |
| 10′ | 16 | 8 + 8 | 7′ 8 3/16″ | 14′ 8″ × 3′ | 8′ 10″ × 8′ 10″ |
| 12′ | 19 | 10 + 9 | 9′ 9 11/16″ | 17′ 2″ × 3′ | 10′ 6″ × 9′ 8″ |
| 13′ 4″ | 21 | 11 + 10 | 10′ 10 1/2″ | 18′ 10″ × 3′ | 11′ 4″ × 10′ 6″ |
| 16′ | 26 | 13 + 13 | 12′ 9 11/16″ | 23′ × 3′ | 13′ × 13′ |
A standard stair has a riser of about 7 to 7¾ in and a tread of 10 to 11 in. The first table shows the angle each pair makes (arctan of riser over tread, same as the calculator), so you can see how much a taller riser or a shorter tread steepens things. The second lists the code limits the calculator checks against. A dash means that code sets no such number.
| Riser height | 10 in tread | 10½ in tread | 11 in tread |
|---|---|---|---|
| 6 1/2″ | 33.02° | 31.76° | 30.58° |
| 7″ | 34.99° | 33.69° | 32.47° |
| 7 1/4″ | 35.94° | 34.62° | 33.39° |
| 7 1/2″ | 36.87° | 35.54° | 34.29° |
| 7 3/4″ | 37.78° | 36.43° | 35.17° |
| Dimension | IRC (US) | England, Approved Document K |
|---|---|---|
| Maximum riser height | 7¾ in (197 mm) | 220 mm |
| Minimum tread or going | 10 in (254 mm) | 220 mm |
| Twice the rise plus the going | — | 550 to 700 mm |
| Maximum pitch of the stair | — | 42° |
| Largest riser against the smallest in a flight | ⅜ in (10 mm) | — |
| Rise of one flight before a landing | 151 in (12 ft 7 in) | — |
A stair stringer calculator does the arithmetic. This section is the layout on the board, using its default stair: 36 in (914 mm) of rise, 5 risers of 7 3/16″ and 4 treads of 10 in (254 mm). Type your own rise above and swap in your own numbers.
US limits shown are from IRC R311.7: maximum riser 7¾ in, minimum tread 10 in, riser variation ⅜ in, headroom 6 ft 8 in, and 12 ft 7 in (151 in) of rise between floors or landings. Open-riser stairs and stair width have their own rules in the same section. Read the text in IRC 2021 Chapter 3, Building Planning.
England's Approved Document K for a private stair allows a rise up to 220 mm, a going of at least 220 mm, twice the rise plus the going between 550 and 700 mm, and a pitch of no more than 42°. The official text is Approved Document K on GOV.UK. Scotland, Wales, Northern Ireland and local amendments differ. This page flags the England private-stair numbers; it does not certify compliance.
IRC R311.7.6 asks for a landing at the top and bottom of every stair, as wide as the stair, and at least 36 in deep where the stair runs straight. The landing option here checks an intermediate landing against those numbers and shows its footprint. It does not size the landing framing, posts or guards.
The stringer board allowance is a rule of thumb (one board depth). Lay the cuts out on the real board before you buy the last length.
Section numbers refer to IRC 2021 section numbers; England Approved Document K. Local amendments are common, so confirm with your building authority.
Hover a question to read the answer. Click to keep it open.Tap a question to open it.
Square the total rise, square the total run, add them and take the square root. Total run is the number of treads times the tread depth. That gives the line between the plumb cuts. The board you buy has to be longer, because the top and bottom cuts need extra wood, so add one board depth and round up to the next stock length.
Four with 5/4 decking or composite treads, which want stringers no more than about 16 in (400 mm) apart. Three with 2× lumber treads, which can span about 24 in (600 mm). Composite makers often ask for 12 in, so read the tread box before you commit. Pick the spacing in the calculator and the count updates.
Standard stair rise and run is a riser of about 7 to 7¾ inches and a tread of 10 to 11 inches. A 7½ inch riser with a 10 inch tread is a stair angle of 36.87°, arctan(7.5 ÷ 10). The stair dimensions table on this page has the angle for other riser and tread pairs.
7¾ inches at most (IRC R311.7.5.1), with treads at least 10 inches deep (R311.7.5.2). The tallest and shortest riser in a flight can differ by ⅜ inch at most. Headroom is 6 ft 8 in minimum, and one flight can rise 151 inches (12 ft 7 in) before it needs a landing.
In England, Approved Document K allows a rise up to 220 mm and wants a going of at least 220 mm, with twice the rise plus the going between 550 and 700 mm and a pitch of 42° or less. Any stair under the IRC 7¾ in riser limit is also under 220 mm. The calculator shows both sets of checks side by side.
An L-shaped staircase is two straight flights joined by a landing at a 90° turn. Set Landing to 90° turn and enter the total rise. The calculator splits the risers into two flights, sizes each stringer and draws the footprint. A U-shaped stair turns 180° over a wider landing, which is not drawn here. Enter each flight's rise on its own and check the landing against the 36 in minimum depth.
Measure from the ground to the top of the deck surface and type that in as the total rise. As a deck stair calculator it picks the riser count, riser height and tread depth, then gives the stringer length. Choose the stringer spacing for your tread material. The stair width sets how many stringers you need.
IRC R311.7.6 wants a landing as wide as the stair and at least 36 inches (914 mm) deep in the direction of travel. You also need one when the rise passes 151 inches (12 ft 7 in), because R311.7.3 limits a single flight. For a 90° turn, a landing as deep as the stair is wide is the practical minimum. Switch Landing on and the calculator checks both and draws the plan.