How to calculate stair risers and treads

Start with the total rise

Every stair layout begins with one number: the total rise, which is the vertical distance from the finished surface of the lower floor to the finished surface of the upper floor. Everything else is derived from it, so an error here carries through to every step.

Measure it carefully, and measure to the surfaces people will actually walk on. If the upper floor will get tile or hardwood and the lower floor a different covering, the thickness of those coverings changes the real rise. Many stair builders also like to check the rise in two or three spots, because floors are not always level. The Stair Calculator accepts total rise from 12 to 300 inches (30 to 760 cm), which covers everything from a single porch step to a tall two-story flight.

The formula and how the rounding works

The calculator does four things in order. First it divides the total rise by your target riser height and rounds to the nearest whole number, which is the number of risers. A staircase cannot have 14.4 risers, so the tool rounds to 14. Second, it divides the full rise by that whole number to get the actual riser height. Third, it sets the number of treads to one fewer than the number of risers, because the top of the flight lands on the upper floor, which acts as the last tread. Fourth, it multiplies the treads by your target tread run to get the total horizontal run.

The key point is that your target riser is a guide, not a promise. The only thing that is fixed is that every riser is the same height, because the whole rise is split evenly across a whole number of steps. The riser you get back is almost never exactly the riser you typed.

Worked example in inches

Take a total rise of 100 inches, a target riser of 7 inches, and a target tread run of 11 inches. The division is 100 / 7 = 14.29, which rounds to 14 risers. The actual riser height is 100 / 14 = 7.14 inches. With 14 risers there are 14 - 1 = 13 treads, and the total run is 13 x 11 = 143 inches, or about 11.92 feet.

If you also want the length of the stringer, the long board that carries the steps, treat the rise and run as the two short sides of a right triangle. The diagonal is the square root of (100 squared + 143 squared), which is about 174.5 inches, or 14.54 feet. The angle of the flight is the inverse tangent of 100 / 143, about 35 degrees. These two extras are not outputs of the calculator, but they follow directly from its rise and run.

• Risers: round(100 / 7) = round(14.29) = 14
• Actual riser: 100 / 14 = 7.14 in
• Treads: 14 - 1 = 13
• Total run: 13 x 11 = 143 in (11.92 ft)
• Stringer length: about 174.5 in; angle about 35 degrees

Worked example in centimeters

Metric mode works the same way. Say the rise is 274 cm, the target riser is 18 cm, and the target tread is 28 cm. The division is 274 / 18 = 15.22, which rounds to 15 risers. The actual riser is 274 / 15 = 18.27 cm. There are 14 treads, so the total run is 14 x 28 = 392 cm, or 3.92 m.

Internally the calculator converts centimeters to inches, does the arithmetic once, and converts back, so inch and centimeter inputs for the same stair give the same layout. A 254 cm rise (exactly 100 inches) with an 18 cm target and a 28 cm tread also gives 14 risers, a riser height of about 18.1 cm, 13 treads, and a run of 364.0 cm.

When rounding pushes you past a limit

Because the riser count is rounded to the nearest whole number, the actual riser can land on either side of your target. A rise of 108 inches with a 7.5 inch target gives 108 / 7.5 = 14.4, so 14 risers at 7.71 inches. Thirteen risers would be 8.31 inches each and fifteen would be 7.20, so 14 is the closest fit, but it is 0.21 inches taller than you asked for.

That matters if you are close to a maximum riser height set by your local building code. Codes vary by jurisdiction and edition, so this guide does not quote one as fact; look up the limit that applies to you. For illustration only, suppose a code capped risers at 7.75 inches. A rise of 108.6 inches with a 7.5 inch target gives 108.6 / 7.5 = 14.48, which rounds down to 14 risers of 7.757 inches, just over that hypothetical cap, even though the target was comfortably under it.

The fix is to pick a lower target, not to fight the rounding. Entering a 7.25 inch target gives 108.6 / 7.25 = 14.98, which rounds up to 15 risers of 7.24 inches, and the flight gains one riser and one tread. Aim for the middle of your allowed range rather than the edge, then always read the actual riser height the tool returns before you cut anything.

Treads, total run, and nosing

The treads count is risers minus one, and the total run is that count times the tread run you entered. Two details deserve attention. First, the tool multiplies by your target tread run, not by some adjusted value, so you control the run directly. Second, total run does not include nosing, the overhang of each tread past the riser below it. If your finished treads project past the riser, the flight's footprint on the floor changes slightly, so add that allowance separately when you check available floor space.

A deeper tread makes a gentler, longer stair, and a shallower one makes a steeper, shorter stair. Using the 108 inch rise from above, 13 treads at 10 inches need 130 inches of run (10.83 feet), while 13 treads at 11 inches need 143 inches (11.92 feet), more than a foot longer. If the stair has to fit a fixed opening, work backward from the available run: divide it by the number of treads to see the deepest tread you can afford.

Real-world adjustments the calculator does not make

The tool assumes a clean flight from one floor to another with every step the same. Real jobs add wrinkles. If the lower floor will get a thicker or thinner covering after the stair is built, the first riser changes by the difference, and the cleanest approach is to account for finished surfaces in the rise you enter. Landings are usually figured as their own platform with their own rise, so a stair with a mid-flight landing is calculated as two flights.

Uniformity is the property that keeps stairs safe. New Zealand's building research body BRANZ notes that even very small variations in riser height can cause a person to stumble, and its stair guidance allows a maximum variation in riser height and tread depth of 5 mm (about 3/16 inch) in a flight. That figure is from New Zealand's acceptable solution, not from a United States code, but the lesson applies anywhere: even riser heights matter more than hitting an exact target.

Tiny rises are a special case. If the total rise rounds to a single riser, such as 12 inches with a 9 inch target, the tool reports 1 riser and 0 treads, because the floor itself serves as the tread. Treat that as a signal to design a single step or a platform, not a staircase.

Common mistakes

Most stair layout problems come from a short list of errors.

• Measuring to the subfloor instead of the finished floor surface.
• Using the target riser as if it were the real riser height instead of reading the actual value the tool returns.
• Setting the target riser at the very edge of the allowed range, so rounding can push the real riser outside it.
• Counting treads equal to risers; the flight has one fewer tread than risers.
• Forgetting that total run excludes nosing, then finding the footprint is slightly too long for the space.
• Skipping the local code check for riser height, tread depth, headroom, and handrails before building.

How the target riser reshapes the whole stair

Two people with the same floor-to-floor height can end up with noticeably different staircases just by typing different targets. Take a total rise of 105 inches and a 10 inch tread. A 7 inch target gives 105 / 7 = 15 risers of exactly 7 inches, 14 treads, and a run of 140 inches. A 7.5 inch target gives 14 risers of 7.5 inches, 13 treads, and a run of 130 inches. An 8 inch target gives 105 / 8 = 13.1, which rounds to 13 risers of 8.08 inches, 12 treads, and a run of 120 inches.

Each step down in riser count shortens the run by one tread, but it makes every step steeper. A handy comfort check is to add twice the riser to the tread. Traditional guidance, often credited to the French architect Francois Blondel, puts a comfortable sum at roughly 24 to 25 inches, or about 62 to 64 centimeters. It is a rule of thumb, not a code requirement. Run it against the three layouts above:

The 7 inch layout lands at 24.0, the 7.5 inch layout at 25.0, and the 8.08 inch layout at about 26.2. The last one is the steepest and the most tiring on the legs, and its riser would also fail many residential limits. When the numbers drift high, lengthen the tread or choose a lower target so the count rounds up.

• Target 7 in: 15 risers at 7.00 in, 14 treads, run 140 in, 2R + T = 24.0
• Target 7.5 in: 14 risers at 7.50 in, 13 treads, run 130 in, 2R + T = 25.0
• Target 8 in: 13 risers at 8.08 in, 12 treads, run 120 in, 2R + T = 26.2

Fitting a stair into a fixed run

Often the space decides the stair, not the other way around. A basement stairwell might allow exactly 120 inches of horizontal run. Start by working out the most treads you can afford: at a 10 inch tread, 120 / 10 = 12 treads, which means 13 risers. Then see whether the rise suits that count. For a 96 inch rise, 96 / 13 = 7.38 inches per riser. That is a comfortable stair, and the calculator confirms it: 13 risers at 7.38 inches and a run of exactly 120 inches.

Now suppose the rise is 108 inches in the same 120 inches of space. Thirteen risers would each be 108 / 13 = 8.31 inches, which is steep and likely above the riser limit where you live. Fourteen risers drop the riser to 7.71 inches but need 13 treads, and 120 / 13 = 9.23 inches per tread, shallower than the 10 inch minimum that many residential codes use. The space simply cannot hold a conventional straight stair.

At that point the choices are to enlarge the opening, add a landing and turn the stair, or use winders or a compact alternative if your code permits. Do the arithmetic first, because discovering the shortfall on paper costs nothing, while discovering it after the floor is framed costs a lot.

Headroom and the length of the stairwell opening

A stair needs clear space overhead, and the opening in the upper floor must be long enough to provide it. The model International Residential Code, which many US jurisdictions adopt with their own amendments, asks for 6 ft 8 in (80 inches) of headroom, measured vertically from the sloped line that touches the front edges of the treads. Check your own jurisdiction before relying on that figure.

Here is how to estimate the opening. Use a 108 inch rise with 14 risers of 7.71 inches and 10 inch treads, and a floor system 10 inches thick, from the top of the finished upper floor to the underside of the framing. The ceiling under the upper floor sits at 108 - 10 = 98 inches above the lower floor. To keep 80 inches of clearance, the nosing line may be no higher than 98 - 80 = 18 inches at the point where the floor framing begins.

The nosing line starts at 7.71 inches at the first riser and climbs 7.71 inches per 10 inches of run. It reaches 18 inches after (18 - 7.71) / 0.771 = 13.3 inches. The total run to the top riser is 13 x 10 = 130 inches, so the opening must be about 130 - 13.3 = 116.7 inches long, just under 9 ft 9 in, measured to the top riser. Treat this as a planning estimate and confirm it with a drawn cross-section, because floor thickness and nosing both move the answer.

Cutting the stringer: the first-step adjustment

Once the riser count and equal riser height are fixed, the stringer is laid out by stepping those dimensions along the board with a framing square. One detail trips up first-time builders: the treads add thickness. If you mark every notch at the full riser height, the first step ends up taller than the others by exactly the tread thickness, once the treads are installed, and the top step comes up short.

The fix is to shorten the first riser cut on the stringer by the tread thickness. Using the 108 inch rise, the riser is 108 / 14 = 7.714 inches. With 1.5 inch thick treads (the actual thickness of a nominal 2x board), the first notch from the floor is cut at 7.714 - 1.5 = 6.21 inches. Once the treads are on, every step from the floor to the upper floor measures 7.714 inches from top of tread to top of tread.

Stringer length follows from the right triangle formed by the rise and run. With a 108 inch rise and 130 inch run, the diagonal is the square root of (108 squared + 130 squared), about 169 inches, or 14.1 feet, and the slope angle is the inverse tangent of 108 / 130, about 39.7 degrees. The board must be longer than 169 inches to leave material at both ends, and enough solid wood must remain in the throat behind each notch, as span tables and code limits dictate.

Exterior and deck stairs

Deck stairs use the same arithmetic but have their own habits. Treads are often made from two decking boards side by side. Two boards that are 5.5 inches wide, plus a small gap between them, give a tread a little over 11 inches deep, so an 11 inch target run matches common lumber. For a deck surface 30 inches above the landing pad and a 7 inch target, 30 / 7 = 4.29 rounds to 4 risers of 7.5 inches. There are 3 treads, and at 11 inches the run is 33 inches. Taller decks add more steps: a 42 inch height gives 6 risers of exactly 7 inches, 5 treads, and 55 inches of run at an 11 inch tread.

Measure the rise to the finished walking surface at the top and to the finished surface of the bottom landing, not to bare soil that will settle or be covered. Stringer ends should rest on a firm, level pad such as concrete, not directly on ground that can heave or erode, since a small movement changes the bottom riser and breaks the equal-riser rule.

Code requirements on exterior stairs are not the same as on interior ones, and they vary by jurisdiction. In the model International Residential Code, for example, a flight with four or more risers needs a handrail, and a guard is required where the walking surface is more than 30 inches above the grade below. The 30 inch deck above has exactly 4 risers, so it falls under the handrail rule. Confirm both thresholds with your local building department. Whatever the target, cut one stringer exactly and use it as the template for the rest, so every riser stays identical.