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.