Stair Calculator

A stair calculator is a tool that converts a floor-to-floor height into a buildable set of stair dimensions. You enter the total rise and a target riser height, and it works out the number of risers, the actual riser height, the number of treads, the total run, the stair angle, and the stringer length. It removes the trial-and-error of dividing a rise by hand and checking the remainder.

Start by measuring the total rise (finished floor to finished floor). Divide the total rise by your target riser height and round to the nearest whole number to get the number of risers, then divide the total rise by that riser count to get the actual riser height. Pick a tread depth, multiply it by the number of treads (risers minus 1 for a flush top) to get the total run, and use those two numbers to find the stair angle and stringer length.

The number of risers equals the total rise divided by your target riser height, rounded to the nearest whole number. For example, an 84 in total rise with a 7.25 in target riser gives 84 ÷ 7.25 = 11.6, which rounds to 12 risers. The riser height is then recalculated as 84 ÷ 12 = 7.0 in exactly, so every riser in the flight is identical.

Total rise is the vertical floor-to-floor height; total run is the horizontal distance the stair covers. Divide total rise by the number of risers to get the riser height, and multiply the number of treads by the tread depth to get the total run. For a 108 in rise with 15 risers of 7.2 in and 14 treads of 10.5 in, the total run is 14 × 10.5 = 147 in.

Stair angle in degrees equals the arctangent of riser height divided by tread depth: angle = arctan(rise ÷ run). Using a 7.2 in riser and a 10.5 in tread, arctan(7.2 ÷ 10.5) is about 34.4 degrees. Most interior stairs fall in the 30 to 37 degree range; steeper angles feel more like a ladder and shallower angles need more floor space.

IRC-style residential reference values commonly cite a 10 in minimum tread depth, while IBC-style commercial reference values commonly cite 11 in as a minimum. Many builders target 10.5 to 11.5 in for comfortable footing. Local codes control the actual minimum in your jurisdiction, so always confirm before finalizing a design.

A common target for residential stairs is around 7 to 7.75 in, with IRC-style reference values commonly citing 7 3/4 in as a maximum. IBC-style commercial reference values commonly cite a 7 in maximum and a 4 in minimum. All risers in a single flight should be as close to identical as possible, since uneven risers are a common trip hazard.

Stringer length is the hypotenuse of a right triangle formed by the total rise and total run: stringer = √(rise² + run²). For a 108 in rise and a 147 in run, the stringer length is √(108² + 147²) ≈ 182.4 in. Add extra board length for the bottom riser cut and top plumb cut when ordering lumber.

When the upper floor acts as the final step (a flush top), the number of treads equals the number of risers minus one. A stair with 15 risers has 14 treads, because the last riser lands you on the upper floor itself rather than on another tread.

Measure the deck height from finished grade (or the landing surface) up to the top of the decking, then treat that as the total rise with a flush top, since the deck surface serves as the top step. For a 48 in deck height with a 7 in target riser, 48 ÷ 7 rounds to 7 risers, giving an actual riser height of 48 ÷ 7 ≈ 6 7/8 in and 6 treads.

First calculate the riser height, tread depth, riser count, and tread count for the flight. The stringer's overall layout length is √(total rise² + total run²). The bottom riser cut is shortened by the tread's board thickness (riser height minus tread thickness) so the first step above the floor matches the height of the rest.

Total run equals the number of treads multiplied by the tread depth. With 14 treads at 10.5 in each, the total run is 14 × 10.5 = 147 in, or 12.25 ft. This is the horizontal floor space the stair will occupy, not counting any nosing overhang.

Floor-to-floor height is simply the total rise. Measure from the finished surface of the lower floor to the finished surface of the upper floor, then divide by your target riser height and round to get the number of risers, exactly as with any other stair calculation. For a 9 ft (108 in) floor-to-floor height and a 7.25 in target riser, you get 15 risers at 7.2 in each.

There is no single universally ideal stair angle, but interior stairs are commonly built in the 30 to 37 degree range, with roughly 32 to 35 degrees considered comfortable for everyday use. Angles below about 30 degrees require more horizontal space; angles above about 40 degrees start to feel steep and are typically reserved for utility or attic stairs where codes allow it.

Rise is the vertical measurement: the height of one riser, or the total floor-to-floor height when referring to total rise. Run is the horizontal measurement: the depth of one tread, or the total horizontal distance the stair covers when referring to total run. Stair angle relates the two through arctan(rise ÷ run).

A 7 ft (84 in) floor-to-floor height with a 7.25 in target riser gives 84 ÷ 7.25 = 11.6, which rounds to 12 risers. Recalculating, 84 ÷ 12 = 7.0 in exactly, so you would build 12 risers of 7 in each with 11 treads.

An 8 ft (96 in) floor-to-floor height with a 7.25 in target riser gives 96 ÷ 7.25 ≈ 13.24, which rounds to 13 risers. Recalculating, 96 ÷ 13 ≈ 7.385 in, which is about 7 3/8 in, with 12 treads.

A 9 ft (108 in) floor-to-floor height with a 7.25 in target riser gives 108 ÷ 7.25 ≈ 14.9, which rounds to 15 risers. Recalculating, 108 ÷ 15 = 7.2 in, which is about 7 3/16 in, with 14 treads.

A 10 ft (120 in) floor-to-floor height with a 7.25 in target riser gives 120 ÷ 7.25 ≈ 16.55, which rounds to 17 risers. Recalculating, 120 ÷ 17 ≈ 7.0588 in, which is about 7 1/16 in, with 16 treads.

Enter every measurement, total rise, target riser height, and tread depth, in inches and the same formulas apply directly: risers = round(total rise ÷ target riser height), riser height = total rise ÷ risers, total run = treads × tread depth. Inches are the most common unit for stair layout in the United States because riser and tread dimensions are typically specified to the nearest 1/16 in.

If your floor-to-floor height is given in feet, convert it to inches first (multiply by 12) so it matches the riser and tread dimensions typically used in stair layout, then apply the standard formulas. A 9 ft height becomes 108 in, giving 15 risers of 7.2 in at a 7.25 in target.

Yes. The same formulas work in millimeters or meters; only the units change. For a 2700 mm floor-to-floor height with a 180 mm target riser, 2700 ÷ 180 = 15 risers exactly, giving 14 treads at 270 mm each for a total run of 3780 mm and a stair angle of about 33.7 degrees.

A stair calculator is as accurate as arithmetic allows, the formulas are exact, so results reflect the numbers you enter precisely. Accuracy in the field also depends on how carefully you measure total rise, account for finished flooring thickness on both levels, and cut materials to the calculated dimensions.

The arithmetic of stair calculation is universal, but the resulting dimensions must still satisfy the building code adopted in your jurisdiction, which can vary by state, city, or occupancy type. This tool references commonly cited IRC-style and IBC-style values for context, but it is not a substitute for checking with your local building department or a qualified professional before construction.