Stair Calculator
Plan a full flight of stairs from the floor-to-floor rise. The calculator splits the rise into equal steps, then returns the exact riser, tread run, total run, the diagonal stringer length and height, the stair angle, a headroom check and an optional material cost. Choose a target riser or a fixed number of steps, set a standard or flush stringer mount, and switch between imperial and metric.
Formula
Worked example
A floor-to-floor rise of 112 in with a 7 in target gives N = round(112 / 7) = 16 risers, so each riser is 112 / 16 = 7 in. With a standard mount there are 15 treads, so an 11 in tread gives a total run of 15 x 11 = 165 in. The stringer length is sqrt(112^2 + 165^2) = 199.4 in, and the stair angle is arctan(112 / 165) = 34.2 degrees.
How the staircase dimensions are derived
A staircase has to climb the total rise, the floor-to-floor height, in a whole number of equal steps, because every riser in a flight should be the same height for safety. In target-riser mode the calculator divides the total rise by your target riser height and rounds to the nearest whole number to get the step count, then divides the total rise back by that count to find the exact riser each step must be. In fixed-step mode you set the count directly and the riser follows. The total run is the horizontal distance the stairs cover: with a standard mount the top step lands on the upper floor itself, so a flight with N risers has only N minus 1 treads, while a flush mount keeps a full tread at the top and so has N treads. The stringer, the diagonal board that supports the treads, follows the Pythagorean theorem as the hypotenuse of the total rise and total run, and the stair angle is the arctangent of the rise over the run.
Comfort, the 2R + T rule and building codes
Comfortable stairs follow well-established proportions. The Blondel formula says that twice the riser plus the tread (2R + T) should fall between roughly 24 and 25 inches (610 to 635 mm), which keeps a stride natural whether going up or down. In the United States the International Residential Code generally limits risers to a maximum of 7.75 inches (196 mm) and requires a minimum tread depth of 10 inches (254 mm); other jurisdictions and commercial codes use different limits. A comfortable stair angle is usually between 30 and 37 degrees; above about 42 degrees a flight becomes steep and tiring. Risers that are too tall make stairs dangerous, while treads that are too shallow leave nowhere safe to place a foot, so the greatest variation between any two risers in a flight is also tightly capped, often to 3/8 inch (about 10 mm).
Headroom, stringer mounts and costing the job
When a staircase passes under a floor opening, you need enough headroom so a tall person does not hit their head on the edge of the opening above. Turn on the headroom check and enter the length of the floor opening along the run and the thickness of the upper floor; the calculator finds the clear height at the head of the opening and compares it with the usual 6 foot 8 inch (2030 mm) minimum. The stringer mount setting changes the tread count: a standard mount treats the upper floor as the final tread, while a flush mount keeps a full tread at the top, which lengthens the run slightly. Turn on the cost estimate to price the carpentry: enter how many stringers the flight uses (two outer plus a centre one for wide treads is common), the price of each stringer board and the price per tread, and the calculator totals the material cost. The figures here are planning estimates; confirm every dimension and the headroom against your site and local code before cutting.
Common stair dimension guidelines
| Dimension | Typical / recommended | Limit |
|---|---|---|
| Riser height | 7 in (178 mm) | Max 7.75 in (196 mm) |
| Tread depth (run) | 11 in (279 mm) | Min 10 in (254 mm) |
| 2 x riser + tread | 24-25 in (610-635 mm) | Comfort range |
| Stair angle | 30-37 degrees | Steep above 42 degrees |
| Headroom above stairs | 6 ft 8 in (2030 mm) | Minimum |
| Riser variation in a flight | 0 | Max 3/8 in (10 mm) |
Typical residential values; always defer to your local building code.
Frequently asked questions
Why is the actual riser height different from my target?
The total rise must divide into a whole number of equal steps, so the calculator rounds the step count to the nearest integer and then recomputes the exact riser by dividing the total rise by that count. The actual riser is usually very close to your target but rarely identical, because a fractional number of steps is not allowed. Switch to fixed-step mode if you want to set the count yourself.
What is the difference between a standard and a flush stringer mount?
With a standard mount the top riser brings you up to the upper floor and the floor itself acts as the final landing, so a flight with N risers has only N minus 1 treads. A flush mount keeps a full tread at the very top, level with the upper floor, so it has N treads and a slightly longer total run. The mount you choose changes the total run, the stringer length and the stair angle.
How is the stair angle and stringer length calculated?
The stringer is the diagonal hypotenuse of a right triangle whose vertical side is the total rise and whose horizontal side is the total run, so by the Pythagorean theorem its length is the square root of the total rise squared plus the total run squared. The stair angle is the arctangent of the total rise divided by the total run. A comfortable flight sits between about 30 and 37 degrees.
How much headroom do stairs need?
Most building codes require at least 6 feet 8 inches (2030 mm) of clear headroom measured vertically from the tread nosing to the ceiling or the edge of any floor opening above. Turn on the headroom check and enter the floor opening length and the upper floor thickness to see whether your opening is long enough to keep that clearance.