Stair Calculator

How to use this calculator

Measure the total rise from finished floor to finished floor. Enter it with a tread depth (10 inches is pre-filled, the IRC minimum), then try numbers of risers until the riser height is comfortable — 7 to 7¾ inches for homes. If you enter a maximum riser height instead of a count, the number of risers is shown with a note to round it up; enter that whole number to get the final layout.

Every other combination works as well: from a fixed run available on the floor plan and the total rise, the calculator gives the tread depth and angle for a chosen number of risers. Warnings appear under the riser and tread fields when values fall outside the IRC R311.7 limits.

The formula

r = H / n

L = (n − 1) × d

S = √(H² + L²)

θ = atan(r / d)

H: total rise (floor to floor)
n: number of risers
r: riser height
d: tread depth (run per step)
L: total run
S: stringer length (hypotenuse)
θ: stair angle

Worked example

The finished floor-to-floor height is 105 in (8 ft 9 in). You plan 14 risers and 10-inch treads.

Riser height = 105 ÷ 14 = 7½ in — under the 7¾-inch IRC maximum.
There is one fewer tread than risers: total run = 13 × 10 = 130 in.
Stringer length ≈ √(105² + 130²) = 167.1 in; stair angle = atan(7.5 / 10) = 36.9°.

Cut stringers from 16-ft boards (at least 14 ft of usable length) and allow 10 ft 10 in of floor space for the run.

Residential stair limits (IRC R311.7)

Dimension	Requirement
Riser height	7¾ in (196 mm) maximum
Tread depth	10 in (254 mm) minimum, measured nosing to nosing
Variation within a flight	⅜ in (9.5 mm) maximum between largest and smallest
Headroom	6 ft 8 in (2032 mm) minimum
Nosing	¾–1¼ in where treads are under 11 in

Local codes may differ; commercial stairs (IBC) allow at most 7 in risers and need 11 in treads.

Assumptions and limits

A straight flight with equal risers, and the top tread is the upper floor (so there is one fewer tread than risers).
Stringer length is the hypotenuse of rise and run; add the extra needed at the top and bottom cuts when buying lumber.
The rule of thumb 2r + d ≈ 24–25 in gives comfortable stairs.

Frequently asked questions

How many steps do I need for a 9-foot rise?

108 in ÷ 7¾ in = 13.9, so at least 14 risers of 7.71 in each, and 13 treads.

What is a comfortable stair angle?

Between about 30° and 37°. Residential maximums (7¾ in risers on 10 in treads) give 37.8°.

Why is there one fewer tread than risers?

The top step is the upper floor itself, so the final riser leads onto the landing rather than onto another tread.