How do you calculate the number of stairs from total rise?

Divide the total floor-to-floor rise by your preferred riser height and round to the nearest whole number. That whole number is your count of risers (steps). The exact riser height is then total rise divided by that count, so every step is identical.

What is the difference between rise and run on stairs?

Rise is the vertical floor-to-floor height the staircase climbs; run is the horizontal distance the flight covers. Each individual step has a riser (the vertical face) and a tread or going (the horizontal depth you step on). Total rise divided by steps gives the riser; total run divided by treads gives the tread depth.

How is stringer length calculated?

The stringer is the diagonal board that carries every step, so its length is the hypotenuse of a right triangle whose legs are the total rise and the total run. The tool uses length equals the square root of rise squared plus run squared, which is the minimum cut length before you add any landing or overhang.

What is a comfortable riser height and tread depth?

Common private-stair guidance puts risers around 150 to 220 mm (about 4 to 7.75 in) and treads at 220 mm (10 in) or more. The comfort or Blondel rule says twice the riser plus the tread should land near 600 to 660 mm (24 to 25 in); the calculator flags any step that drifts outside that band.

How steep can a domestic staircase be?

For a private dwelling stair, UK Approved Document K caps the pitch at 42 degrees, and most US codes work out close to the same maximum. The tool reports the exact angle from the arctangent of riser over tread and marks it with a cross if it exceeds 42 degrees.

Why does the calculator use one fewer tread than risers?

A straight flight that lands on the upper floor steps onto the floor surface for its final move, so the top riser has no separate tread board. That makes the number of treads one less than the number of risers, which matters when you order timber and lay out the stringer.

Stairs Calculator — Gera Tools

A stair calculator that converts a total rise and an optional total run into a complete, buildable flight: the number of steps, the exact riser height, the tread depth (going), the stair angle and the stringer cut length — then checks every figure against common private-stair building-code limits. It is built for DIY builders, carpenters, deck and loft projects, and anyone sizing a staircase before ordering timber. Work in metric (mm) or imperial (in); the tool converts your inputs when you switch so the physical stair stays the same.

How it works

The calculation starts from the one measurement you can always take accurately: the floor-to-floor rise. You give a preferred riser height, and the tool divides the rise by it and rounds to the nearest whole number to get a count of identical risers (steps). It then recomputes the exact riser as rise divided by that count, so there is never an odd short step at the top.

The number of treads is one fewer than the number of risers, because a flight that lands on the upper floor uses the floor itself for the final step. If you supply an available run, the tread depth is the run divided by the tread count. If you leave the run blank, the tool sizes the tread from the comfort rule (twice the riser plus the tread should sit near 635 mm or 25 in), which keeps the stair feeling natural to climb.

From riser and tread it derives the pitch angle as the arctangent of riser over tread, and the stringer length as the hypotenuse over the full rise and run. Finally it runs each value past private-stair limits — riser range, minimum going, maximum 42-degree pitch, the comfort band, and an optional headroom check — and shows a tick or cross for each so you can tune the inputs before cutting anything.

Worked example

Suppose a loft has a 2700 mm floor-to-floor rise and you prefer a 190 mm riser. Dividing gives 2700 / 190 = 14.2, which rounds to 14 steps. The exact riser becomes 2700 / 14 = 193 mm. With 14 risers you have 13 treads. With no run entered, the comfort rule sets the going to about 635 − 2 × 193 = 249 mm, so the footprint is 13 × 249 = 3237 mm. The pitch is arctan(193 / 249) = about 38 degrees, comfortably under the 42-degree limit, and the stringer length is the hypotenuse of 2700 and 3237, roughly 4215 mm. Every check passes, so this is a sound private flight.

Reference and formulas

Steps (risers) = round(total rise ÷ preferred riser)
Riser height = total rise ÷ steps
Treads = steps − 1 (flight lands on the upper floor)
Tread depth = total run ÷ treads, or comfort − 2 × riser when no run is given
Stair angle = arctan(riser ÷ tread)
Stringer length = square root of (rise squared + run squared)
Comfort rule = 2 × riser + tread, ideally 600–660 mm (24–25 in)

Typical private-stair limits used for the checks: riser 150–220 mm (4–7.75 in), tread 220 mm (10 in) minimum, pitch 42 degrees maximum, headroom 2000 mm (80 in) minimum. These follow widely used guidance such as UK Approved Document K and the US IRC; always confirm your local code before building.

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