Stair Calculator

Design a straight staircase from its total rise — riser count and height, tread depth by Blondel's rule, total run, stringer length and stair angle. Runs entirely in your browser — your numbers never leave this device.

Unit

Total rise, floor to floor (in)

Riser height (in)

7.71

Evenly divided across all risers — never vary riser heights within a flight.

Riser count: 14
Tread count: 13
Tread depth (in): 9.57
Total run (in): 124.43
Stringer length (in): 164.76
Stair angle: 41.0°

Typical comfort ranges: riser height 7–7.75 in (17.8–19.7 cm) and tread depth 10–11 in (25.4–27.9 cm), following Blondel's rule that twice the riser plus the tread should total about 25 in (63.5 cm).

At this total rise, the riser height or tread depth lands outside those typical comfort ranges. The Blondel 25 in target forces a trade-off here: adding or removing a riser shifts both numbers, so one of them has to give — check the layout against your available run before cutting stringers.

How it works

Typical comfort ranges — general guidance, not a code verdict

Element	Typical comfort range
Riser height	7 – 7.75 in
Tread depth	10 – 11 in minimum typical
2R + T	24 – 25 in
Stair angle	30 – 37°

A staircase is fixed by its total rise — the finished floor-to-floor height — and everything else is derived. The riser count is the total rise divided by a target riser height of 7.5 in and rounded to a whole number, because a flight cannot have a fractional step; the true riser height is then the total rise divided by that count, so every riser in the flight is identical, which is a safety property as much as a convenience — irregular risers are a trip hazard. Treads number one fewer than risers, because the top riser arrives at the upper floor, which is itself the final tread surface.

Tread depth comes from Blondel's rule, the centuries-old proportion 2 × riser + tread = 25 in, which ties the depth of each step to twice its height so the geometry matches a natural stride. Total run is treads times tread depth; the stringer — the diagonal board the steps sit on — is the hypotenuse of the whole flight, √(rise² + run²) by Pythagoras; and the angle is the arctangent of rise over run. All three follow from the riser and tread figures with no further choices.

The first worked example shows the trade-off in the open. At a total rise of 108 in the riser count rounds to 14, the riser height becomes 7.71 in, and Blondel's rule returns a tread of 9.57 in — under the typical 10 in tread in the comfort table — because a 25 in Blondel target is a comfort proportion, and holding it exactly on this rise trades tread depth for riser height. The table prints typical comfort ranges as general guidance, not a code verdict: stair dimensions are regulated, and the governing code for the location sets the binding limits for any real build.

Worked examples

Total rise 108 in

Input: Total rise = 108 in, Target riser = 7.5 in, Blondel target = 25 in
Working: Risers = round(108 ÷ 7.5) = 14. Riser height = 108 ÷ 14 = 7.71 in. Treads = 13. Tread = 25 − 2 × 7.71 = 9.57 in. Total run = 13 × 9.57 = 124.4 in. Stringer = √(108² + 124.4²) = 164.8 in. Angle = atan(108 ÷ 124.4) = 41.0°. The tread falls under the typical 10 in because the 25 in Blondel target is a comfort rule — the trade-off is shown rather than hidden.
Result: 14 risers of 7.71 in · 13 treads of 9.57 in · Run 124.4 in · Stringer 164.8 in · Angle 41.0°

Total rise 102 in

Input: Total rise = 102 in, Target riser = 7.5 in, Blondel target = 25 in
Working: Risers = round(102 ÷ 7.5) = 14. Riser height = 102 ÷ 14 = 7.29 in. Treads = 13. Tread = 25 − 2 × 7.29 = 10.43 in. Total run = 13 × 10.43 = 135.6 in. Stringer = √(102² + 135.6²) = 169.7 in. Angle = atan(102 ÷ 135.6) = 37.0°.
Result: 14 risers of 7.29 in · 13 treads of 10.43 in · Run 135.6 in · Stringer 169.7 in · Angle 37.0°

Frequently asked questions

Why is there one fewer tread than risers?

Because the last riser steps onto the upper floor itself. A flight with 14 risers climbs 14 heights, but only 13 built treads are needed — the floor at the top serves as the fourteenth surface, which is why the run is calculated from 13 treads in both worked examples.

What is Blondel's rule?

The proportion 2 × riser height + tread depth = about 24–25 in, dating to the 17th-century architect François Blondel. It keeps step geometry in step with a natural stride: as risers grow taller, treads grow shallower to keep the sum constant. This calculator uses a 25 in target and prints the rule in its formula.

Why did the 108 in example produce a 41° stair?

Because the riser count, Blondel's rule and the total rise together leave no freedom: 14 risers of 7.71 in force a 9.57 in tread, and that pairing is steeper than the typical 30–37° comfort range in the table. The calculator reports the geometry honestly rather than relaxing a rule silently — on a real project that result is the signal to revisit headroom, run length or the floor opening.

Are the comfort ranges building code?

No. The table is labelled general guidance: typical ranges drawn from common practice. Stair dimensions are set by the building code in force where the stair is built, which governs any real construction and can differ from the ranges shown.

How long is the stringer board to buy?

The stringer figure is the geometric diagonal of the flight — 164.8 in in the first example. Stock must also cover the cuts at both ends (the top and bottom plumb and level cuts and any tail beyond the first tread), so the purchased board is longer than the geometric figure; the calculator reports the geometry, and allowances are added when cutting.

Are measurements stored?

No. The calculation runs entirely in the browser and nothing entered is uploaded, stored or tracked.

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