Stair Stringer Calculator

How the math works

A stair is just a right triangle. The total rise (floor to floor) is one leg, the total run is the other, and the stringer is the hypotenuse. The hard part isn't the trig — it's hitting it while staying inside the building code's limits on how tall each step can be and how deep it has to be.

Start with the rise. Divide it by your target riser height to get a step count, then round to a whole number — you can't have a fractional step. The calculator then checks that count against the code: if dividing the rise by it would leave a riser taller than the maximum, it adds a step and recomputes. The actual riser height is the total rise divided by the final number of risers, so every step comes out identical.

Risers, treads, and the stringer

There is always one more riser than tread — the top riser lands you on the floor above, which isn't a tread. So treads = risers − 1, and the total run is that tread count times your tread depth. The stringer length is the hypotenuse of the rise and run, √(rise² + run²), plus about a foot of extra board for the top plumb cut and the bottom attachment to the floor. That stock is almost always a 2x12.

Where stairs fail inspection

• Riser too tall. Over 7-3/4 in (IRC) or 7 in (IBC) is an automatic fail. Add a riser to bring it down.
• Tread too shallow. Under 10 in (IRC) or 11 in (IBC) and the stair is steeper than code allows.
• Risers not uniform. The most-cited stair defect: every riser must be within 3/8 in of every other. Lay them all out from one total-rise measurement, not by stacking step on step.
• Headroom. Both codes want 80 in of clear headroom measured plumb from the tread nosing — easy to lose under a low ceiling or a stair above.

IRC vs. IBC — pick the right code

The IRC covers one- and two-family dwellings; the IBC covers commercial and most multi-family work. The IBC is the stricter of the two on geometry, so a basement stair that passes as residential can fail if the same building is later classed commercial. When in doubt, build to the tighter IBC numbers — a 7 in max riser and 11 in tread ride more comfortably anyway. Either way, verify your local amendments: jurisdictions tweak these limits.

Riser, tread, and headroom limits from IRC R311.7 and IBC 1011 — model codes, enacted into law and not copyrightable per Veeck v. SBCCI. Stringer geometry is plain trigonometry. Verify local amendments.