How the risers are worked out
Divide the total rise by the riser you would like, then round to the nearest whole number. That is how many risers the stair will have.
Dividing the total rise by that whole number gives the actual riser, which every step must match. A 108 inch rise with 7.5 inch preferred risers gives 14.4, so 14 risers of 7.714 inches each.
The IRC caps a riser at 7.75 inches and the tallest riser sets the whole stair, so a result above 7.75 fails even if only one step is out.
Worked example
A 108 inch rise with 7.5 inch preferred risers gives 14 risers at 7.714 inches. With a 10 inch tread the pitch is 37.6 degrees.
That satisfies the IRC: the riser is under 7.75 inches and the tread is at least 10 inches.
Pitch, tread and how the stair feels
Pitch is the angle of the line joining the nosings: the arctangent of the riser divided by the tread. Residential stairs usually land between 30 and 38 degrees.
The IRC also allows a nosing of up to 1.25 inches on a tread at least 10 inches deep, and that nosing counts towards the going you actually stand on.
A 7.75 inch riser with a 10 inch tread is the steepest legal residential stair. It is legal and it is unpleasant to use every day.
Limits of this calculator
It calculates the geometry of one straight flight. It does not check headroom, which needs 6 ft 8 in measured vertically, or the width, which is 36 inches.
It does not design the stringers, the guard or the landings, and it does not check the code edition your jurisdiction enforces.
It uses the IRC limits for a dwelling. Commercial stairs fall under a different code with different proportions.
For metric riser and going limits, use the UK stair calculator.
Inputs for the US stair calculator
Total rise
Floor to floor height in inches, which is what the stair has to climb.
Preferred riser height
The riser you would like. The stair is built from a whole number of them.
Tread depth
Depth of each tread from nosing to nosing. The IRC minimum is 10 in.
CALCULATOR QUESTIONS
US stair calculator questions
How many risers will I need?
Divide the rise by about 7.5 inches and round to the nearest whole number, then divide again to get the exact riser.
What is the maximum riser height?
7.75 inches under the IRC, with a minimum tread of 10 inches.
Can I have a shorter top riser?
No. Every riser must be equal within 3/8 inch, or the stair fails inspection.
Does this check headroom?
No. Headroom needs 6 ft 8 in measured vertically, and it is a separate check.