Builder's Math

Calculators / Stair calculator

Stair calculator

Enter the height from floor to floor and get the number of steps, the exact riser height, the total run and how long the stringers need to be.

in
in

Result

How to use it

Measure the total rise from the top of the lower floor to the top of the upper floor. The calculator splits it into equal risers no taller than the limit you set, then works out the run and the stringer.

Side view of a staircase showing total rise, total run, a riser, a tread and the stringer Total rise Total run Riser Tread Stringer
Total rise is measured floor to floor. There is always one tread fewer than risers.

The formulas

Risers          = total rise ÷ tallest riser, rounded up
Riser height    = total rise ÷ risers
Treads          = risers − 1
Total run       = treads × tread depth
Stringer length = √(total rise² + total run²)

Example: a 108-inch rise (9 feet) divided by 7.75 is 13.9, so 14 risers of 7 11/16″ each. 13 treads of 10″ give a total run of 10′ 10″, and each stringer is about 14′ 1″ long.

Quick answers for common heights

10 in treads, risers no taller than 7¾ in.
Total riseRisersRiser heightTreadsTotal run
24 in (2 ft deck)46″32′ 6″
30 in (2½ ft deck)47 1/2″32′ 6″
36 in (3 ft deck)57 3/16″43′ 4″
48 in (4 ft deck)76 7/8″65′ 0″
96 in (8 ft ceiling, floor to floor)137 3/8″1210′ 0″
108 in (9 ft floor to floor)147 11/16″1310′ 10″
120 in (10 ft floor to floor)167 1/2″1512′ 6″

Code limits

The International Residential Code (IRC), used in most US states, allows risers up to 7 3/4 inches and treads at least 10 inches deep, with no more than 3/8 inch difference between the tallest and shortest riser in a flight. Your local code may differ, and decks can have their own rules, so check before you cut.

A common comfort rule: two risers plus one tread should add up to about 24 to 25 inches.

Sources and assumptions

Limits from the 2021 International Residential Code, section R311.7.5: 7¾ inch maximum riser, 10 inch minimum tread. Stringer length is the straight line from the bottom of the first riser to the top of the last, before cuts.

Questions

How many steps do I need for 8 feet?

For a 96-inch rise, 13 risers of about 7 3/8 inches, with 12 treads.

How many steps for a 3 foot deck?

For a 36-inch rise, 5 risers of about 7 3/16 inches and 4 treads.

What is the standard riser height?

Most stairs use risers between 7 and 7 3/4 inches. The IRC maximum for homes is 7 3/4 inches.

Is the number of steps the risers or the treads?

Usually the risers. There is one less tread than risers, because the upper floor acts as the last step.

How long should a stair stringer be?

Start from the stringer length above, then allow a little extra for the cuts at the top and bottom. 2×12 lumber is the usual choice.

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