Stair Rise and Run: How to Calculate Steps and Lay Out Stringers

Step 1: Measure Total Rise

Measure from the finished floor of the lower level to the finished floor of the upper level, including any flooring you plan to add. Say it is 108 inches. Accurate measurement is crucial because errors accumulate over all the risers.

Measure at the actual stair opening, since floors may not be level.

Step 2: Choose the Number of Risers

Divide the total rise by a target riser height of about 7 to 7¾ inches and round to the nearest whole number. 108 ÷ 7.5 = 14.4, so use 14 risers. The exact riser height is 108 ÷ 14 = 7.714 inches (about 7 23/32), which stays under the 7¾ inch limit. With 15 risers the height would be 7.2 inches, a gentler stair that uses more floor space.

There is always one fewer tread than riser, because the top floor acts as the last tread. So 14 risers need 13 treads.

Step 3: Choose Tread Depth and Check Comfort

A common comfort formula says twice the riser plus the tread should equal about 24 to 25 inches. With a 7.71-inch riser and a 10-inch tread, 2 × 7.71 + 10 = 25.4, slightly steep but within an acceptable range. Increasing the tread to 10.5 inches gives 25.9; a lower riser with a deeper tread feels gentler.

Total run is the number of treads times the tread depth: 13 × 10 = 130 inches, or 10 feet 10 inches of horizontal space. Make sure you have room, or the stair will need a landing or turn.

Step 4: Calculate Stringer Length

The stringer, the sloped board that supports the treads, is the hypotenuse of a right triangle with legs equal to the total rise and total run: √(108² + 130²) = √(11,664 + 16,900) = √28,564 = 169 inches, about 14.1 feet. Buy a board long enough to include the cut from the stringer layout; a 2×12 that is 16 feet long is a typical choice.

The stair angle is arctan(7.714 ÷ 10) = 37.6°, within the common range of 30° to 40° for residential stairs.

Layout and Cutting Tips

Use a framing square with stair gauges set at the riser and tread values, marking each step along the board. Adjust the first step because the bottom riser will be shorter by the thickness of the tread material, and the top will connect to the framing. Cut the first stringer, test it, then use it as a template for the others. Space stringers no more than 16 inches apart for standard treads, and use three stringers for a stair 36 inches wide.

Add a handrail between 34 and 38 inches high where required, and meet any local requirements for guards, headroom, and landings.

Common Mistakes

Forgetting to subtract the finished floor thickness, assuming rises are equal when floors are uneven, using the wrong number of treads (one fewer than risers), and ignoring headroom. Always dry-fit the stringer before cutting the rest.