How to Calculate Stair Dimensions: Rise, Run, and Stringer Layout

Learn how to calculate stair dimensions including riser height, tread depth, stringer length, and total run. Covers building code requirements and layout techniques.

Building Code Requirements for Stairs

The International Residential Code (IRC) sets strict limits on stair dimensions to ensure safety. The maximum riser height is 7-3/4 inches, and the minimum tread depth is 10 inches. All risers in a flight must be within 3/8 inch of each other in height, and all treads must be within 3/8 inch of each other in depth. The minimum stair width is 36 inches. Headroom must be at least 6 feet 8 inches measured vertically from the tread nosing to any overhead obstruction. Handrails are required on at least one side and must be between 34 and 38 inches above the stair nosing. These are minimums and maximums; comfortable stairs typically have risers between 7 and 7-1/2 inches and treads of 10 to 11 inches.

Calculating the Number of Risers

Start by measuring the total rise, which is the vertical distance from the finished floor at the bottom to the finished floor at the top. This measurement must include the thickness of any floor finishes on both levels. If the total rise is 108 inches (9 feet), divide by your desired riser height. Using 7.5 inches per riser gives 108 / 7.5 = 14.4 risers, which you must round to a whole number. Rounding to 14 risers gives a riser height of 108 / 14 = 7.714 inches, which slightly exceeds the 7-3/4-inch code maximum. Rounding to 15 risers gives 108 / 15 = 7.2 inches per riser, which is comfortable and well within code. Always divide the total rise by the number of risers to get the exact riser height.

Determining Tread Depth and Total Run

The number of treads is always one less than the number of risers, because the top floor serves as the final tread. With 15 risers, you have 14 treads. If each tread is 10 inches deep (not counting the nosing), the total run (horizontal distance from the face of the bottom riser to the face of the top riser) is 14 x 10 = 140 inches, or 11 feet 8 inches. This is the horizontal floor space the staircase will occupy. If the available space is limited, you can increase the riser height (within code limits) to reduce the number of risers and treads, but be careful not to make the stairs too steep for comfortable use. The 7-11 rule (7-inch riser, 11-inch tread) is considered the gold standard for comfortable stairs.

The Riser-Tread Relationship

There are several time-tested rules for the relationship between riser height and tread depth. The most common is that the sum of two risers plus one tread should equal 24 to 25 inches (2R + T = 24 to 25). Another rule states that the riser times the tread should be between 70 and 75 (R x T = 70 to 75). A third rule says the riser plus the tread should equal 17 to 18 inches (R + T = 17 to 18). All three rules point to the same range of comfortable proportions. Stairs that violate these relationships feel either too steep and cramped or too shallow and sprawling. The 7-inch riser with an 11-inch tread satisfies all three rules perfectly.

Stringer Layout and Calculation

The stringer is the diagonal board that supports the treads and risers. To calculate the stringer length, use the Pythagorean theorem: stringer length equals the square root of (total rise squared plus total run squared). For a stair with 108 inches of total rise and 140 inches of total run, the stringer length is the square root of (11,664 + 19,600) = the square root of 31,264 = about 176.8 inches, or roughly 14 feet 9 inches. Stringers are typically cut from 2x12 lumber. After cutting the notches for treads and risers, the remaining uncut width of the stringer must be at least 3.5 inches to maintain structural integrity. This minimum throat width determines whether a 2x12 is adequate or whether a wider board or engineered stringer is needed.

Laying Out the Stringer with a Framing Square

Mark the riser height on one leg of a framing square and the tread depth on the other. Stair gauges (small brass clamps) attached to the square at these marks make it easy to repeat the layout consistently. Place the square on the stringer board with both marks touching the edge, and trace along the outside of the square to mark one step. Slide the square along the board so the riser mark aligns with the end of the previous tread line, and trace again. Repeat for every step. At the bottom, shorten the first riser by the thickness of one tread to account for the fact that the bottom tread will add that height. At the top, the last tread is the floor itself, so no tread board is cut there.

Winding Stairs, Landings, and Special Cases

Intermediate landings are used when a staircase needs to change direction or when the total run is too long for a single straight flight. A landing functions as a large tread and must be at least as deep as the stair width (36 inches minimum). L-shaped stairs have one 90-degree landing, and U-shaped stairs have a 180-degree turn with two landings or one large landing. Winder treads, which are pie-shaped treads used instead of a landing to turn a corner, must have a minimum tread depth of 10 inches measured at a point 12 inches from the narrow end. Spiral staircases have specific code provisions and are generally limited to secondary access unless they meet generous minimum tread and width requirements.

Practical Tips for Stair Construction

Always double-check the total rise measurement after the subfloor and finish floor materials are installed on both levels, because even a quarter-inch difference changes every riser height. Use a story pole (a straight board marked with each riser height stacked on top of the previous) to verify that the layout is correct before cutting any stringers. Most residential stairs have three stringers: one on each side and one in the center to prevent bounce. If the stair width exceeds 36 inches, adding a center stringer is highly recommended. Attach the stringers to the upper floor framing with joist hangers or a ledger board, and secure the bottoms to the lower floor with angle brackets or a kick plate anchored to the concrete or framing below.

Try These Calculators

Put what you learned into practice with these free calculators.

Stair Stringer Calculator Staircase Riser Calculator Lumber Calculator Deck Board Calculator