Key Takeaways
- The total rise is the vertical distance from the lower floor to the upper floor, measured precisely
- Standard residential rise is 7 to 7.75 inches per step, with 10 to 11 inches of run
- The stringer length is calculated using the Pythagorean theorem on total rise and total run
- Headroom of at least 6 feet 8 inches is required by most building codes
- Each step has a tread (the part you step on) and a riser (the vertical face)
Total rise is the vertical distance from the finished floor at the bottom of the stairs to the finished floor at the top, which determines the number of steps needed.
Stringer is the structural member that supports the treads and risers, typically cut from a 2x12 board with a notched profile.
Building a staircase is one of the more precise carpentry tasks on a residential project. The dimensions have to be consistent from step to step because even small variations create a tripping hazard. The math is not complicated, but it has to be exact.
Here is how to work through the calculation from start to finish.
Measure the total rise
The total rise is the vertical distance between the finished floor surfaces. Measure from the subfloor at the bottom to the subfloor at the top, then account for the finished floor thickness at both ends.
A basement to first-floor staircase might have a total rise of 108 inches (9 feet). A deck staircase might rise 42 inches (3.5 feet). The number determines everything else.
Determine the number of steps
Divide the total rise by the target riser height. Building codes in most jurisdictions require a maximum riser height of 7.75 inches for residential stairs, with a minimum of 4 inches. A comfortable riser height is 7 to 7.5 inches.
For a 108-inch total rise at 7.5 inches per riser:
108 / 7.5 = 14.4 steps
Round up to 15 steps, then recalculate the actual riser height:
108 / 15 = 7.2 inches per step
That is within the acceptable range and gives you consistent step heights.
Calculate the total run
The total run is the horizontal distance the staircase covers. Each step has a run (tread depth), and the total run equals the number of treads times the run per tread.
Standard residential tread depth is 10 to 11 inches. With a 10.5-inch run per tread and 15 steps:
15 x 10.5 = 157.5 inches of total run
That is about 13.1 feet of horizontal space the staircase needs.
The stringer length
The stringer is the diagonal structural member that carries the treads and risers. Its length is the hypotenuse of the right triangle formed by the total rise and total run.
Using the Pythagorean theorem:
stringer length = sqrt(total rise^2 + total run^2)
For our example:
sqrt(108^2 + 157.5^2) = sqrt(11,664 + 24,806) = sqrt(36,470) = 191 inches
That is about 15.9 feet. A standard 16-foot 2x12 board would work, but you would want a little extra length for trimming and fitting. Order or cut stringers at least 12 inches longer than the calculated minimum.
Headroom clearance
Most building codes require a minimum headroom of 6 feet 8 inches (80 inches) measured vertically from the nosing of the tread to the ceiling or obstruction above. This is the measurement that trips up many staircase projects.
Calculate headroom at the point where a person standing on the stair is tallest. On a straight run, that is typically the middle of the staircase. On a landing or turn, it depends on the geometry.
If headroom is tight, options include reducing the tread depth (within code limits), adding a landing, or repositioning the stair opening above.
Tread and riser consistency
Every tread must be within 3/8 inch of every other tread in the same flight. Every riser must be within 3/8 inch of every other riser. This is a building code requirement, not a suggestion, because inconsistent steps are a leading cause of stairway falls.
Measure and cut each stringer from the same template. Do not adjust individual steps to make up for measurement errors. If the math does not work out evenly, redistribute the difference across all steps, not just the top or bottom one.
Open versus closed risers
Closed risers have a solid board behind each step. Open risers have gaps between the treads that allow light and air through. Building codes typically require that open risers not allow a 4-inch sphere to pass through, which means the gap between treads cannot exceed about 3.75 inches.
Open risers look lighter and more modern but require stricter dimensional control because the gaps are visible and any inconsistency is obvious.
Landing requirements
Most codes require a landing at the top and bottom of every stair flight. A landing must be at least as wide as the stair and at least 36 inches deep. For stairs with a total rise greater than 12 feet, an intermediate landing is often required.
Landings add to the total run calculation and affect the stringer length. Factor them into your layout before cutting any lumber.
The stair calculator determines the number of steps, riser height, tread depth, stringer length and headroom clearance for your specific dimensions.
Editorial note: This article is reviewed for accuracy and updated regularly. All calculations use standard building code formulas. For the latest code requirements, consult your local building department directly.
Frequently asked questions
What is the standard rise and run for residential stairs?
The standard residential riser height is 7 to 7.75 inches, and the standard tread depth is 10 to 11 inches. Building codes typically cap the riser at 7.75 inches and set a minimum tread depth of 10 inches for residential construction.
How do I calculate the number of steps?
Divide the total rise (vertical distance between floors) by the desired riser height. Round up to the nearest whole number, then divide the total rise by that number to get the actual riser height for each step.
How long should a stair stringer be?
The stringer length is the hypotenuse of the triangle formed by the total rise and total run. Use the Pythagorean theorem: stringer length equals the square root of (total rise squared plus total run squared). Add 12 inches for trimming.
How much headroom do stairs need?
Most building codes require a minimum of 6 feet 8 inches (80 inches) of headroom, measured vertically from the nosing of the tread to the ceiling or obstruction above. Check your local code for the exact requirement.