Calculation method
Risers = ceiling(total finished rise ÷ target maximum rise). Equal rise = total rise ÷ risers. Intermediate treads = risers − 1, with the upper floor serving as the final landing. Horizontal run = treads × tread depth. Pitch-line reference = intermediate treads × square root(equal rise² + tread depth²). Endpoint diagonal = square root(total rise² + horizontal run²); this is not a cut-stringer or stock-board length. Compare rise ≤ 7¾ in and tread depth ≥ 10 in with the 2021 IRC reference only.
Worked example: input to purchase quantity
For a 108 in total rise (274.32 cm), a 7.75 in maximum (19.685 cm) yields 14 risers at about 7.7143 in (19.5943 cm). With 13 intermediate treads at 10 in (25.4 cm), run is 130 in (330.2 cm). The endpoint diagonal is about 169.0089 in (429.2825 cm).
Count vertical rises before drawing the stair
A straight stair connects two finished elevations through equal vertical rises. This calculator begins with that total height and a target maximum rise. Dividing the height by the target and rounding upward gives the number of risers. Dividing the original height by that whole count gives the equal finished rise. The result also reports intermediate treads, horizontal run, and an endpoint diagonal often useful when discussing the approximate scale of a stringer. It does not specify the lumber or cuts required to carry the stair.
The upper finished floor acts as the final landing in this model. Consequently, a flight with fourteen risers has thirteen intermediate treads. Some drawings count a top tread differently because their connection detail differs. Confirm the assumed endpoint arrangement before comparing results with another calculator or a framing drawing. Adding one extra tread changes horizontal run and diagonal length. The riser count cannot be transferred blindly to a different top connection just because the total height is unchanged.
Measure between finished surfaces
Measure vertically from the lower finished walking surface to the upper finished walking surface. Account for planned flooring, decking, tread material, and landing finishes before final layout. Measuring from unfinished framing at one end and finished flooring at the other creates a different first or last rise. This calculator distributes one total evenly; it cannot detect inconsistent field elevations or compensate for an incorrect endpoint measurement. Recheck elevations after foundations, slabs, and framing are established.
The target maximum rise is a design input, not a command to make every step exactly that high. A total of 108 inches divided by 7.75 needs fourteen risers, each about 7.714 inches. Lowering the target can add a riser and an intermediate tread. The actual rise changes in discrete jumps as the count changes. Tread depth is entered separately as the horizontal leading-edge-to-leading-edge distance. A tread board's full physical depth, including any projecting nosing, is not automatically that effective run.
Understand the cited IRC comparison
The dimensional reference is the 2021 International Residential Code, sections R311.7.5.1 and R311.7.5.2, for ordinary stair treads and risers. The cited maximum rise is 7¾ inches and the cited minimum tread depth is 10 inches. The calculator compares its equal rise and entered tread depth with those two limits and labels that comparison explicitly. It does not determine the locally adopted edition, amendments, stair classification, inspection outcome, or applicability of exceptions. A result inside both limits is not a code approval.
Section R311.7.5.3 addresses nosings and includes an exception to required projection for tread depths of at least eleven inches. The tool displays a reminder relevant to the entered depth. Uniformity, landings, headroom, clear width, handrails, guards, support, and other provisions still require review. Winder, spiral, alternating-tread, commercial, and accessible-route stairs need a different assessment. Keep the reference edition visible when asking the building department about requirements; section numbering and local amendments can differ.
The diagonal is a geometry result
Horizontal run equals intermediate tread count times effective tread depth. The displayed diagonal is the square root of total finished rise squared plus horizontal run squared. These endpoints produce a useful envelope dimension. They do not describe the full cut stringer, its remaining throat, bearing seats, overhang, connector placement, or stock-board length. A cut stringer's repeating pitch and actual end details need a separate layout. Never buy or cut lumber solely from this diagonal, even if it happens to resemble an available board length.
When the height needs only one riser, the model reports zero intermediate treads and zero horizontal run. Its diagonal then equals the height, and an explicit message explains that this is not a usable flight stringer layout. All dimensions switch between inches and centimetres without changing the physical stair. Print the inputs, calculated count, equal rise, and assumptions for review. Resolve structure and code details before converting that worksheet into a framing plan.
A slope reference for the repeating steps
The calculator also reports a pitch-line reference using the actual equal rise and tread run: intermediate tread count multiplied by the square root of one rise squared plus one run squared. For the example, thirteen equal intervals give about 164.1866 inches (417.0338 centimetres). This line follows the repeating rise-to-run slope, unlike the separate full-height endpoint diagonal. It still excludes top and bottom connections, bearing, cleanup and stock allowance. Neither geometric reference is a ready-to-cut stringer or a board order.
Product and method reference
Reference limits and default yields are identified separately from user-entered values; verify the adopted local code and current product label. 2021 IRC Chapter 3, R311.7.5.1–R311.7.5.3.
Calculation and editorial review: November 3, 2026. Arithmetic runs in your browser; project inputs are not submitted to TwoCut.