How to Calculate Stair Rise, Run & Stringer

How to calculate stairs from total rise

How to calculate stairs starts with one measurement: the total rise — finished lower floor to finished upper floor. Divide that by the code maximum riser (7.75 in) and round up to get the riser count N. Then R = total rise ÷ N is the riser height, going is T = N − 1 for a standard mount, total run is T × tread depth, and stringer length is √(rise² + run²). This guide walks the full stair rise and run workflow with IRC 2024 checks and a cut list you can actually build from.

Quick answer: for a 105 in total rise with a 7 in target riser, N = ⌈105 ÷ 7.75⌉ = 14 risers, R = 105 ÷ 14 = 7.5 in, going T = 13, and with an 11 in tread the total run is 143 in. Stringer length = √(105² + 143²) ≈ 177.4 in. Comfort check: 2(7.5) + 11 = 26 in — slightly flat, so drop the target riser or tread until 2R + T lands in 24–25.5 in.

Stair calculation formulas

Every result on the panel comes from these formulas (inches internally, converted for metric display):

• Riser count: N = ⌈total rise ÷ 7.75 in⌉ (never fewer than 2). A target riser below 7.75 in is used first, then capped by code.
• Riser height: R = total rise ÷ N
• Going (treads): T = N − 1 (standard) or T = N (flush — top step level with the floor)
• Total run: Run = T × D, where D is the tread depth
• Stringer length: S = √(R² + Run²) — the hypotenuse you mark on the 2×12
• Slope angle: θ = arctan(R ÷ D) × 180 ÷ π
• Comfort formula: C = 2R + D — keep it between about 24 and 25.5 in (610–648 mm)
• Bottom riser cut: R − tread thickness (the first step sits on the floor, so you subtract the tread stock)
• Headroom: total rise − subfloor thickness − R (clear height from the first nosing to the underside of the upper floor)

IRC 2024 and IBC stair code limits

How to calculate stair rise and run to code means checking the layout against IRC R311.7.5 (residential) and IBC 1011.5 (commercial). IBC is stricter on going.

Check	IRC 2024	IBC
Max riser height	7.75 in (196 mm)	7.75 in (196 mm)
Min tread / going	10 in (254 mm)	11 in (279 mm)
Riser variation	≤ 0.375 in (9.5 mm)	≤ 0.375 in (9.5 mm)
Min headroom	80 in (2032 mm)	80 in (2032 mm)
Nosing projection	0.75–1.25 in typical	0.5–1.25 in typical

Because every step uses the same riser and tread, computed riser variation is 0. The 0.375 in rule matters when you cut stringers by hand and drift between steps — dry-fit the first stringer before ripping the rest.

Standard vs flush top mount

Standard mount: the top step finishes one riser below the upper floor — going T = N − 1, total run = (N − 1) × D. Default for most interior stairs where floor finish eats the last rise.

Flush mount: the top step lands level with the upper floor — going T = N, total run = N × D. Use it when framing and finish build-up let the last tread finish flush. Flush adds one tread of run, so the angle gets slightly shallower.

How to lay out a stair stringer

How to calculate stair stringers ends on the shop floor. Mark the total rise and total run on the framing square, step off N risers and T treads along the 2×12, and cut the notches:

• 1. Mark the total rise on the stringer stock and square off the top cut so it bears on the upper floor / header.
• 2. Step the riser and tread — set the square to R on the rise leg and D on the run leg, and walk it down N times (T going steps plus the final riser).
• 3. Cut the bottom riser short by the tread thickness (R − tread thickness) so the first tread lands at the same height as the rest.
• 4. Check the length — your stringer diagonal should match the calculated stringer length; if it is longer than your stock, the cut list tells you how many 2×12s you need.
• 5. Verify headroom — clear height from the first nosing to the soffit above must be at least 80 in (default).

The comfort formula (2R + T)

The stair comfort formula — twice the riser plus the tread — approximates a natural stride. Land between 24 and 25.5 in and the flight walks well. Under 24 it feels steep and choppy; over 25.5 it feels flat and slow. The calculator flags anything outside that band as a comfort warning, separate from the hard code checks.

Example: a 7.0 in riser with an 11 in tread gives 2(7) + 11 = 25 in — right in the sweet spot, which is why those are the defaults.

Frequently Asked Questions