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BuildMath

Glossary · Stairs

Stair Stringer Rise and Run

Total rise, total run, unit rise (riser) and unit run (tread) on a stair stringer — definitions, IRC limits, the 2R + T comfort rule and how to lay out a stringer.

Also called: riser height, tread depth, unit rise, unit run, total rise, total run

A stair stringer is the notched board (usually a 2x12) that carries the treads and risers of a staircase. Laying one out comes down to four numbers: two for the whole stair and two for each step.

The four measurements

Term Meaning
Total rise Vertical distance from finished floor (or grade) at the bottom to finished floor at the top.
Total run Horizontal distance the stair covers, from the face of the first riser to the face of the last.
Unit rise (riser height) Height of one step: total rise ÷ number of risers.
Unit run (tread depth) Horizontal depth of one step, measured nosing to nosing.

A stair always has one more riser than treads, because the top floor acts as the last “tread.” Total run = unit run × (risers − 1).

Code limits (2024 IRC, R311.7)

  • Maximum riser height: 7-3/4” (R311.7.5.1).
  • Minimum tread depth: 10”, measured nosing to nosing (R311.7.5.2).
  • Uniformity: the tallest riser and the deepest tread may not exceed the smallest by more than 3/8” within a flight.
  • Nosing of 3/4”–1-1/4” is required where treads are less than 11” deep.
  • Width at least 36”; headroom at least 6’-8”.

Local codes can be stricter, and commercial stairs follow the IBC (7” max riser, 11” min tread).

Finding the riser height

  1. Measure total rise in inches — say 48”.
  2. Divide by the maximum riser: 48 ÷ 7.75 = 6.19 → round up to 7 risers.
  3. Divide again for the exact riser: 48 ÷ 7 = 6.857”, about 6-7/8”.
  4. Treads = 7 − 1 = 6. With 10” treads, total run = 60”.

The comfort rules

Stairs inside code can still feel wrong. Two old rules of thumb check the balance between rise and run:

  • 2R + T ≈ 24”–25” (two risers plus one tread).
  • R + T ≈ 17”–18”.

A 7-1/4” riser with a 10-1/2” tread (2R + T = 25”) is a classic comfortable residential stair.

Laying out the stringer

Set a framing square with the unit rise on the tongue and the unit run on the blade (stair gauges help), and step it along the board. Then:

  • Drop the stringer: cut the bottom riser short by one tread thickness so the first step matches the rest after treads go on.
  • Leave enough wood: keep a solid “throat” below the notches — at least 3-1/2”, and 5” per AWC’s DCA 6 guide for deck stairs.
  • Space stringers no more than about 16”–18” apart for 2x treads; a 36” stair typically uses three.