Stair Rise and Run: Getting the Numbers Right

Stairs are the most unforgiving carpentry in a house. Get a deck board a quarter-inch out and nobody notices. Get one riser a quarter-inch out and people trip on it for the next thirty years — which is exactly why the code writes the tolerance down.

The vocabulary

• Total rise — vertical distance from finished floor to finished floor.
• Unit rise (riser) — the height of one step.
• Unit run (tread depth) — the horizontal depth of one step, measured nosing to nosing.
• Total run — how far the staircase reaches out horizontally.
• Nosing — the lip of the tread overhanging the riser below.
• Stringer — the sawtooth-cut board carrying the treads.

What the code allows

US residential stairs follow IRC section R311.7. The commercial IBC and workplace OSHA rules are tighter, which is why an office stair feels shallower than a house stair.

Dividing the rise

You cannot choose the riser height first. The total rise is fixed by the building, and it has to divide into a whole number of equal steps. Work backwards:

1. Measure total rise, finished floor to finished floor.
2. Divide by 7 — a comfortable target riser — to get an approximate step count.
3. Round to a whole number.
4. Divide the total rise by that count for the exact riser height.
5. Check it against the 7¾ in maximum. If over, add a step and divide again.

Say the total rise is 112 in, from a deck surface down to a patio slab. 112 ÷ 7 = 16 exactly, so 16 risers at 7.00 in each. That leaves 15 treads. At a 10½ in run, the total run is 15 × 10.5 = 157.5 in, or 13 ft 1½ in — worth checking against the space you actually have before cutting anything.

The comfort rules

Code sets the outer limits; these older rules of thumb say which combinations inside those limits feel right underfoot. All three come from the way stride length shortens as you climb.

A stair passing all three lands around 30–37° — the range where people neither shuffle nor lunge. The example above sits at arctan(112 ÷ 157.5) = 35.4°.

Stringer length

The stringer is the hypotenuse over the total rise and total run, so Pythagoras gives the minimum board length:

Add roughly a foot for the cuts at each end and buy 18 ft stock, or accept that a 16 ft board will be tight. Stringers are cut from 2×12 because the sawtooth notches remove so much material that anything narrower has too little wood left behind the cut — most codes require at least 3½ in of solid stringer remaining.

The two mistakes that cause most rework

Measuring to the subfloor. Total rise must be finished floor to finished floor. If ¾ in of hardwood is going down upstairs and tile downstairs, and you measured bare deck to bare slab, every riser is wrong the moment the flooring arrives.

Forgetting the stringer drop. When the treads are fitted, the bottom step ends up taller than the rest by exactly the tread thickness — unless you cut the bottom of the stringer down by that amount first. A 1 in tread means trimming 1 in off the foot of the stringer. Skip it and the first step is over the ⅜ in variation limit on its own.

Both are checkable before a single cut, and both are the reason experienced framers measure the rise twice and write the finished-floor build-up on the wall in pencil.