How to Calculate Stair Rise and Run

The rise is easy. The run is what doesn't fit

A 108-inch floor-to-floor — a standard 9-foot storey — with a 7.75-inch maximum riser and a 10-inch tread:

• 14 risers, each 7.7143 inches
• 13 treads
• Total run: 130 inches — 10 feet 10 inches

Almost eleven feet of floor. Plus clear space at the top and at the bottom.

Nearly everyone works the rise out first and is fine. It's the total run that turns out not to fit, and it's usually discovered after the layout has already been drawn.

The arithmetic

Number of risers = total rise ÷ maximum riser height, rounded up.

108 ÷ 7.75 = 13.94 → 14 risers

Rounded up, because every riser has to come in at or under the limit. Thirteen risers would be 8.31 inches each — over.

Actual riser height = total rise ÷ that whole number.

108 ÷ 14 = 7.7143 inches

That's the number you build to, and it's shown to four decimal places on purpose — the error compounds over fourteen of them.

Number of treads = risers − 1. Total run = treads × tread depth.

Every riser must be identical — and here's the arithmetic that breaks it

This is the most important thing on the page, and it's a safety requirement rather than a preference.

The tempting shortcut is to cut every riser at the maximum and let the last one take whatever's left:

13 × 7.75 = 100.75 → the final riser gets 7.25 inches

That's a half-inch difference. Codes commonly limit the variation between the largest and smallest riser in a flight to around ⅜ inch across the whole run — so that shortcut fails by a comfortable margin, and it fails at the top step.

People climb stairs by rhythm, not by looking. After two steps your body predicts where the next tread will be and commits your weight before your eyes confirm anything. A riser that differs from its neighbours breaks that prediction at exactly the wrong moment. It's one of the most common causes of falls on stairs.

Divide the rise by a whole number of risers. Never let the last one absorb the remainder.

One fewer tread than riser

Always. The top riser brings you level with the floor above, and that floor is the final tread.

14 risers → 13 treads.

Getting this off by one is the classic stair error, and it produces a staircase a full tread too long or too short. Not something you adjust afterwards.

What the max riser costs you in floor space

Lowering the maximum riser makes a gentler stair. It also makes a longer one, and the trade is steeper than people expect:

Max riser	Risers	Actual riser	Treads	Total run
7.75 in	14	7.7143 in	13	130 in (10 ft 10 in)
7.00 in	16	6.75 in	15	150 in (12 ft 6 in)

Three quarters of an inch off the riser limit costs 20 inches of floor — because it added two risers, and therefore two treads.

Tread depth does it too, and more directly. Going from a 10-inch tread to an 11-inch one keeps all 14 risers but pushes the run from 130 to 143 inches — 13 more inches of floor for one extra inch per tread, because it lands 13 times.

Total rise means finished floor to finished floor

Not subfloor. Not "roughly the ceiling height".

If you measure to a subfloor and lay flooring afterwards, the top and bottom risers change by the thickness of that finish — and since the whole flight has to stay within a fraction of an inch, that's precisely the error the equal-riser rule can't absorb.

Decide your floor finishes before you cut a stringer.

The comfort rules, and where they disagree

Two rules of thumb describe stairs that feel right underfoot:

• Riser + tread ≈ 17–18 inches
• 2 × riser + tread ≈ 24–25 inches

On the default figures: 17.71 and 25.43.

The first sits comfortably in range. The second is marginally over — some versions of the rule quote 24.5–25.5, which it fits, and some quote 24–25, which it doesn't.

That's worth saying plainly rather than papering over: these are guidance about comfort, they don't always agree with each other, and neither one overrides a code limit. A staircase can satisfy every regulation and still feel wrong to walk, and this is usually what that difference comes down to.

The limits are code, not arithmetic

This calculator does geometry. Every constraint in it is a legal question with a jurisdiction-specific answer:

• Maximum riser height
• Minimum tread depth
• Minimum headroom, along the whole flight
• Handrail height, graspability and both-sides requirements
• Landing size and where one is required

They vary by locale, and they differ again between a dwelling, a commercial building and a loft conversion. Stairs are among the most heavily regulated parts of a building, for the obvious reason.

The defaults here are common residential figures. They are not permission.

Cut one, fit it, then cut the rest

Standard practice, and it's the same discipline as cutting rafters: lay out one stringer, fit it on the actual opening, and only then use it as the pattern for the others.

Print the stair layout sheet — it has a table for measuring every riser after it's built, because a flight that was laid out correctly and cut slightly wrong has exactly the same hazard as one that was laid out wrong.

Stair geometry is arithmetic; riser, tread, headroom and handrail limits are set by your local building code.