How to size a staircase (Blondel formula)

Sizing a staircase solves a comfort problem and a safety problem at once. There is a formula, it is nearly 350 years old, and it works — but the most dangerous error in a staircase is not in the formula: it is in steps that differ in height from one another.

The two terms you need

• Rise: the vertical part, the distance from one tread to the next.
• Tread (or run): the horizontal part your foot lands on.

The Blondel formula

Proposed by the French architect François Blondel in 1675, it relates the two values to the average human stride:

2 × rise + tread = 24 to 25 inches

The logic: climbing costs roughly twice the effort of moving the same distance horizontally. The sum reproduces a natural pace.

Rise	Tread (by the formula)	Typical use
6.5 in	11.0 to 12.0 in	comfortable, high-traffic stairs
7.0 in	10.0 to 11.0 in	the most common residential range
7.75 in	8.5 to 9.5 in	steeper, where space is tight

The International Residential Code caps the rise at 7.75 inches and sets a minimum tread of 10 inches. Commercial and accessible stairs are more restrictive still — always check the code in force locally.

Worked example

A total rise of 9 feet (108 inches) floor to floor:

1. Divide by a target rise: 108 ÷ 7.2 = 15 steps exactly.
2. Check the tread with the formula: 24 − (2 × 7.2) = 9.6 in; 25 − 14.4 = 10.6 in. Tread between 10 and 10.6 inches.
3. Horizontal run required: 14 treads × 10.5 in ≈ 12 ft 3 in — the top landing is the last step, so there is always one fewer tread than risers.

If the division does not land on a whole number, adjust the rise, never the step count: 108 ÷ 15 steps = 7.2 in exactly; 108 ÷ 14 steps = 7.71 in, still inside code.

The error that causes falls: unequal steps

This is the most important point in the guide. Every riser in a flight must be exactly the same height — most codes allow no more than 3/8 of an inch of variation across the flight.

The reason is neurological: after two or three steps the brain memorises the height and starts climbing without looking, on autopilot. A step three-quarters of an inch taller or shorter than the others breaks that prediction — and the trip happens precisely because the person was trusting the pattern.

The classic case is the last step adjusted at the end of the job, to absorb the finished floor thickness that raised the level. That single odd step accounts for a disproportionate share of household stair accidents.

What the formula does not cover

• Minimum width. Code minimums start around 36 inches; 42 to 48 inches is comfortable and lets furniture pass.
• Headroom. A minimum of 6 ft 8 in measured vertically from the nosing of each tread. Ignoring this produces the staircase you hit your head on — hard to fix afterwards.
• Handrail. Between 34 and 38 inches high, continuous along the flight, and graspable.
• Landings. A landing is required at least every 12 feet of vertical rise, with a length at least equal to the stair width.
• Nosing. A projection of up to 1.25 inches buys foot room without costing horizontal run, but beyond that it becomes a trip point.

Frequently asked questions

Do spiral stairs save space? They save floor area, at a real cost: the treads are narrow at the inner edge, which makes them unsafe to descend carrying anything and impossible for moving furniture. As a home's primary staircase, they are rarely a good choice.

What is the ideal slope? Between 30° and 35° is the comfortable band — a 7.2 inch rise on a 10.5 inch tread works out to 34°. Above 38° the stair needs a hand on the rail to descend safely; above 45° it behaves like a ship's ladder.

Can risers differ between flights? Between flights separated by a landing, technically yes — but it remains poor practice. Keeping one height throughout is what preserves the automatic rhythm of anyone climbing.

Is it worth calculating before hiring? Yes, because the result determines how much floor the staircase will consume — 12 ft 3 in in the example above. Discovering that after the framing is up is the kind of error that only resolves into a steeper staircase than you wanted.

Disclaimer: informational content for planning and budgeting. Structural design and construction must follow local building code and be carried out by a qualified professional.