Stair Rise and Run: Getting the Geometry Right First Time

There is exactly one measurement in a staircase you cannot change: the total height from the finished floor below to the finished floor above. Everything else follows from it, and the order you do the arithmetic in determines whether the result is comfortable or dangerous.

The sequence

steps      = round(total height ÷ target rise)
exact rise = total height ÷ steps
treads     = steps − 1
total run  = treads × going

For a 2,600 mm floor-to-floor height with a target rise of 180 mm: 2600 ÷ 180 = 14.4, so 14 risers. The exact rise is 2600 ÷ 14 = 185.71 mm.

That awkward decimal is the correct answer. What matters is that every riser is identical, not that the number is round.

The mistake that matters most

Rounding the rise to 185 mm and letting the last step absorb the difference is the classic error, and it produces exactly the hazard the regulations exist to prevent.

After the first two steps, people climb stairs on a learned rhythm rather than by looking. The foot is placed where the body predicts the step will be. A single step differing by even 10 mm breaks that prediction, and the result is a trip going up or a stumble coming down.

Falls on stairs are a leading cause of accidental injury in the home, and inconsistent risers are a well-documented contributor. Most codes limit the variation between the largest and smallest riser in a flight to about 5 mm for this reason.

Rise, going, and the difference from tread width

Rise is the vertical height of one step.

Going is the horizontal depth measured from the face of one riser to the face of the next.

Tread width is the physical board, which is usually wider than the going because treads overhang with a nosing. Ordering timber by the going, or setting out by the tread width, are both ways to end up with a staircase that is not the one you calculated.

There is also always one fewer tread than riser, because the top riser brings you level with the upper floor and that floor serves as the final tread. A 14-riser staircase needs 13 treads. Ordering 14 is among the most common material mistakes.

The 2R plus G rule

Two rises plus one going should total between 550 mm and 700 mm, with roughly 600 to 640 mm considered ideal.

For our example: (2 × 185.71) + 250 = 621 mm. Comfortable.

The rule comes from the mechanics of a walking stride. On the flat, an average pace is about 600 mm. Climbing converts some horizontal movement into vertical at roughly two units of horizontal per one of vertical, and a staircase respecting that relationship feels natural without anyone consciously noticing why.

Get it wrong and it is immediately obvious even to someone who could not say what is wrong. Too low a total and the steps feel cramped and hurried; too high and you are stretching for each one.

This is a comfort rule rather than a legal one, and it is the check most worth doing, because a staircase can satisfy every regulation and still be unpleasant to use.

What the regulations require

Numbers vary by country and by whether the stair is private, public or in a workplace. For a private dwelling in England and Wales, broadly:

• Maximum rise: 220 mm
• Minimum going: 220 mm
• Maximum pitch: 42 degrees
• Minimum headroom: 2,000 mm above the pitch line
• Every rise and going in a flight must be equal
• Handrail on at least one side, 900 to 1,000 mm above the pitch line

The US International Residential Code differs in ways that catch people out: maximum rise around 7¾ inches (196 mm) and minimum tread depth 10 inches (254 mm). A staircase designed to UK numbers will frequently fail US inspection, and a 250 mm going that is comfortably legal in Britain is 4 mm short in the States.

Always check the current code where you are building. These figures change, and a staircase is expensive to rebuild.

Headroom is what usually kills a design

Rise and going are easy. Headroom is the constraint that ruins otherwise sensible plans, particularly in loft conversions.

You need 2,000 mm measured vertically from the pitch line, the imaginary line joining the tread nosings, to whatever is above: a ceiling, a beam, or the underside of the floor you are cutting through. The critical point is almost always where the stair passes through the opening.

If headroom fails, your options are to lengthen the stairwell opening, make the stair steeper (which quickly hits the pitch limit), or move the staircase entirely.

Check this before anything else. Discovering it after the timber is cut is the expensive way to learn it.

The bottom stringer cut

One detail that catches first-time builders.

The bottom riser cut on the stringer must be shorter than the others by the thickness of one tread. Otherwise, once the treads are laid, the first step ends up a full tread thickness taller than the rest, which reintroduces exactly the inconsistency you were being careful to avoid.

For a 185.71 mm rise with 22 mm treads, the bottom cut is 163.71 mm.

Measuring the height properly

Two things go wrong here.

Measure in three places if the floor is at all uneven, and use the largest. A stair set out from the low point will be short at the high end.

Measure to finished floor levels, not structural ones. If 20 mm of tile is going down upstairs after the stair is built, that changes every riser. Add the finishes in before you calculate, not after.

Trying alternative step counts

If the geometry does not work, changing the number of risers is usually more effective than adjusting the going.

For a 2,600 mm height: 13 risers gives 200 mm and a steeper 38.7 degrees; 14 gives 185.7 mm at 36.6 degrees; 15 gives 173.3 mm at 34.7 degrees but adds 250 mm to the total run.

More steps means a gentler stair that eats more floor space. Fewer means a steeper stair that fits a smaller opening. That trade is the whole design problem, and it is worth seeing several options before committing.