Stair Geometry, Ramps and Guarding

You choose the count; the height follows

A stair spans a fixed distance — finished floor to finished floor — and every riser in the flight must be the same height. Those two facts together mean the riser height is not a design choice: it is the total rise divided by a WHOLE NUMBER, and the only free decision is which whole number.

There are two ways to pick that number and they behave differently. Dividing the total rise by the MAXIMUM riser the code allows and rounding UP guarantees compliance by construction, because the resulting height cannot exceed the limit. Dividing by a TARGET riser and rounding to the nearest whole number lands closer to the height you wanted and can overshoot the maximum, so it has to be followed by a check.

The pages here take the second route, because a target is what people actually have in mind, and they then test the resulting height against the code maximum and report a violation when it fails. The remedy the badge gives — add another riser — is the first route arriving by a different road: one more riser divides the same rise into smaller steps. Either way the ceiling behaviour is a safety requirement rather than a purchasing convenience, which is unusual on this site.

The going — the horizontal tread depth — is then chosen against the riser, conventionally through a relationship that has been in use since the seventeenth century: twice the riser plus the going lands in a narrow band, because that is roughly the geometry of a human stride on an incline. Codes express it as separate minima and maxima, but the comfort of a stair is in the combination rather than in either number alone.

There is always one more riser than there are treads in a straight flight, because the top riser lands on the upper floor and needs no tread of its own. Off-by-one errors here are the commonest arithmetic mistake in the family, and every page states which it is returning.

Uniformity, and why the tolerance is so tight

Codes permit only a few millimetres of variation between the tallest and shortest riser in a flight. The North American limit is three-eighths of an inch — 9.5 mm — across the whole flight, and it is the figure the checker here uses. That is a tighter tolerance than almost anything else in a building, and it is not about appearance.

After the first two or three steps, people stop looking at a staircase. The gait becomes proprioceptive: the foot is placed where the last one was, at the height the last one was. A single riser that differs by a centimetre arrives with no visual warning and is the classic cause of a fall, which is why the requirement is on the DIFFERENCE across the flight rather than on any individual step.

The practical consequence sits at the two ends. Floor finishes change the total rise, and they usually differ between the upper and lower floor — carpet at the top, tile at the bottom. A stringer cut to the structural dimensions and then finished produces a first and last riser that differ from the rest by exactly the difference in finish thickness. The calculation therefore has to be done on FINISHED levels, and where the finish is not yet decided, the assumption has to be recorded on the drawing.

The drop cut is the same problem solved at the bottom

When a stringer is marked out, each step is cut as an identical notch. If the stringer is then set on the lower floor as cut, every tread sits on top of its notch — and the first step is one tread thickness too tall, because it gains the tread while the floor below it does not.

The fix is to reduce the bottom of the stringer by the thickness of the tread material before it is set, which is the DROP CUT. It is a single subtraction, it is the difference between a compliant flight and one whose first riser is nineteen millimetres out of tolerance, and it is the most commonly forgotten operation in stair building.

Two details change the number. If the stringer lands on a finished floor the drop is the tread thickness; if it lands on a subfloor that will later receive a finish, the drop is the tread thickness less that finish. And where the top of the flight is fixed to the upper floor structure rather than sitting on it, the same reasoning applies inverted at the head.

Headroom, and why spiral stairs run out of it

Headroom is measured vertically from the NOSING LINE — the sloping line touching the front edge of every tread — to the ceiling, soffit or landing above, and the limit applies at every point on the flight rather than at one convenient location.

On a straight flight the constraint is usually a floor opening that is too short, and the remedy is to lengthen the opening. On a SPIRAL stair the constraint is structural to the geometry, because the stair passes directly beneath itself once per revolution. The clearance available is the rise accumulated over one full turn less the thickness of the tread and its structure.

So a spiral stair's headroom is decided by the number of treads per revolution: fewer, steeper treads gain height faster and clear the turn, while a gentler spiral with many treads per turn may not reach the required clearance at all for a given floor-to-floor. That is why spiral stairs feel steep — they are solving a headroom problem, not a comfort one — and why a spiral that fits a given opening at one floor height will not fit at a lower one.

Guarding: a sphere, and a load applied where the rail is weakest

Guard infill is specified with a SPHERE rather than a dimension: an object of a stated diameter — a hundred millimetres, four inches in the imperial codes — must not be able to pass through any opening. The rule exists because the hazard is a small child's body passing through and the head not following, so it is written as a three-dimensional test rather than as a gap width.

Baluster spacing therefore has to be computed as a CLEAR opening, which means the baluster's own width enters the count. Spacing centres set from the clear dimension without adding the section width produce openings that are too wide by exactly that width, on every bay. The same rule is relaxed slightly for the triangular opening formed at the tread, riser and bottom rail of a stair, where a larger sphere is allowed.

Cable railings are where this becomes a structural question rather than a setting-out one. A tensioned cable DEFLECTS when pushed, and the sphere test is applied to the deflected geometry — so a cable spacing that passes at rest can fail under the load the test applies. That is why cable systems need closer spacing than rigid balusters, higher tension, and intermediate posts at spacings the manufacturer specifies rather than at the spacing that suits the deck.

Guards themselves carry two separate load cases that are not additive but must each be satisfied: a concentrated load applied at the top in any direction, and a distributed load along it, with the infill checked separately against its own area load. A rail that resists the concentrated load through a post can still fail through its infill, and the two checks catch different failures.

Ramps and handrail extensions

An accessible ramp is limited by gradient — commonly one in twelve as an absolute maximum, with gentler slopes preferred — and by run length between landings, because a long ramp at the maximum slope is exhausting even where it is compliant. The length that follows from a given rise is therefore usually longer than people expect, and the landings are part of the length rather than an addition to it.

Handrail EXTENSIONS beyond the top and bottom of a ramp or flight are a requirement that looks like a detail and is not. The rail continues horizontally past the last riser or the end of the slope so that a person can take hold of it BEFORE committing to the slope and keep hold of it until they are level. For someone with a visual impairment the extension is also the cue that the flight is about to start or has just ended.

That makes the extension a functional length rather than a decorative return, and it is why the handrail length for a flight is not simply the rake length. Temporary ramps on construction sites are governed by different rules and different gradients, and a temporary ramp built to the accessible standard is usually over-specified while one built to neither is the common site hazard.

Sightlines: the riser height has to grow up the rake

Seating tiers look like stairs and are not. The governing quantity is the C-VALUE: the vertical clearance between a spectator's eye and the top of the head of the person in front, measured to a defined point of focus on the stage or pitch.

Because the sightlines from successive rows diverge as they get further from the focus, holding the C-value constant requires the riser height to INCREASE up the rake. A tier built with a constant rise gives good sightlines at one part of it and poor ones elsewhere, and the resulting profile is a curve rather than a straight rake — which is why the calculation proceeds row by row rather than in one step.

Two practical consequences follow. Raising the C-value even slightly steepens the whole tier, so the difference between seeing past the head in front and seeing between two heads is a large difference in building height. And the point of focus is a design decision that changes everything downstream: a sightline set to the front edge of a stage and one set to the back of it produce different buildings.

Where the arithmetic stops

Every dimensional limit on this page is jurisdictional. Maximum riser, minimum going, headroom, guard height, sphere size, ramp gradient and handrail geometry all differ between codes and between occupancies within one code — a dwelling, a workplace and an assembly building are held to different numbers for the same flight.

Existing stairs complicate it further. Many are legally non-conforming and may remain so until they are replaced, at which point current requirements apply in full. A replacement stair that reuses the existing opening frequently cannot meet current headroom or going in that opening, and discovering that after the old one has been removed is a familiar and expensive sequence.

The calculators here work the geometry and return the counts and dimensions that follow from it. They are a design and setting-out aid; the permitted values are a matter for the applicable code, and compliance is determined by the authority having jurisdiction rather than by any figure produced here.