Stair tread run:
formula and worked example

What total tread run decides on a plan

A staircase has two directions to design. The vertical part is the floor-to-floor height divided into risers. The horizontal part is the run, the footprint the stairs take on the floor below. Run is what decides whether the staircase fits in the space you have, or whether the landing will hit a wall or a doorway.

The calculation is a plain multiplication, but its inputs deserve care: tread depth must be the going (the horizontal distance between nosings), and the number of treads must match your actual layout.

Headroom is the partner constraint. Total run decides how far the stair travels horizontally, but the vertical clearance at the point where the stair passes under the floor above decides whether the user can walk up without bending. Plans that fit on the run alone often fail on headroom, so check both before fixing the opening in the floor.

Formula and inputs

• Tread depth: the going of each step in millimetres, measured from one nosing to the next on the horizontal plane.
• Treads: how many full steps in the flight that have a horizontal surface to stand on.

A landing, if there is one, is added to the result separately because it is not a tread of standard depth.

Worked example for 17 treads of 270 mm

A straight flight has 17 treads each with a 270 mm going. Illustrative figures for a domestic staircase.

1. 1Write the going: 270 mm.
2. 2Multiply by the number of treads: 270 × 17 = 4,590 mm.
3. 3Convert for the drawing if needed: 4,590 mm is 4.59 m of horizontal run.

Reading the figure against the building

Compare 4.59 m with the clear floor length available. The run has to fit from the first riser at the bottom to the nosing of the top step, with room for the landing at either end that building rules or comfort require. If it does not fit, the usual options are a shallower tread, a winder or a turn with a landing, none of which is automatically acceptable.

Going and riser height work together. Building codes in many places set limits on each and on a combined rule, and rules differ by country and by type of building, so the value must be checked against the code that applies. A deep tread with a short riser is comfortable but long; a short tread with a tall riser is compact and tiring.

A quick comfort check some designers use is to compare going and riser through a rule of thumb, such as twice the riser plus the going falling within a comfortable range. These rules vary and the code that applies to your building has the final say. Use the check to compare two options rather than to prove one is compliant.

What a deeper going does to the footprint

Each millimetre added to the tread is multiplied by every step in the flight.

Adding 10% to the going, from 270 to 297 mm, lengthens the run by 459 mm, nearly half a metre. That is why small increases in comfort have a visible effect on the plan, and why designers often try a couple of tread sizes before fixing the layout.

Counting and measuring errors

• Using the number of risers as the number of treads. In a straight flight that ends at the upper floor, there is one fewer tread than risers because the top floor acts as the last tread.
• Measuring the tread surface instead of the going, so the nosing overlap is lost or doubled.
• Forgetting landings, which are often as long as the stair is wide.
• Mixing metres and millimetres, producing a figure that is off by a factor of a thousand.

Before fixing the stair on a drawing

1. 1Measure the floor-to-floor height and divide into equal risers within code limits.
2. 2Count treads as one fewer than risers for a straight flight.
3. 3Choose a going within code and compute total run.
4. 4Add landings and check the footprint against walls and doors.

Equal risers and equal goings throughout the flight matter for safety, because people expect a regular rhythm and trip when it changes.

If the footprint is too long for the space, consider where the stair could turn. A quarter landing or a half landing splits the run into two shorter flights, each of which is calculated the same way, and the landing adds its own length and width. Always check that the landing is large enough for safe use.