What this calculator does
The angle of a staircase, also called its pitch, is the angle the line of the stair nosings makes with the floor: arctan of total rise divided by total run. It is the single number that tells you whether a staircase will feel like a gentle ramp, a normal set of stairs, or something closer to a ladder, before a single step is cut.
Most residential stair codes and comfort guidance sit the pitch somewhere between 30 and 42 degrees. Below that range a staircase eats up a lot of floor space for the height it climbs; above it, each step gets steeper and shorter, and the stairs become tiring and harder to descend safely, particularly for anyone carrying something or less steady on their feet.
The formula
Divide the total floor-to-floor rise by the total horizontal run, then take the arctangent to get the angle in degrees. Dividing the same rise and run by the number of steps gives the rise and going of each individual step, and the stringer length comes from the diagonal of the rise-run triangle.
| Term | Meaning |
|---|---|
| Rise | The total vertical height being climbed, from the lower floor level to the upper one. |
| Run | The total horizontal distance the staircase covers, measured from the first riser to the last. |
| Going | The horizontal depth of a single step, sometimes called the tread depth. |
| Stringer | The diagonal structural member that runs under the steps, sized from the rise-run diagonal. |
The inputs explained
| Field | What to enter |
|---|---|
| Total rise (floor to floor) (m) | The total vertical height from the lower finished floor to the upper finished floor. |
| Total run (horizontal length) (m) | The total horizontal distance available for the staircase to travel over. |
| Number of steps | How many individual steps the staircase will have, used to work out rise and going per step. |
When to use it
Checking a design against comfort guidance
Before committing to a floor plan, converting the planned rise and run into a pitch angle shows immediately whether the staircase sits in the comfortable 30-42 degree band or needs more horizontal space to work with.
Fitting a staircase into a tight floor plan
When run is limited by the space available, the angle shows how steep the compromise gets, which helps decide between a steeper straight run, a winder, or a spiral stair instead.
Comparing an existing staircase to a new design
Measuring the rise and run of an existing staircase that feels comfortable gives a benchmark angle to aim for when designing a new one elsewhere in the same building.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the stair angle changes with total rise at a fixed run
The same 3.4 m run, climbed by a range of total rise heights.
How the stair angle changes with total run at a fixed rise
The same 2.6 m rise, spread over a range of total run lengths.
Questions
What stair angle is considered comfortable?
Most residential guidance points to roughly 30 to 42 degrees. Below that range a staircase uses a lot of floor space for its height; above it, steps get steep and can feel closer to a ladder than a staircase.
How is this different from a roof pitch calculation?
The underlying arctangent of rise over run is the same trigonometry, but a roof pitch calculation is sized for rafters and roof area, while this one is sized for stairs and reports the rise and going of each individual step, which a roof calculation has no reason to show.
Does a steeper angle mean fewer steps?
Not directly. The angle depends on total rise and run, not step count. For a fixed rise and run, adding more steps shortens each individual rise and going without changing the overall stair angle at all.
What if my staircase has landings or turns?
Measure the rise and run for each straight flight separately. A landing breaks the run, so the angle of a dog-leg or winder staircase should be worked out flight by flight rather than across the whole floor-to-floor height at once.
For the riser height, step count and comfort check on a straight run, see the stair rise and run calculator. For the equivalent angle calculation applied to a roof instead of a staircase, see the roof pitch calculator.