How the angle is calculated
The pitch angle of a staircase is the angle the stringer (or the imaginary pitch line running through the nosings) makes with the horizontal floor. It is found with basic trigonometry: angle = arctan(rise / run), where rise is the total vertical height of the flight and run is the total horizontal distance it covers. The same formula works on a single step using riser height and tread going, since the ratio is identical along a consistent flight — a 180mm riser over a 250mm going gives arctan(180/250) = 35.75 degrees, whether you calculate it per step or for the whole staircase.
It is worth being precise about which distances go into the formula. Run should be the horizontal distance only, not the sloped length of the stringer, and rise should be the vertical floor-to-floor height, not the length of a tape measure held diagonally. Mixing these up is the most common source of a wrong angle reading, and it usually produces an angle that looks plausible but is off by several degrees.
| Riser | Going | Angle (degrees) | Feel |
|---|---|---|---|
| 150mm (5.9in) | 300mm (11.8in) | 26.6° | Very shallow, gentle |
| 170mm (6.7in) | 280mm (11.0in) | 31.3° | Comfortable, relaxed |
| 190mm (7.5in) | 250mm (9.8in) | 37.2° | Standard domestic |
| 200mm (7.9in) | 220mm (8.75in) | 42.3° | UK maximum private stair, steep |
| 220mm (8.7in) | 180mm (7.1in) | 50.7° | Space-saver / alternating tread |
Know your numbers in 30 seconds
Enter your step count, tread depth and riser height — the stair runner calculator gives you the exact length to order, in metres and feet, with waste included.
Open the stair runner calculatorComfortable angle range: 30-37 degrees
Ergonomic research consistently points to 30-37 degrees as the range most people find comfortable and safe for everyday stairs, which is why the vast majority of production staircases in both the UK and US land somewhere in the middle of that band, typically around 33-35 degrees. Below 30 degrees a flight starts to feel like a gentle ramp and consumes a lot of floor space for the height it gains; above 37 degrees the climb starts to feel steep enough that most people instinctively reach for a handrail.
UK maximum pitch: 42 degrees
Approved Document K sets 42 degrees as the maximum pitch for a private stair in England and Wales, which is steeper than most people would choose voluntarily but is permitted where floor space genuinely will not allow a shallower flight, such as in a loft conversion. Above 42 degrees, UK regulations move into the territory of fixed ladders and alternating tread stairs, which have entirely separate rules covering handhold spacing and tread shape rather than conventional riser and going limits.
US angle conventions and IRC limits
The US IRC does not specify a maximum angle directly; instead it constrains angle indirectly through the 7.75in maximum riser and 10in minimum tread depth, which together cap the steepest compliant residential stair at roughly arctan(7.75/10) = 37.8 degrees. This lands very close to the UK's comfort ceiling even though the two codes are structured completely differently — one specifies an angle limit directly, the other arrives at a similar practical limit through riser and going minimums.
Angle, pitch and slope are often used loosely
In everyday conversation 'angle', 'pitch' and 'slope' are frequently used interchangeably for stairs, but pitch technically refers to the angle of the pitch line (through the nosings) and can differ slightly from the angle of the stringer itself if the nosing projects significantly. For most domestic stairs the difference is under a degree and can be ignored.
Ladders, loft stairs and steep angles
Once a flight climbs past about 45 degrees it is generally classified as a ladder or a space-saver stair rather than a conventional staircase, and different rules apply to tread shape, handhold provision and even direction of descent. Loft ladders and fixed vertical-access ladders commonly sit between 56 and 75 degrees, at which point alternating-tread designs become necessary because a conventional flat tread is unsafe to descend at that pitch. If you are converting a loft and the available headroom forces an angle above 42 degrees, expect the building inspector to require an alternating tread or space-saver design rather than approving a conventional steep staircase.
- 30-35 degrees: standard comfortable domestic stair, suitable for main flights.
- 36-38 degrees: steeper but still fully compliant in both UK and US as a conventional stair.
- 39-42 degrees: UK maximum for private stairs, typically found in loft conversions and tight retrofits.
- 43-55 degrees: space-saver and alternating-tread territory, separate regulations apply.
- 56-75 degrees: fixed ladder range, used for loft hatches and plant access, not for everyday living spaces.
How angle affects a fitted stair runner
A steeper flight puts more pull on the nosing crease of a fitted runner, because gravity works harder against the tension at each step. Fitters generally recommend a slightly firmer gripper fixing and a shorter staple spacing on any flight steeper than about 38 degrees, and a Hollywood fit (rather than waterfall) tends to hold its shape better on steep stairs because it locks more tightly around the nosing. None of this changes the length calculation, but it is worth mentioning to your fitter or noting for yourself if you are using the stair runner calculator on a notably steep flight, since it may affect material choice as much as layout.
Working the calculation backwards
If you have a target angle in mind — say you want a 35 degree stair to match an existing flight in the house — you can work backwards to find a compatible riser and going pair: choose a riser height within the comfortable 170-200mm range, then divide it by tan(35°) = 0.700 to find the matching going. A 180mm riser divided by 0.700 gives a 257mm going, which is comfortably within both UK and US minimums and delivers exactly the target angle.
Once the geometry is settled, the finishes follow: work out the covering with the stair runner calculator on the homepage, and use the same stair runner length calculator to price the carpet or runner before you order it.
Know your numbers in 30 seconds
Enter your step count, tread depth and riser height — the stair runner calculator gives you the exact length to order, in metres and feet, with waste included.
Open the stair runner calculatorFrequently asked questions
What angle should a staircase be?
Most comfortable domestic staircases sit between 30 and 37 degrees. The UK permits up to 42 degrees for private stairs where space is tight, and the US IRC indirectly caps residential stairs at around 37.8 degrees through its riser and tread minimums.
How do you calculate stair angle from rise and run?
Take the arctangent of rise divided by run: angle = arctan(rise/run). Using a single step's riser height and tread going gives the same result as using the total rise and run for the whole flight, since the ratio stays constant on a straight staircase.
What is the maximum stair angle allowed in the UK?
Approved Document K sets 42 degrees as the maximum pitch for a private domestic staircase in England and Wales. Steeper flights fall under separate rules for alternating-tread stairs and fixed ladders rather than conventional stair regulations.
At what angle does a stair become a ladder?
There is no single universal cutoff, but most codes and manufacturers treat anything above roughly 45 degrees as a space-saver or ladder-type stair requiring alternating treads or handholds, rather than a conventional flat-tread staircase.
Does stair angle affect how much carpet runner I need?
Angle itself does not directly change the length formula, but a steeper stair generally means taller risers relative to going, which increases the amount of runner used per step. It is worth checking your actual riser and going figures in the stair runner calculator rather than assuming a standard angle.
Why do UK and US stair angle rules look so different?
The UK regulates pitch directly with a 42 degree maximum, while the US IRC regulates riser height and tread depth separately, which only indirectly caps the angle at around 37.8 degrees. Both approaches produce broadly similar real-world staircases despite the different structure.
Know your numbers in 30 seconds
Enter your step count, tread depth and riser height — the stair runner calculator gives you the exact length to order, in metres and feet, with waste included.
Calculate my stair angleEvery guide is written from hands-on measuring and fitting experience, checked against the calculator’s own maths, and re-reviewed whenever prices or methods change. Read our editorial standards.