Pitch & geometry tool
Stair Angle Calculator
Work out stair pitch in degrees, the diagonal stringer cut line and comfort checks from rise and run — with a live section diagram. Free, no account needed.
Finished floor to finished floor.
7-7.5in is comfortable; risers are equalised.
Horizontal depth, nosing excluded.
Plumb from the nosing line to the ceiling above.
Landings, stringers & handrail
Half-landings or quarter-turns in this flight.
16in suits most treads; 12in for thin or composite.
Measured above the nosing line.
4in (100mm) sphere rule.
Sets the bottom stringer drop.
Your flight
15 risers × 7.33in
14 treads at 10.50in / 26.7cm · 36.8 degree pitch
- Riser height (equal)
- 7.33in / 18.6cm
- Tread run (going)
- 10.50in / 26.7cm
- Total run
- 147.00in / 373.4cm
- Cut line (diagonal)
- 183.60in / 466.3cm
- Stringer stock length
- 195.60in / 496.8cm (16.3ft)
- Pitch
- 36.8 degrees
- 2R + G
- 25.17in / 63.9cm
- Stringers
- 4 at 12.0in centres (65.2ft stock)
- Handrail length
- 207.60in / 527.3cm (17.3ft)
- Balusters
- 39 at 5.2in centres
Code & comfort checks
IRC (US) allows a maximum 7.75in riser. Every riser in a flight must match within 3/8in.
Minimum going is 10.00in. Shallow treads are the single biggest cause of descending falls.
Comfortable domestic flights sit between 30 and 37 degrees; 42 degrees is the absolute ceiling.
Two risers plus one going should land between 24in and 25in (600-640mm) for a natural stride.
IRC (US) expects at least 36.0in of clear width above the handrail height.
Minimum headroom is 80in measured plumb from the tread nosing line.
IRC wants a graspable handrail 34-38in above the nosing line, continuous for the full flight, and no gap that passes a 4in sphere.
Guidance only — confirm against your local building control before you cut or pour.
Compare riser counts
| Risers | Riser | Going | Run | Pitch |
|---|---|---|---|---|
| 14 | 7.86in | 10.50in | 11.4ft | 38.9° |
| 15 | 7.33in | 10.50in | 12.3ft | 36.8° |
| 16 | 6.88in | 10.50in | 13.1ft | 34.9° |
The highlighted row is your current flight. Nudging the riser count is usually the cheapest way to bring a steep or shallow stair back inside code.
Advanced layout
Mark-out schedule, framing deductions & take-off
Quick answer
How do you calculate stair angle or pitch?
Stair angle, or pitch, is the arctangent of total rise divided by total run: angle = atan(rise / run). A staircase with a 108in rise and a 147in run has a pitch of atan(108/147) = 36.3 degrees. Comfortable residential stairs generally fall between 30 and 37 degrees; most codes cap private stairs around 42 degrees, and anything steeper is usually classed as a ladder or an alternating-tread stair rather than a standard flight.
- Pitch = atan(total rise / total run), in degrees.
- Comfortable residential pitch is roughly 30-37 degrees.
- UK Approved Document K caps private-stair pitch at 42 degrees.
- Above 42 degrees, most codes require alternating treads or a ladder-style stair.
- A steeper pitch shortens the footprint but shortens the going too — check both.
- Pitch can also be read off a speed square held against the stringer line.
Pitch is trigonometry, not guesswork
Every staircase forms a right triangle: the vertical leg is total rise, the horizontal leg is total run, and the hypotenuse is the stringer's cut line. Stair angle, more often called pitch in the trade, is simply the angle between that hypotenuse and the horizontal — the arctangent of rise divided by run. Because every step in a flight is geometrically similar to the whole triangle, the same angle applies whether you calculate it from total rise and run or from a single riser and going.
| Riser | Going | Pitch (degrees) | Feel |
|---|---|---|---|
| 6.00in | 12.00in | 26.6 deg | Shallow, ramp-like, generous run |
| 7.00in | 11.00in | 32.5 deg | Comfortable, common on main stairs |
| 7.50in | 10.00in | 36.9 deg | Standard, brisk but comfortable |
| 7.75in | 9.50in | 39.2 deg | Steep, near the UK working limit |
| 8.25in | 8.00in | 45.9 deg | Ladder-like, needs alternating treads |
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 calculatorWorked example: checking an existing flight
Measure a total rise of 96in and a total run of 130in. Pitch = atan(96/130) = 36.4 degrees — comfortably within the 30-37 degree band and under the 42-degree UK ceiling. If instead the run measured only 100in for the same 96in rise, pitch jumps to atan(96/100) = 43.8 degrees, over the private-stair maximum, which usually means the flight needs a landing, a winder, or an alternating-tread design rather than a straight run.
Angle changes the diagonal cut line too
Pitch and stringer length move together. The diagonal cut line is the hypotenuse, calculated as the square root of rise squared plus run squared, and it lengthens as the angle steepens for a fixed rise because the stringer has to travel further to reach the same height over less horizontal distance in a landing-limited layout — or shortens, for a fixed run, as the angle steepens because rise increases for a fixed run. Either way, cut the stringer to the calculated diagonal, not to a stock angle, and double-check the throat depth where the notch meets the board edge.
Angle and headroom interact
A steeper pitch needs less horizontal run to clear a given headroom obstruction, which is one reason loft stairs run steeper than main stairs — but steeper pitch also makes the treads feel shallower underfoot for the same going, so it is a genuine trade-off rather than a free win.
Converting angle to a buildable flight
Once you have settled on a target pitch, work forward to riser height and tread run rather than trying to cut stringers to an angle directly — a speed square set to degrees is far less precise on site than a riser-and-run layout snapped with a tape and a level. The stair calculator converts a target pitch back into whole-number risers and a matching going, and the concrete stair calculator applies the same angle logic to poured steps where the formwork has to be cut to the same diagonal.
Whatever you decide, get the numbers first: the stair runner calculator doubles as a stair runner length calculator, adding nosing wrap, landings, winders, pattern repeat and waste so you order the right length the first time.
Frequently asked questions
How do I calculate the angle of a staircase?
Divide total rise by total run and take the arctangent: angle = atan(rise / run). If you only know riser height and tread run for a single step, the ratio is the same — atan(riser / going) gives the identical pitch, since every step in a flight has the same angle by definition.
What is a good or standard stair angle?
Most comfortable interior stairs sit between 30 and 37 degrees. Below 30 degrees a stair starts to feel more like a ramp and eats a lot of floor space; above 37 degrees it starts to feel steep, and by 42 degrees — the common UK private-stair maximum — most people are reaching for the handrail on the way down.
What is the maximum legal stair angle or pitch?
UK Approved Document K sets 42 degrees as the maximum pitch for a private stair, and lower for stairs in flats or that the public uses. The US IRC does not regulate pitch directly, instead controlling it indirectly through the maximum riser (7 3/4in) and minimum run (10in), which caps most residential stairs at roughly 37 degrees anyway.
How do I reduce a stair's angle without changing the rise?
Lengthen the run — either with deeper treads or by adding a landing partway up and continuing the flight at a different angle. If floor space genuinely will not allow a longer run, a winder or a quarter-landing turn lets you add going without extending the straight-line footprint.
What is the difference between stair angle, pitch and slope?
In stair-building they are generally used interchangeably to mean the same arctangent-of-rise-over-run figure, expressed in degrees. 'Slope' in a roofing or ramp context is more often given as a ratio like 1:12, which is a different convention — worth checking which one a spec means before you calculate.
How steep is too steep for a loft or attic stair?
Many loft conversions push close to or slightly beyond the 42-degree UK maximum because the available run is fixed by the landing below. At that point the usual options are an alternating-tread stair (paddle stairs), a spiral stair, or increasing the floor opening to lengthen the run — all of which the stair layout calculator can help you compare footprint for.
Can I measure stair angle without a calculator?
Yes — hold a digital angle finder or a speed square against the underside of an existing stringer, or measure a horizontal and vertical distance along the string line and divide. The arithmetic is identical to the arctangent method above; a calculator just saves the trig.
Is the stair angle calculator free?
Yes. Pitch, the diagonal cut line, riser height, tread run and code checks are all free with no account. A free account adds the mark-out schedule and headroom clearance run for the same flight.
Related tools & guides
Start with the numbers: our stair runner calculator also works as a stair runner length calculator, adding nosing wrap, landings, winders, pattern repeat and waste so you order the right length first time.