🪜 Stair Calculator
From the total floor-to-floor height, this works out how many steps you need, the exact rise and run of each, the stringer length, and whether the result passes the usual building code limits.
Designing a staircase that passes inspection and feels right
A staircase is governed by one fixed quantity and two you choose. The total rise, floor to floor, cannot change. The riser height and the tread depth are yours to set, within limits that exist because stairs are where people fall.
number of risers = total rise / target riser, rounded → actual riser = total rise / number of risers
The rounding matters. You cannot have 15.56 steps, so you round to 16 and divide the total rise equally between them. Every riser must then be within about 5 mm of every other; an uneven step is the classic cause of a trip, because people stop looking at stairs after the second one.
The limits
| Measure | UK Part K (domestic) | US IRC |
|---|---|---|
| Maximum riser | 220 mm | 7¾ in (196 mm) |
| Minimum tread (going) | 220 mm | 10 in (254 mm) |
| Maximum pitch | 42° | about 37° |
| Minimum headroom | 2,000 mm | 6 ft 8 in (2,032 mm) |
| Variation between risers | within 5 mm | within 9.5 mm |
| Minimum width | No fixed minimum | 36 in (914 mm) |
US codes are generally stricter on riser height and tread depth, producing shallower stairs that take more floor space. Always check your own local code: these are typical figures and amendments are common.
The comfort rules
Codes set what is legal; two old rules of thumb set what feels right. The blondel formula, named after an eighteenth-century French architect, says:
2 × riser + tread = 600 to 640 mm (23 to 25 in)
It encodes the natural length of a human stride. A 175 mm riser with a 250 mm tread gives 600 mm, which is comfortable. A 200 mm riser with a 220 mm tread gives 620, also fine. A 220 mm riser with a 300 mm tread gives 740, which feels wrong to climb even though both measurements pass code individually.
The second rule is riser plus tread between 430 and 450 mm. The two rules agree in the comfortable zone and diverge at the extremes, which is exactly where they are most useful as a warning.
Treads and risers are not the same count
A flight always has one more riser than tread, because the top tread is the floor above. Sixteen risers means fifteen treads, and the total horizontal run is fifteen times the going, not sixteen. Getting this wrong is the most common error in first-time stair layouts and it produces a staircase 250 mm too long for the space.
Stringer length and floor space
stringer = √(total rise² + total run²)
Pythagoras, applied to the whole flight. For a 2,800 mm rise and a 3,750 mm run the stringer is 4,681 mm, so you need timber over 4.7 m long plus waste for the cuts. The floor space the stairs consume is the run plus the landing at the bottom, which is often forgotten until the staircase arrives.
Headroom
Headroom is measured vertically from the nosing of each tread to the ceiling or the underside of the floor above. It is the constraint that most often forces a redesign, particularly in loft conversions, because it interacts with where the stair lands rather than with the stair itself. Check it at the tightest point, usually where the flight passes through the floor opening.
A worked example
A 2,800 mm floor-to-floor rise with a target riser of 180 mm. 2,800 / 180 = 15.6, so 16 risers at exactly 175 mm each. With a 250 mm going that is 15 treads and a 3,750 mm run. The pitch is 36.7°, the stringer is 4,681 mm, and 2R + G is 600 mm, comfortably inside the blondel range. Everything passes.
Two neighbours worth knowing: the triangle calculator, for the question this one leads into, and the concrete calculator, which answers it from the other direction.
Frequently Asked Questions (FAQs)
What is the ideal riser height?
Between 175 and 190 mm, or about 7 to 7.5 inches, for domestic stairs. UK codes allow up to 220 mm and US codes up to about 196 mm, but the comfortable zone is well below either limit. Shallower risers need more floor space.
How many steps do I need?
Divide the total floor-to-floor rise by your target riser and round to the nearest whole number, then divide the rise by that count to get the actual riser height. Rounding changes the riser slightly, which is correct: all risers must be equal.
Why do I have one fewer tread than riser?
Because the floor above acts as the top tread. Sixteen risers give fifteen treads, and the horizontal run is fifteen goings. Counting sixteen produces a staircase one tread too long for the opening.
What is the 7-11 rule?
An American rule of thumb for a comfortable stair: a 7 inch riser with an 11 inch tread. It sits neatly inside most codes and inside the blondel comfort range, and it is a good starting point before adjusting for the space available.
How much floor space do stairs take?
The total run, which is the number of treads times the going, plus landing space at top and bottom. A typical domestic flight with fifteen 250 mm treads needs 3.75 m of run, which is why tight spaces end up with winders or a spiral.
Do these figures apply everywhere?
They are the common UK and US domestic limits, and local amendments are frequent. Commercial and public stairs have stricter requirements again. Always confirm against your local building regulations before cutting anything.