Staircase Calculator
Enter the finished floor-to-floor height and the maximum riser and going you have to work to. The staircase calculator counts the risers and treads, gives the run, pitch angle and pitch line, checks 2R + G against a comfort range you set, and estimates how long the opening in the floor above must be for headroom.
Staircase calculator
Planning aid, not a building-code check. Requirements vary by jurisdiction and building type. Confirm with your local rules or a qualified professional. Handrails, guarding, landings, winders and fire escape rules are not checked.
Bare numbers are meters; 190 mm works too.
Assumptions
Change any value to match your product or local rules.
Basis: Example only. Maximum riser, minimum going and headroom vary by jurisdiction and stair type; enter the figures from your local rules
Basis: Example only. Maximum riser, minimum going and headroom vary by jurisdiction and stair type; enter the figures from your local rules
Basis: Example. Measure your tread; 0 means no overhang
Basis: Example only. Maximum riser, minimum going and headroom vary by jurisdiction and stair type; enter the figures from your local rules
Basis: Example. Measure your floor build-up (joists or slab plus finishes)
Basis: A traditional comfort rule (Blondel’s formula). Some codes adopt a version: England’s Approved Document K, Table 1.1, asks for 2R + G of 550 to 700 mm. Set your own code’s range
Basis: A traditional comfort rule (Blondel’s formula). Some codes adopt a version: England’s Approved Document K, Table 1.1, asks for 2R + G of 550 to 700 mm. Set your own code’s range
- Risers
- 15
- Riser height
- 186.7 mm (7.35 in)
- Treads
- 14
- Going
- 250.0 mm (9.84 in)
- Total run
- 3.50 m
- 11′ 6″
- Pitch angle
- 36.7°
- Pitch line length
- 4.48 m
- 14′ 8″
- 2R + G
- 623.3 mm (24.54 in), inside your range
- Floor opening for headroom (estimate)
- 2.88 m
- 9′ 5″
- Plan footprint (width × run)
- 0.90 m (2′ 11″) × 3.50 m (11′ 6″)
- Fits the available run?
- Not checked (enter an available run)
15 risers of 186.7 mm (7.35 in) and 14 treads of 250.0 mm (9.84 in) make a run of 3.50 m (11′ 6″) at 36.7°.
How this was calculated
- Risers = height ÷ maximum riser, rounded up
- Riser height = height ÷ risers
- Treads = risers − 1 (the upper floor is the last step)
- Run = treads × going
- Pitch angle = atan(riser ÷ going); pitch line = √(run² + height²)
- Opening ≈ (headroom + floor depth) ÷ (riser ÷ going), at most the run
- Risers = 2.80 m ÷ 190.0 mm (7.48 in) = 14.74, rounded up = 15
- Riser height = 2.80 m ÷ 15 = 186.7 mm (7.35 in)
- Treads = 15 − 1 = 14
- Run = 14 × 250.0 mm (9.84 in) = 3.50 m
- Pitch angle = atan(186.7 mm (7.35 in) ÷ 250.0 mm (9.84 in)) = 36.7°
- 2R + G = 2 × 186.7 mm (7.35 in) + 250.0 mm (9.84 in) = 623.3 mm (24.54 in)
- Opening = (2.00 m + 150.0 mm (5.91 in)) ÷ 0.747 (riser ÷ going) = 2.88 m
- Pitch line = √((3.50 m)² + (2.80 m)²) = 4.48 m
How it works
Count the risers
Height divided by your maximum riser, rounded up to a whole number. Rounding up keeps every riser at or below your maximum.
Even out the risers
The height divided by that count gives the riser height, the same for every step, so the stair has no odd step.
Count the treads
One fewer than the risers, because the last riser lands you on the upper floor rather than on a tread.
Run and pitch
Run = treads × going. The pitch angle is atan(riser ÷ going), and the pitch line is the diagonal √(run² + height²).
Worked example
A floor-to-floor height of 2800 mm with a maximum riser of 190 mm needs 2800 ÷ 190 = 14.74, rounded up to 15 risers of 186.7 mm. With a 250 mm going, the 14 treads make a run of 3500 mm at 36.7°, and the pitch line is 4482 mm. 2R + G is 2 × 186.7 + 250 = 623.3 mm. With 2000 mm of headroom and a 150 mm floor, the opening above needs to be about 2150 ÷ (186.7 ÷ 250) ≈ 2879 mm long.
In imperial, 9 ft 4 in (112 in) with a 7¾ in maximum riser also gives 15 risers, of 7.47 in. With a 10 in going, the 14 treads run 140 in (11 ft 8 in) at 36.7°, and 2R + G is 24.9 in.
How steps are counted: risers and treads
A riser is the vertical rise of one step; a tread is the part you stand on, and the going is its depth measured nosing to nosing. A straight stair always has one more riser than treads: you step up from the lower floor onto the first tread, and the last riser takes you onto the upper floor.
Asked how many steps a stair has, give the riser count. This calculator leads with that figure.
Choosing riser and going within your limits
The maximum riser, minimum going and headroom are set by the rules where you build and by the type of stair, so the calculator starts with example figures and asks you to replace them with yours. A lower maximum riser adds steps and makes the stair longer and shallower; a deeper going does the same without adding steps.
The 2R + G check is a traditional rule of thumb, credited to Blondel, that relates step height to stride length. Some building rules adopt a version of it: England’s Approved Document K (Table 1.1) says 2R + G should be between 550 and 700 mm. Where your rules do not set it, it is a comfort guideline. Set the range to what your rules or your own comfort say.
Headroom and the stair opening
Where a stair passes under the floor above, the floor needs an opening long enough that nobody climbing hits their head on its edge. The estimate here divides your headroom plus the floor structure depth by the stair’s slope (riser ÷ going), which gives the horizontal distance over which the stair climbs that far. It is shown as an estimate and capped at the run.
Check the result against a section drawing: trimmers, finishes and the exact nosing line all move the edge by a few centimeters.
Straight, L and U stairs
This calculator works on one straight flight. For an L or U stair, decide where the landing goes, split the height between the flights and enter each flight separately; the riser height should match across the flights.
The floor plan editor can draw straight, L, U and spiral stairs, but it sizes them from the floor height with its own riser target, so its riser count can differ from yours. This page does not send a stair to the editor yet: start a plan and draw the stair to the run you found here.
Frequently asked questions
How many steps do I need for a given height?
Divide the floor-to-floor height by the maximum riser height you are allowed or want, and round up. For 2800 mm at a 190 mm maximum that is 15 risers; for 10 ft (120 in) at 7¾ in it is 16. The treads are one fewer.
What is the difference between a riser and a tread?
The riser is the vertical height of a step; the tread is the horizontal part you stand on. The going is the tread depth measured from the front of one step to the front of the next, which is what sets the stair’s run.
How do I calculate the stair angle?
Take the arctangent of riser height divided by going. A 186.7 mm riser on a 250 mm going is atan(0.747) ≈ 36.7°. The angle depends on that ratio alone; the number of steps does not change it.
Why is there one fewer tread than risers?
The top riser brings you up to the upper floor, which acts as the last “tread”. Counting it as a tread as well would make the stair one going too long.
What is the 2R + G rule?
Twice the riser plus the going, compared with a comfortable stride. It is an old rule of thumb for stairs that feel natural to climb. Some codes include it: England’s Approved Document K gives 550 to 700 mm. Elsewhere it is a guideline; the calculator checks it against the range you enter.
Ready to plan your space?
It is free, runs in your browser and needs no account. Projects are saved privately on this device.