Calculators

Stair rise and run calculator

A stair is one division sum, and the divisor has to be a whole number. Everything else follows.

On this page (7 sections)
  1. Stair rise and run calculator
  2. Finished floor to finished floor, and nothing else
  3. IRC, Part K and ADA: 7.75 in, 220 mm and 7 in
  4. 108 in divided 14, 15, 16 and 17 ways
  5. The six checks the panel runs on a flight
  6. Which of the four legal flights to build
  7. No winders, no handrails, no local amendments

Short answer

A 108 in (2.74 m) floor to floor height with a 10.5 in (267 mm) going comes out at 15 risers of 7.2 in (183 mm), a total run of 147 in (3.73 m) over 14 treads, and a floor opening about 117 in (2.97 m) long to keep headroom. Fourteen risers also passes the IRC but climbs at 7.71 in, which is close to the 7.75 in ceiling and reads as steep.

The numbers, at a glance

IRC maximum riser
7.75 in (197 mm)Tread top to tread top
IRC minimum tread
10 in (254 mm)Going, nosing to nosing
Approved Document K, private stair
220 mm rise, 220 mm going8.66 in each, UK
Accessible stair, ADA and IBC
7 in (178 mm) rise, 11 in (279 mm) treadAlso caps nosing projection
Headroom
80 in (2,032 mm)78.7 in (2,000 mm) under Part K
Riser uniformity in one flight
3/8 in (10 mm)Largest minus smallest
Comfort formula, 2R plus G
24 to 25.5 in (610 to 648 mm)Blondel, not a code rule
Worked example height
108 in (2.74 m)15 risers at 7.2 in (183 mm)
Floor opening for that flight
117 in (2.97 m)Measured back from the upper floor edge

Stair rise and run calculator#

Enter the total floor to floor height. The calculator divides it into equal risers, checks each option against the IRC and Approved Document K limits, and reports the total run and the headroom you will need.

Enter your measurements above.

Riser heights are measured from the top of one finished tread to the top of the next, so the finished floor thicknesses at both ends have to be in the total height you enter.

Nothing you type leaves your browser: the maths runs on this page, and no values are stored or sent anywhere.

Finished floor to finished floor, and nothing else#

Total floor to floor height is the vertical distance from the finished surface of the lower floor to the finished surface of the upper floor. Not the subfloor, not the joist top, not the ceiling height of the room below. Every riser in the flight is that number divided by a whole number, so an error in it is repeated in every step and shows up as the one riser that trips people.

Take it with a tape held plumb at the position the flight will actually sit, then again at the other end of the opening. If the two differ, the floor is not level and that is a decision to make before you cut anything. Where the finishes are not yet chosen, add the intended build-up at both ends before you divide, and read the warning below for what happens when only one end is counted. Build-ups are in floor transitions and threshold heights, and tread and riser thicknesses in stair tread and riser flooring dimensions.

The going is the second input, and it is a preference rather than a measurement. If you enter a going below the minimum for the rule set you have chosen, the calculator quietly raises it to the minimum and works with that.

IRC, Part K and ADA: 7.75 in, 220 mm and 7 in#

Rule setMaximum riserMinimum going or treadHeadroom
IRC, US residential7.75 in (197 mm)10 in (254 mm)80 in (2,032 mm)
Approved Document K, UK private stair220 mm (8.66 in)220 mm (8.66 in)2,000 mm (78.7 in)
ADA and IBC, accessible7 in (178 mm)11 in (279 mm)80 in (2,032 mm)

The gap between them is larger than it looks. A 220 mm rise with a 220 mm going passes the calculator's Part K check and fails the IRC on both counts, and Approved Document K separately caps a private stair at a 42 degree pitch, which that combination breaks. An accessible stair at 7 in and 11 in is 32 degrees. Take the same 108 in height at the minimum going each rule set allows: 14 goings of 220 mm is 121 in (3.08 m), 14 goings of 10 in is 140 in (3.56 m), and the accessible rules force 16 risers, so 15 goings of 11 in is 165 in (4.19 m). Nearly 4 ft of floor separates them, for the same climb. The full set of code figures and where they come from is in stair dimensions: rise, run, headroom and handrails and the codes themselves in standards, codes and sources.

108 in divided 14, 15, 16 and 17 ways#

Height 108 in, preferred going 10.5 in, IRC.

  1. Minimum number of risers: 108 divided by 7.75 is 13.9, so 14 is the fewest that stay legal.
  2. Fourteen risers: 108 divided by 14 is 7.71 in each. Legal, but 0.04 in off the ceiling.
  3. Fifteen risers: 7.20 in each. Sixteen: 6.75 in. Seventeen: 6.35 in.
  4. Comfort test on each: 2R plus G. Fourteen gives 25.93, fifteen gives 24.90, sixteen gives 24.00, seventeen gives 23.21.
  5. Fifteen risers is nearest to 25, so that is the recommendation: 15 risers at 7.20 in, 14 treads at 10.5 in.
  6. Total run: 14 x 10.5 = 147 in (12 ft 3 in, 3.73 m).

Note step 6. A flight of 15 risers has only 14 goings, because the last riser lands on the upper floor, which is its tread. Counting 15 is the most common slip in stair setting out, and it puts the bottom step 10.5 in into a room with no space for it.

Section through a 15 riser flight climbing 108 in with a 147 in total run.Section of a straight flight between two floors, with the total height dimensioned vertically and the total run dimensioned along the lower floor.15 risers at 7.2 in14 goings at 10.5 inLower floorUpper floorTotal run 147 in (3.73 m)108 in (2.74 m)Section. Height is finished floor to finished floor, both finishes included.
The flight envelope: 108 in of height, 147 in of run, and 14 goings rather than 15.

The six checks the panel runs on a flight#

Alongside the recommendation the calculator returns the checks that decide whether a flight is buildable: riser against maximum, going against minimum, the 2R plus G figure against the 24 to 25.5 in comfort band, the headroom for the rule set, the floor opening needed to keep it, and the reminder that every riser must be within 3/8 in (10 mm) of every other. It then lists the next three ways of dividing the same height.

All of it runs in your browser as you type. Nothing you enter is sent anywhere, and no part of the answer comes back from a server.

The calculator will tell you that four divisions of the height are legal. It cannot tell you which to build.

  • Who uses it. A stair that a child and an older adult use daily wants the shallower option even at the cost of run. The changes in step negotiation with age are covered in child and older adult dimensions.
  • What is at the bottom. A flight needs a landing at least as long as the stair is wide, and it must not discharge into a door swing or a route. Widths for the hall it lands in are in hallway widths that work.
  • Handrails and guards. Neither appears in the output. Handrail height, guard height and baluster spacing are in stair trim, newel and balustrade dimensions.
  • Where the storey height came from. If the height itself is still movable, that is the cheapest variable in the whole problem, and it is examined in ceiling heights and datum lines.

No winders, no handrails, no local amendments#

It sizes a single straight flight. It does not lay one out, and it is a planning tool rather than a shop drawing.

  • No winders, landings or tapered treads. A landing resets the flight, so run each flight separately and add the landing depth between them.
  • No stringer, carriage or newel sizes, no handrail geometry, no guard heights.
  • No structural check on the opening, the trimmer joists or the header.
  • No ramps: slopes, runs and landings for those are in ramp slopes, lengths and landing sizes.
  • No local amendment: the figures it uses are the base national ones.

For the rest of the set, including the tools that size what goes at the top and bottom of the flight, see the calculators index.

Frequently asked questions#

How many stairs do I need for a 9 ft ceiling?

A 9 ft ceiling usually means about 108 in (2.74 m) floor to floor once the joists and both floor finishes are counted, which divides into 15 risers of 7.2 in (183 mm). Fourteen risers at 7.71 in also passes the IRC. The calculator lists both, along with 16 and 17 risers, because the choice is about how much floor you are willing to give the run.

What is the maximum riser height for stairs?

7.75 in (197 mm) under the IRC for a residential stair, 7 in (178 mm) on an accessible stair under the ADA and IBC, and 220 mm (8.66 in) for a private stair under Approved Document K in England and Wales. Pick the rule set in the calculator and it applies that maximum, then rejects any division of the height that breaks it.

Why does the calculator not use the riser I want?

Because the riser is an output, not an input. The height is fixed and the risers must be equal, so the only free variable is how many of them there are, which is a whole number. It divides the height by every workable count and reports the results. Your control is the going, which you enter, and the number of risers you pick from the list.

What is the 2R plus G rule?

Twice the riser plus the going should land between about 24 and 25.5 in (610 to 648 mm). It comes from Blondel in the seventeenth century and models the fact that a walker's stride shortens as it rises. The calculator scores each compliant option against a target of 25 in and picks the closest as its recommendation. It is a comfort test, not a code requirement.

How long does the floor opening above a stair need to be?

About 117 in (2.97 m) for the worked example, and the calculator reports it for whatever you enter. It works back from the headroom requirement: the number of goings you travel before the flight has dropped a full 80 in (2,032 mm) below the upper floor. A shorter opening is the most common reason a drawn stair does not build.

Does the nosing projection change the answer?

No. The calculator works in risers and goings, and the total run it reports is the going multiplied by the number of treads, measured nosing to nosing. The projection you enter is the difference between the going and the physical depth of the tread board, typically 3/4 to 1.25 in (19 to 32 mm). It changes the timber, not the geometry of the flight.

Sources and standards referenced#

  1. International Residential Code, R311.7 Stairways International Code CouncilMaximum riser, minimum tread, headroom and the 3/8 in uniformity tolerance
  2. Approved Document K: Protection from falling, collision and impact UK Government, Ministry of Housing220 mm maximum rise and minimum going for a private stair, 2 m headroom
  3. 2010 ADA Standards for Accessible Design, section 504 US Department of Justice7 in maximum riser and 11 in minimum tread on an accessible stair
  4. Architects' Data Ernst Neufert, Wiley-BlackwellThe 2R plus G stepping formula and comfortable stair proportions
  5. Time-Saver Standards for Interior Design and Space Planning De Chiara, Panero and Zelnik, McGraw-HillStair geometry, floor opening lengths and headroom construction

We cite published codes, industry planning guidelines and manufacturer specifications. Where a figure is our own recommendation rather than a published standard, the text says so. See how we measure.