How to Calculate Stair Rise and Run (and the Rounding Trap)

2026-10-15

To calculate stair rise and run, measure the total rise from finished floor to finished floor and divide it by the tallest riser you are willing to accept. Round the result up to a whole number of risers. The total rise divided by that number is your exact riser height. There is one tread fewer than risers, so the total run is the number of treads times the tread depth. Take a 2600 mm floor-to-floor height and a 180 mm maximum riser: you get 15 risers of 173.3 mm each.

That's the whole formula, and every stair guide has it. The trouble is in the details around it. Popular guides round the wrong way, count one tread too many, or measure from the wrong surface. Below is each of those mistakes, with numbers you can check, plus the difference between a stair that is legal and one that is comfortable.

Stair rise and run, step by step

Here is the full sequence. All dimensions are in millimetres, with inches where the source example used them.

• Total rise: the vertical distance from the finished lower floor to the finished upper floor.
• Number of risers: total rise ÷ maximum riser, always rounded up.
• Exact riser height: total rise ÷ number of risers.
• Number of treads: risers − 1.
• Total run: treads × tread depth. Tread depth here is the going, measured nosing to nosing.
• Stair angle: the arctangent of riser ÷ tread.
• Comfort check: 2 × riser + tread, compared with an adult's stride.

A worked example from the trade magazine Professional Deck Builder runs the whole chain. The total rise is 102.5 in (2603.5 mm), the US maximum riser is 7¾ in (196.85 mm) and the tread is 11 in (279.4 mm). The result is 14 risers of 186.0 mm (7.32 in) and 13 treads. That gives a total run of 3632 mm (143 in), an angle of 33.6° and a pitch line 4363 mm (171.78 in) long. Under the US International Residential Code, both the riser and the tread are within limits.

Round up, not to the nearest whole number

Some well-ranked guides say to round the riser count "to the nearest whole number." That works only when the decimal happens to fall below .5. When it doesn't, the stair breaks the limit you started from.

The same deck example shows how. 102.5 ÷ 7.75 comes to about 13.2. Round that to the nearest whole number and you get 13 risers of 200.2 mm (7.88 in). That is over the IRC maximum of 7¾ in (196 mm), even though every input looked fine. Round up and you get 14 risers, which pass. The riser height you enter is a ceiling, and rounding down always pushes you through it.

Rounding up gives the minimum number of risers, not the only option. On the same 2603.5 mm rise, 15 risers come out at 173.6 mm and 16 risers at 162.7 mm. Lower steps are easier to climb, but each extra riser adds one more tread of depth to the run. So the real trade-off is riser height against floor space, and you should decide it with the run in front of you.

One small trap: when the division comes out exact, don't add a step. 2700 mm with a 180 mm maximum is exactly 15 risers, not 16. A careless round-up in a spreadsheet can turn a tiny floating-point remainder into an extra step, so check exact cases by hand.

Count one tread fewer than risers

On a normal straight stair, the last riser lands you on the upper floor, and that floor acts as the final tread. So 15 risers means 14 treads to buy, cut and lay out.

ArchDaily's widely shared staircase guide describes its 2.60 m example as "15 steps" of riser and tread, which reads as 15 treads for 15 risers. Count that way and you overestimate the run by a full tread depth of floor you think you need but don't. The Country Plans design guide gets it right: a 108 in (2743.2 mm) floor-to-floor height gives 15 risers, 14 treads and a run of 141¾ in (3600 mm).

The exception is when your design puts a full tread at the top, below the edge of the upper floor. Then add one tread to the run.

Measure finished floor to finished floor

The total rise is not the ceiling height and not the distance between bare subfloors. It runs from the finished surface downstairs to the finished surface upstairs. That includes the floor structure between storeys, and tile, boards or carpet that haven't been laid yet.

Get this wrong and the error doesn't spread evenly over all the steps. It all ends up in the first or last step, which comes out a different height from the rest. Uneven steps are a classic trip hazard. The IRC allows no more than 3/8 in (9.5 mm) of variation between risers within a flight. If you are measuring before the finishes go in, add their thickness now, at both ends.

Comfortable is not the same as legal

Building codes set limits for each dimension. Comfort is about how the dimensions work together. The usual check is Blondel's step formula: twice the riser plus the tread should be close to a normal stride. References give slightly different bands. ArchDaily uses 630 to 650 mm, and the calculator uses 600 to 640 mm.

England's Approved Document K sets a much wider legal band of 550 to 700 mm for 2R + G, alongside rise 150–220 mm, going 220–300 mm and a pitch of no more than 42°. Three examples show how these checks relate.

• 180 mm riser and 280 mm tread: 2R + G = 640 mm, right at the comfortable edge. ArchDaily calls 18/28 the optimal pair.
• 130 mm riser and 390 mm tread: 650 mm. That is within Approved Document K but outside the comfortable range, the long, loose stride of a garden stair.
• 220 mm riser and 220 mm tread: each number is within the Approved Document K limits on its own, but together they make a 45° stair, steeper than the 42° maximum.

The last case is the one people miss. Checking each dimension against its own limit isn't enough, because the angle and the step formula are checks of the pair.

The US IRC has no step-formula rule, only a riser of no more than 7¾ in (196 mm) and a tread of at least 10 in (254 mm). A US stair can therefore pass the code and still be tiring to climb. Run the comfort check anyway. A 3000 mm rise with a 180 mm maximum riser and a 277 mm tread gives 17 risers and 630 mm, comfortably inside the band.

What these numbers don't cover

This method handles a straight, single-flight stair. Several things sit outside it and need checking separately.

Headroom depends on the thickness of the floor and the position of the opening. It must be at least 2.0 m above the pitch line under Approved Document K, and 6 ft 8 in under the IRC. The pitch-line length is a geometric line, not a stringer board. The real stringer is longer, and its size and supports are a structural question. Treads are deeper than the going by the nosing overhang. Winders, landings, width, handrails and guarding follow their own rules, and local amendments can change any of the limits above. A "within limits" result is a sanity check, not sign-off from building control.

To run your own stair, the stair calculator below needs just three numbers: the finished floor-to-finished floor rise, the tallest riser you will accept and the tread depth. It rounds up for you, counts treads correctly, shows the run, angle and pitch line, and checks the step formula. You can also compare the result with Approved Document K or the IRC. Try one more and one fewer riser to see how much floor each option costs before you commit.