Stair design comes down to two relationships. The first is 2R + T: twice the riser plus the tread should sit around 630 mm, or 25 inches, because that is the length of a natural stride. The second is that every riser in a flight must be identical to within a few millimetres — a regulation in both the UK and US codes, not a preference.
Everything else is arithmetic. Divide the total floor-to-floor rise by a comfortable riser height, round to a whole number, then divide the rise by that count to get the actual riser.
How does the calculation run?
A worked example on a 112 inch floor-to-floor rise with a 7 inch target riser.
- 112 ÷ 7 = 16. Sixteen risers, which is already a whole number in this case.
- 112 ÷ 16 = 7 inches exactly. That is the actual riser, and every one of the sixteen is this height.
- 2R + T = 25, so T = 25 − 14 = 11 inches. That is the tread depth.
- Fifteen treads, because the top floor is the last one and does not need a tread of its own.
- Total run = 15 × 11 = 165 inches, which is the horizontal space the flight consumes.
Step 4 is the one that catches people. A flight always has one fewer tread than riser, because the upper floor surface is the final landing.
Why must every riser match?
Because people climb stairs without looking at them. Gait is set after the first two or three steps and then repeats, so a single riser that is 10 mm different from the rest is a trip hazard in exactly the way a consistently steeper flight is not.
The tolerance in the codes is a few millimetres across the whole flight, which is tighter than most carpentry. It is also why the bottom riser is the one that usually goes wrong: fitting the finished floor after the stairs adds its thickness to the first step and to nothing else.
What does the 2R + T rule actually give you?
A comfortable stride at any of the usual proportions. Riser and tread trade against each other — a taller riser needs a shallower tread and produces a steeper, more space-efficient flight; a shorter riser wants a deeper tread and a longer run.
| Riser | Tread from 2R + T = 25 in | Character |
|---|---|---|
| 6 in | 13 in | Shallow, generous, long run |
| 7 in | 11 in | The domestic default |
| 7.5 in | 10 in | Steeper, saves floor space |
| 8 in | 9 in | At or past the domestic limit in most codes |
The codes cap the riser and set a minimum tread, and the caps differ between jurisdictions, so a flight that is legal in one place may not be in another. Check the local figure before committing to a rise count.
How does roof pitch use the same idea?
Roof pitch is the same rise-over-run relationship written differently: rise per 12 units of run. A 6:12 roof rises 6 inches for every 12 horizontal, which is an angle of 26.57 degrees and a 50 per cent slope.
The number that does the work on site is the rafter multiplier — the ratio of the sloping length to the horizontal run. For 6:12 it is 1.118, so any horizontal run multiplied by 1.118 gives the rafter length, and any roof area calculated on plan multiplied by the same figure gives the actual surface.
That multiplier is also what makes a roof more expensive than its footprint suggests. A 30-degree roof has 15 per cent more surface than the building it sits on, and every covering, membrane and batten is bought against the larger figure.
Does pitch decide the covering?
It decides what is allowed. Below about 10 degrees a roof is low-slope and needs a continuous membrane rather than lapped tiles, because water no longer runs off fast enough for laps to work.
Interlocking concrete tiles generally want 17.5 degrees or more, plain clay tiles closer to 35, and slate somewhere between depending on the size and the lap. Fitting a covering below its minimum pitch does not fail immediately — it fails in driven rain, years later, and it voids the guarantee.
Questions people ask
Why is there one fewer tread than riser? Because the upper floor is the last surface you step onto. Sixteen risers take you up sixteen steps and only fifteen of them need a tread.
How do I measure roof pitch from inside? Hold a level against a rafter, mark 12 inches along it, and measure vertically from that mark to the rafter. That vertical figure is the rise over a 12 run.
Is percentage slope the same as pitch? Related but written differently. A 6:12 pitch is a 50 per cent slope and a 26.57 degree angle — three notations for one geometry.
Can risers vary slightly? Only within the few millimetres the code allows across the whole flight. It is one of the tightest tolerances in domestic construction, and for good reason.
Fix the riser count first, derive everything else, and check the local code before cutting a stringer. The stair calculator works the rise, tread and total run together, and the roof pitch calculator converts between ratio, angle, percentage and the rafter multiplier.