The Same Terrace Needs a 25% Longer Stair in the US Than the UK

Take a two-storey terrace with a floor-to-floor height of 2.6 m. Under the UK limits, the shortest legal straight stair runs about 2.65 m along the floor. Under the US limits, it runs 3.30 m. That is 0.65 m more, or 25%, on a house that may be only 4 m wide inside. I think this gap matters more to the plan than most arguments about style. I also found that my thesis fails in an important way, and I say where below.

Question

Does the national rise and going limit fix the run of a small house's stair? If it does, does the run then place the hall, the first door and the bin store?

I read from the front door inward, as I always do. My sketch is a hypothetical plan, not a real house. Scale bar: 0 to 3 m. North arrow: up the page, front door on the south wall. Plot: 4.2 m wide between party-wall centres. This is my assumption. Two rooms per floor is the standard type [7][8].

Data and where it came from

UK, England: Approved Document K, Table 1.1, edition of 2013 [2]. A calculator page that quotes the table gives these limits for a private stair [1]:

• Rise: 150 to 220 mm.
• Going: 220 to 300 mm.
• Maximum pitch: 42 degrees.
• Headroom: 2 m above the pitch line.
• Twice the rise plus the going: 550 to 700 mm, as guidance only.
• No minimum width inside a dwelling.

I did not read the table itself. The GOV.UK page showed no stair figures [2]. Treat these figures as second-hand until you check the PDF.

US: IRC R311.7. Two summaries agree on the main limits [3][4]:

• Maximum riser: 7¾ in (196 mm).
• Minimum tread: 10 in (254 mm).
• Minimum width: 36 in (914 mm).
• Headroom: 80 in (2,032 mm).

The Boise handout also gave a variation limit of 3/8 in (9.5 mm) within a flight [4]. I could not open its PDF as text. The figure came through the search result. The US rules differ by state and city, and local amendments are common. The UK Government is also reviewing its domestic stair guidance [6], so the UK figures may change.

For the effect on people, I use one survey. It had 1,223 responses from English homes. Households with a recent stair accident had a significantly different mean going from those without. Larger goings went with fewer accidents. Rise showed no significant difference [5]. I saw only the abstract text in search results.

Method

I worked this by hand, without the Lab. A reader can repeat every step. Call the storey height $H$ and the number of risers $n$. Then:

$r = H / n, \qquad \text{run} = (n-1)\, g$

Here $r$ is the rise and $g$ is the going. A flight has one fewer tread than risers. This holds for a straight flight whose top riser meets the upper floor.

The UK pitch limit is 42 degrees, and $\tan 42° = 0.9004$. So the going must be at least $r / 0.9004$. For each $n$ I pick the smallest legal going and the smallest legal run. For the US, I pick the fewest risers that keep $r \le 196$ mm, with the tread at 254 mm.

Result

At $H = 2600$ mm:

UK. I need at least $2600/220 = 11.8$ risers, so $n = 12$ and $r = 216.7$ mm. The pitch limit then needs $g \ge 216.7/0.9004 = 240.7$ mm. The 220 mm minimum going does not control here. Run $= 11 \times 240.7 = 2{,}648$ mm. A 13-riser stair gives $r = 200$ mm, $g \ge 222.1$ mm and a run of $12 \times 222.1 = 2{,}665$ mm. So the shortest UK run is about 2.65 m.

US. I need at least $2600/196 = 13.3$ risers, so $n = 14$ and $r = 185.7$ mm. Run $= 13 \times 254 = 3{,}302$ mm.

Case	Risers	Rise (mm)	Going (mm)	Shortest run (mm)
UK limits, H = 2600	12	216.7	240.7	2,648
US limits, H = 2600	14	185.7	254	3,302

The difference is 654 mm, and 3,302 / 2,648 = 1.25.

What the run does to the plan

Start the stair at the front wall, beside the party wall, 0.9 m wide. This width is my choice, not a UK limit [1]. The US sets 914 mm [3]. The stair then covers 2.65 × 0.9 = 2.4 m² of floor in the UK case and 3.30 × 0.914 = 3.0 m² in the US case.

Now ask where a person can walk under the flight. I assume a clear height of 2.0 m under the flight. This is my figure, not a code figure. I also ignore the thickness of the stair structure, which only makes things worse. The underside of the flight sits at height $H - d \cdot s$, where $d$ is the distance from the top and $s$ is the slope.

• UK: $s = 216.7/240.7 = 0.90$. The underside is 2.0 m or higher only within $600/0.90 = 667$ mm of the top of the flight.
• US: $s = 185.7/254 = 0.73$. The corresponding distance is $600/0.73 = 821$ mm.

So a door to the rear room, taken under the stair, sits at about 2.0 m from the front wall in the UK case and about 2.5 m in the US case. Add the shorter hall at the start and these figures shift by the hall length. I did not draw a full plan, so I call these positions derived limits, not measured doors.

Now the bin. Where does the bin go? Suppose it is a 1.2 m high object (my assumption) and it sits under the stair. It fits only beyond $1.2/0.90 = 1.33$ m from the foot in the UK case and $1.2/0.73 = 1.64$ m in the US case. The cupboard under a short, steep stair is smaller and starts later. A plan with the bin at the front door loses either the bin or the stair space. This is why the 1858 yard rule of 150 sq ft (14 m²) at the rear still matters: it gave the old terrace a place for the bin that the stair did not [7].

What the render hides

A render of a narrow house shows a bright hall and a stair that floats. It shows no scale bar and no rise count. You cannot count the risers, so you cannot tell if the stair is 12 steps or 14. That count decides if the rear door is 2.0 m or 2.5 m from the front wall. A drawing with a section shows the answer at once: the sloping line, the headroom line and the rise marked on each step.

Sensitivity: which assumption moves the result most

I tested three assumptions.

1. Storey height. The ratio is stable. At $H = 2400$ mm: UK $n = 11$, $r = 218.2$ mm, $g = 242.3$ mm, run 2,423 mm. US $n = 13$, $r = 184.6$ mm, run $12 \times 254 = 3{,}048$ mm. The ratio is 1.26. At $H = 2800$ mm: UK $n = 13$, $r = 215.4$ mm, $g = 239.2$ mm, run 2,871 mm. US $n = 15$, $r = 186.7$ mm, run $14 \times 254 = 3{,}556$ mm. The ratio is 1.24. So the 25% gap holds across a 0.4 m range of storey height. It moves little.

2. The minimum is not what people build. This is the assumption that moves the result most, and it is where my thesis fails. The codes set a limit, not a design. A UK designer who picks a comfortable 250 mm going gets $n = 15$ (since $2600/175 = 14.9$), $r = 173.3$ mm and a run of $14 \times 250 = 3{,}500$ mm. That is longer than the US legal minimum of 3,302 mm. The limit fixes the shortest stair, not the actual one. Any home that chooses a gentler stair has a run set by taste and by the plot, not by the clause. The code only draws the lower bound of the hall.

The survey result pushes the same way. Larger goings go with fewer reported accidents [5]. The UK minimum going of 220 mm is 8.7 in, which is shorter than the US 10 in tread. But in my example the UK pitch limit forces a 241 mm going anyway [1]. So the going limit alone does not tell you the stair's real shape. I draw no firm conclusion about injury rates from one survey. It shows association in English homes, not cause.

3. The layout. A stair that turns on a landing, or that has winders, cuts the straight run. Both codes allow such stairs with extra rules that I did not read. A turned stair shortens the footprint in one direction and widens it in the other. In a 4 m wide house that trade can be worth it. I ignored it, so my 2.65 m and 3.30 m figures are for a straight flight only.

Where my claim fails

I said the stair run decides the hall, the first door and the bin more than the architect's style does. I have shown only half of it. The code fixes a minimum run, and that run sets a minimum distance from the front wall to the rear door. I have not shown that real terraces sit at that minimum. I have not read any plan survey. One hypothetical plan cannot test "more than style". It can only show that the geometry leaves little room.

My current view is narrower and, I think, more honest. The stair limits set the shortest possible stair. The shortest stair sets the earliest possible rear door and the earliest usable bin space. A plan must respect that line, and a plan that sits at it has its hall decided by the clause. A plan that sits well past it has its hall decided by a choice. To settle which is common, I would need dimensioned plans of real terraces with the riser count marked. That is the evidence I want next.

One rule shapes the result: count the risers before you read the hall.