Stair Stringer Calculator UK: How to Use It

A stair stringer calculator works out the exact length and cut angles for the sloping boards that support your staircase steps. You enter the total rise (floor-to-floor height), the total run (horizontal distance), and the number of steps, and it returns the rise and run per step plus the stringer length. This is the same math a carpenter does by hand, but without the trial-and-error.

Formula

The calculator uses two basic right-triangle formulas. First, the rise per step is the total rise divided by the number of steps. Second, the stringer length is the hypotenuse of a right triangle where one leg is the total rise and the other leg is the total run (tread depth times number of steps). In symbols:

• Rise per step = R / N (mm)
• Total run = T × N (mm)
• Stringer length = √(R² + (T×N)²) (mm)
• Pitch angle = atan(R / (T×N)) in degrees

Where R is total rise in millimetres, N is the number of steps (not counting the top landing), and T is the tread depth (the horizontal going) in millimetres. The stringer length is the long edge of the board before you cut the notches for the treads and risers.

Worked Example

Using the default values: total rise = 2600 mm, number of steps = 14, tread depth = 250 mm.

1. Rise per step = 2600 / 14 = 185.7 mm (rounded to 185.7 mm).
2. Total run = 250 × 14 = 3500 mm.
3. Stringer length = √(2600² + 3500²) = √(6,760,000 + 12,250,000) = √(19,010,000) = 4359.9 mm (rounded to 4360 mm).
4. Pitch angle = atan(2600 / 3500) = atan(0.7429) = 36.6°.

So for a 2600 mm floor-to-floor height with 14 steps and a 250 mm going, each step rises 185.7 mm and the stringer board needs to be about 4360 mm long before cutting.

UK Building Regulations for Stairs

In the UK, the Building Regulations (Approved Document K) set limits for private stairs. The rise per step must be between 150 mm and 220 mm, and the going (tread depth) must be between 220 mm and 300 mm. The pitch (angle) must not exceed 42° for private stairs. For communal or public stairs, the limits are tighter: rise between 150 mm and 190 mm, going between 240 mm and 320 mm, and pitch no more than 38°. These are legal requirements, not just recommendations, and they apply to new stairs in dwellings, conversions, and extensions. Always check the current edition of Approved Document K with your local building control, as small amendments are made from time to time.

How to Measure the Rise and Run Correctly

Accurate measurement is the difference between a staircase that fits and one that doesn’t. Here’s what to do:

• Total rise: Measure from the finished floor level of the lower storey to the finished floor level of the upper storey. That includes any floor covering, such as carpet or tiles. If you measure before the covering is laid, add the thickness of the covering.
• Number of steps: Decide how many steps you want. A common starting point is to divide the total rise by a comfortable step height (around 175–190 mm) and round to a whole number. Then recalculate the exact rise per step.
• Going: The going is the horizontal distance from the nosing of one tread to the nosing of the next. For a straight staircase, the total run is the going times the number of steps.
• Headroom: Check the headroom above the stairs – it must be at least 2.0 m measured vertically from the pitch line (the line joining the nosings) to the ceiling above. If headroom is tight, you may need fewer steps (which increases rise per step) or a different stair design.

Common Mistakes and How to Avoid Them

Several errors trip up DIY builders and even some professionals:

• Not accounting for the top tread: The number of steps in the calculator should be the number of actual steps, not the number of riser boards. The top riser is usually the floor itself, so if you have 14 steps, you have 14 risers but only 13 treads if the top step is the landing. The calculator’s “number of steps” is the number of rises, which is what matters for the stringer.
• Mixing units: Always work in millimetres. If you measure in inches or feet, convert first. A 25 mm mistake on a single rise becomes a 350 mm error on the whole stringer.
• Forgetting the thickness of the tread: The rise per step is measured from the top of one finished tread to the top of the next. If you use 18 mm thick treads, you must subtract that from the rise when cutting the stringer, otherwise the actual rise will be too high.
• Rounding too early: Round the rise per step to the nearest millimetre only at the end. If you round each step to, say, 186 mm and multiply by 14, you get 2604 mm – 4 mm more than the actual rise. That error accumulates along the stringer.

How to Use the Stringer Length in Practice

The stringer length is the hypotenuse of the triangle, but you don’t cut the board along that line. You mark out the step notches along the top edge of a board that is at least as long as the stringer length. The notch for each step is a right angle: the vertical cut is the rise per step, and the horizontal cut is the going. The stringer’s bottom end is cut to sit on the floor, and the top end is cut to attach to the upper floor joist. Add about 50 mm to the calculated length to allow for the angle cuts at both ends – you’ll trim it to fit on site.

For a typical UK staircase with 14 steps and a 2600 mm rise, you’ll need a board about 4.4 m long. Standard timber lengths are 4.2 m, 4.8 m, and 5.4 m, so you’d likely buy a 4.8 m board and cut it down. Always buy a bit longer than the calculated length – you can cut off, but you can’t add on.

Alternative Methods: Manual vs. Calculator

Before online calculators, carpenters used a steel square (also called a framing square) to mark out steps directly on the board. That method works but requires careful marking and is prone to cumulative error. A calculator is faster and more accurate, but it’s still only as good as your measurements. Many professionals use a combination: they calculate the rise and run, then lay out the first stringer with a square, test it against the actual opening, and use that as a template for the others. If you’re building a staircase with a landing or a turn, a simple stringer calculator won’t be enough – you’ll need to break the staircase into straight flights and calculate each separately.

Frequently Asked Questions

What size timber should I use for stair stringers?

In the UK, a common size is 45 mm × 200 mm (nominal 2″ × 8″) for stringers with a span up to about 2.5 m. For wider stairs or longer spans, use 45 mm × 225 mm or 45 mm × 250 mm. The stringer must be strong enough to support the live load (people) and dead load (the weight of the stairs themselves). Check with your building control officer or a structural engineer if you’re unsure.

Can I use a stringer calculator for an outdoor deck staircase?

Yes, the same geometry applies, but outdoor stairs often have different requirements. The rise and going may be more relaxed (e.g., 180 mm rise and 250 mm going), but you must also consider the material – pressure-treated timber or composite – and the fact that the stringer will be exposed to weather. The calculator gives you the dimensions, but you still need to design for the load and fixings.

What is the maximum rise for a stair step in the UK?

For private stairs, the maximum rise per step is 220 mm. For communal stairs, it’s 190 mm. The minimum is 150 mm in both cases. If your calculated rise per step is outside these limits, you need to adjust the number of steps or the total rise (which you usually can’t change) – so you’d change the number of steps.

Do I need building regulations approval for a new staircase?

In most cases, yes. Adding a new staircase or altering an existing one is building work that falls under the Building Regulations. You’ll need to submit a building notice or full plans to your local authority building control, or use a private approved inspector. They will check that the stairs meet the requirements for rise, going, headroom, and strength. Even if you’re replacing an old staircase like-for-like, it’s wise to check with building control first.

Why does the calculator give a different length than my tape measure?

Because the calculator assumes the stringer is a perfect straight line from the top of the upper floor to the bottom of the lower floor. In reality, you need to add the thickness of the treads and any nosing, and you need to account for the fact that the stringer sits on the floor and against the upper joist. The calculated length is the theoretical minimum – always add 50–100 mm for cutting and fitting.

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in r | Total rise (floor to floor) | mm | 2600 | 0
in n | Number of steps | - | 14 | 1
in t | Tread depth (going) | mm | 250 | 0
out rise | Rise per step | mm | r / n | 1
out run | Total run | mm | t * n | 0
out stringer | Stringer length | mm | sqrt((r/n)^2 + t^2) * n | 0
out angle | Pitch angle | deg | atand(r/n / t) | 1