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How do I calculate the area of a bay window or a curved wall?

A semicircular bay window is half a circle. A shallower bay is measured in strips. Both can be worked out with a tape measure and a calculator — here are both methods, with numbers.

Short answer: Split the room into a rectangle plus the curve. If the curve is a semicircle, the area is π × radius² ÷ 2 — a bay window with a 1.20 m radius is 2.26 m². If the curve is flatter than a semicircle, measure the depth of the curve at regular intervals along the wall, add the depths together and multiply by the distance between measurements. Both methods can be done with a tape measure in under five minutes and land within a couple of per cent.

Split the room: rectangle plus curve

A room with a bay window or a curved wall is never a single calculation. It is two: the rectangular main part, which you work out completely normally as length × width, and the curve, which is added on top.

The same applies in reverse. If the wall curves inward — around a spiral staircase or a chimney breast, for example — you calculate the rectangle and subtract the curve.

Method 1: the semicircular bay window

A classic semicircular bay window is exactly half a circle set against a straight wall. You need one measurement: the radius, the distance from the centre of the bay's opening out to its furthest point.

A room measures 4.00 × 3.00 m, and on one end wall sits a semicircular bay window with a radius of 1.20 m:

The radius can be measured two ways, and both should agree. Either you measure directly from the centre of the opening outward, or you measure the bay's width at the wall — which is 2 × radius, so 2.40 m in the example. If the two figures do not match, the bay is not a semicircle, and you need method 2 instead.

If the curve is a quarter circle — typically a rounded corner — the area is π × radius² ÷ 4.

Method 2: the shallow bay window, measured in strips

Most bay windows are flatter than a semicircle, and the circle formula does not hold for them. The strip method works on any curve and needs no formula beyond adding and multiplying.

A bay window is 2.40 m wide at the wall and 0.90 m deep at its deepest point:

Working out the same section with exact circle mathematics gives 1.59 m². The strip method therefore lands 2 % over — a difference of 0.03 m² in a room. For flooring, paint and furnishing this makes no difference; for anything that has to be cut to the millimetre, use a template instead of a calculation.

Want it closer? Use more, narrower strips. With 12 strips of 0.20 m each, the deviation drops below 1 %.

How to measure the depth of a curve

The curve's depth must be measured at right angles to the straight line the bay window projects from. That line is easiest to find like this:

No string on hand? Lay a plank or a straight batten across the opening instead. What matters is that the baseline is straight, and that the depths are measured perpendicular to it — measure at an angle, and every depth comes out too large.

When can a curve be ignored?

Rounded corners and small curves in the plaster can safely be treated as square corners. A rounded corner with a 5 cm radius costs around 5 cm² compared to a sharp corner — less than a matchbox. Even four such corners in a room add up to under 0.01 m².

Rule of thumb: if the curve's depth is under 10 cm, it makes no difference to the area. Over 30 cm, it needs to be included. In between, it depends on what the figure is for — a contractor's quote tolerates more rounding than a kitchen order.

A curved wall has more wall than the floor suggests

One thing that surprises many people: a curved wall is longer than the straight wall it replaces. The semicircle in the example has an arc length of π × 1.20 = 3.77 m, while the opening is only 2.40 m wide. If the bay window needs painting, there is 57 % more wall than the baseline suggests — and the same goes for skirting, radiators and curtain rails.

For floor area, you use the curve's area. For paint, skirting and wallpaper, you use the curve's length. The two figures must never be swapped.

Measure internally — in the curve too

Curved walls are measured like any other wall: internally, from wall surface to wall surface, at floor height. It is the only measure an ordinary person can verify with a tape measure — and in a bay window the difference is extra large, because a masonry bay wall can easily be 30 cm thick. Measured externally, the bay window in the example is 3.00 m wide and 1.20 m deep; internally, 2.40 × 0.90 m. That is 1.62 m² internally against roughly 2.7 m² measured on the outside — more than a whole square metre that is purely wall.

Curved walls in HouseSense

HouseSense works with rooms as polygons: a room is a series of corners connected by straight lines, and the area is calculated from that shape. A curved wall therefore becomes a series of short, straight segments — exactly the same principle as the strip method above, just with more, shorter segments.

When you draw the home on graph paper, you can add as many corner points along the curve as you like, deciding for yourself how closely the curve is followed. Four or five points in a bay window are plenty for an area you can order flooring by. And like every other measurement in the app, they are internal: two rooms sharing a wall never count the same square metres twice — not even when the wall is curved.

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These articles are general guidance, not advice about your particular home. Rules for areas, building work and permits differ from country to country and change over time — always check with the authorities or a professional before you decide anything.