HouseSense

All articles 6 min read

How do you measure an out-of-square room for a new floor?

Split the room into triangles, measure every side and every diagonal, and work out the area with Heron's formula — that gives you the true area, even when no angle is 90 degrees.

Short answer: An out-of-square room is measured by splitting the floor into triangles. Measure every wall internally, measure the diagonal in each sub-area, and work out each triangle's area with Heron's formula. Add the triangles together, and you have the true floor area — even when no angle is 90°. When buying flooring, add 10-15 % waste on top of that, because an out-of-square room needs more cuts than a square one.

First: is the room actually out of square?

That's decided by the diagonal, not by eye. Measure the room's two sides and then the diagonal from corner to corner. If the room is square, the diagonal should equal the square root of (length² + width²).

Example: The room measures 4.12 m × 3.05 m. A square rectangle with those measurements has a diagonal of the square root of (4.12² + 3.05²) = the square root of (16.97 + 9.30) = the square root of 26.27 = 5.13 m. If you instead measure 5.21 m, the room is out of square — 8 cm off over 5 m.

If the deviation is under about 2 cm, you can in practice treat the room as square: 4.12 × 3.05 = 12.57 m², and the error is well within the waste percentage. If the deviation is bigger, you need to calculate properly — otherwise neither the amount of flooring, the pattern layout, nor a cabinet you want to fit later will be right.

The method: triangulate the room

A triangle can only have one shape once you know all three sides. That's the whole reason surveyors and building measurers triangulate: a quadrilateral can be pushed out of square without its sides changing, but a triangle can't. So the rule is: measure every wall, and measure one diagonal per quadrilateral you split the room into.

  1. Sketch the room's outline freehand — out of square, exactly as it looks, without measurements. The sketch doesn't need to be neat, it needs room for figures.
  2. Number the corners clockwise: A, B, C, D …
  3. Measure each wall internally from corner to corner at floor height, and write the figure in centimetres.
  4. Draw diagonals so the room is split into triangles, and measure each diagonal. A quadrilateral needs 1 diagonal, a pentagon 2, a hexagon 3.
  5. Work out each triangle's area with Heron's formula, and add them together.

Heron's formula — the maths spelled out

Heron's formula gives a triangle's area from its three side lengths a, b and c, without you needing to know a single angle:

s = (a + b + c) ÷ 2, and then area = the square root of (s × (s − a) × (s − b) × (s − c)).

Example, triangle 1: Wall AB = 4.12 m, wall BC = 3.05 m, diagonal AC = 5.21 m.

Triangle 2: Wall CD = 4.05 m, wall DA = 2.98 m, the same diagonal AC = 5.21 m.

Total floor area = 6.28 + 6.02 = 12.30 m². Had you simply multiplied 4.12 × 3.05, you'd have got 12.57 m² — 0.27 m² too much. That sounds small, but across a whole house of out-of-square rooms it adds up, and it's exactly the kind of error that makes officially registered areas and measured figures disagree.

When the room isn't a quadrilateral

Sloped walls and cut corners: Treat it as a pentagon. Measure all five sides and two diagonals from the same corner, giving you three triangles. All three are worked out with Heron's formula.

Bay windows and niches: Work out the main area separately from the bay and add them together. Measure the bay's opening (the width along the wall line), its depth and its two angled sides.

Curved or bowed walls: Measure the arc's chord (the straight line between its endpoints) and its rise (the greatest distance from the chord out to the arc at its midpoint). If the rise is small relative to the chord, you can approximate the arc's area as (2 ÷ 3) × chord × rise. For buying flooring, that approximation is more than good enough — but curved walls cost extra cuts, so add another 5 percentage points of waste.

Sloped wall under a roof: For flooring, the sloped wall is irrelevant — the floor runs to where the wall meets it, and that's the line you measure. Do note, however, that official property areas are calculated under sloped walls according to their own rules — and those rules are something other than the raw floor area you're measuring here. If the figure is needed for anything besides buying flooring, it should be worked out under the rules that apply where the property is located.

The check measurement that catches errors

Always measure both diagonals in a quadrilateral, even though you only need one for the calculation. The second is your check: you can work it out from the four walls and the first diagonal, and if it doesn't match, you've measured something wrong somewhere. If the two diagonals are equal length, and the opposite walls are equal in pairs, the room is a true rectangle.

Also measure each wall twice — once at the floor and once about 1 m up. If there's more than 1-2 cm difference, the wall leans. For flooring you use the floor measurement; for wall tiles and cabinets you use the smaller of the two.

So how much flooring should you buy for an out-of-square room?

Take the measured area and add waste. An out-of-square room needs more cuts than a square one, because every single plank end along the sloped wall has to be cut at its own angle:

Example: 12.30 m² out-of-square room, straight layout, 11 % waste: 12.30 × 1.11 = 13.65 m². The pack covers 2.22 m²: 13.65 ÷ 2.22 = 6.15 → 7 packs = 15.54 m². The supplier's own guidance always takes priority over these rules of thumb.

Skipping the maths

Heron's formula isn't hard, but it's tedious to do by hand for eight rooms. The alternative is to get the area straight out of an accurate floor plan that already knows where the corners sit. HouseSense builds that plan two ways: by scanning the room with the iPhone's LiDAR, where the out-of-square walls come through exactly as they are — or by drawing the room with your finger and typing in the measured centimetres, wall by wall. Either way, the area is calculated from the actual geometry, not from an assumed rectangle, so an out-of-square room doesn't come out neater than it really is.

Whichever method you use, the same principle applies as to all measuring: the drawing may be made to look nice, but the figures may not. A room that's out of square has to stay out of square on the drawing — otherwise you find out the day the cabinet doesn't fit.

Download on the App Storefor iPhone and iPad — draw or scan

One home is free. Plans for more in the app.

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.