Area Calculator

A square is side × side; a rectangle is length × width. Both must be in the same unit before you multiply — a length in feet and a width in inches gives a meaningless number, and it is the most common error on this page.

Area = π × r², where r is the radius. If you measured across the circle rather than from the centre, that is the diameter — halve it first. Using the diameter by mistake gives four times the true area, which is a mistake worth checking for whenever a result looks impossibly large.

Half the base times the perpendicular height: A = ½ × b × h. The height must be measured at a right angle to the base, not along a sloping side. When you only know the three side lengths, Heron's formula gets there instead: with s as half the perimeter, A = √(s(s−a)(s−b)(s−c)).

Area is the surface enclosed, measured in squared units; perimeter is the distance around the edge, measured in plain units. Paint and flooring are priced by area, fencing and skirting board by perimeter — and two rooms with the same perimeter can have very different areas.

Because the conversion factor gets squared. One metre is 3.28084 feet, but one square metre is 3.28084² = 10.7639 square feet. Forgetting to square the factor is the single biggest source of wrong answers when converting an area between systems.

Split it into rectangles, triangles and part-circles, work out each one, and add them. An L-shaped room is two rectangles; a room with a bay window is a rectangle plus a segment. For a genuinely irregular plot, surveyors use the shoelace formula on the corner coordinates, which is the same idea done algebraically.

Work out the area, then add a waste allowance — usually 5-10% for flooring, more like 15% if the material is laid diagonally or has a pattern to match. For paint, subtract the doors and windows, then check the coverage on the tin, which is typically quoted in square metres per litre per coat.

An acre is 4,046.86 m² or 43,560 ft². A hectare is 10,000 m², which is 2.471 acres. A useful mental picture: a hectare is roughly a square 100 m on each side, and an acre is a bit smaller than a football pitch.

It is base × perpendicular height, the same as a rectangle. The slanted side is longer than the height, so multiplying the two side lengths overstates the area. Lean a rectangle over and its area does not change even though one pair of sides now measures longer diagonally.

Average the two parallel sides and multiply by the distance between them: A = ½ × (a + b) × h. It is the formula that turns up constantly in land measurement, because a plot with one irregular boundary can often be treated as a run of trapezoids.