Area Calculator

Rectangle, circle, triangle, trapezoid and ellipse โ€” area and perimeter.

About this calculator

Pick a shape, type its measurements, read area and perimeter with the formula written underneath. It covers the shapes real problems are made of: rectangle, square, circle, triangle by base-and-height, triangle by three sides (Heron's formula โ€” no height needed), trapezoid and ellipse. Impossible triangles are called out rather than silently computed.

Getting real-world areas right

The universal method for rooms, gardens and anything irregular: sketch it, slice it into rectangles and triangles, compute each, add. Nearly every floor plan yields to that decomposition. The details that catch people: a triangle's height is the perpendicular distance to the base, not the slanted side's length (when all you have is the three sides, that's exactly what Heron's formula is for); a circle measured across the middle gives the diameter โ€” halve it before ฯ€rยฒ; and units square along with the lengths, so metres in means mยฒ out, and mixing centimetres with metres in one calculation is the classic silent error. Practical margin: for paint, turf or tiles, add 10% to the computed area for cuts and waste. Convert units first, and for volumes rather than areas, multiply by the depth โ€” a 12 mยฒ patio at 0.1 m deep needs 1.2 mยณ of concrete.

Frequently asked questions

What is the area of a circle?

ฯ€rยฒ โ€” ฯ€ times the radius squared. Measured the distance across the middle? That's the diameter: halve it first. A 10 cm-across circle has area ฯ€ ร— 5ยฒ โ‰ˆ 78.5 cmยฒ.

How do I find a triangle's area from three sides?

Heron's formula: with s = half the perimeter, area = โˆš(s(sโˆ’a)(sโˆ’b)(sโˆ’c)). No height needed โ€” and if the number under the root goes negative, those sides can't form a triangle.

Why is my triangle answer wrong using the slant side?

Area = ยฝ ร— base ร— height needs the perpendicular height, not the slanted edge. Using the slant overstates the area โ€” switch to Heron's three-side formula when the height isn't known.

How much extra should I buy for paint or tiles?

Add about 10% to the calculated area for cuts, waste and pattern matching โ€” more (15%) for diagonal tile layouts.