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Area of a Circle Calculator

Enter a radius, diameter, or circumference and we'll use π to find the exact area of the circle.

Area
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How to calculate the area of a circle

The area of a circle is the amount of flat space enclosed inside its edge — the paint you'd need to fill it, the dough in a pizza, the grass in a round lawn. The formula is famously short:

A = π · r²

Here r is the radius (the distance from the centre to the edge) and π ≈ 3.14159… is the ratio that shows up in every circle ever measured. To use the formula, square the radius first, then multiply by pi. That order matters: π · r² means square the radius, then multiply, not (πr)².

Why πr²? A quick intuition

Imagine slicing a circle into many thin wedges, like a pie, then rearranging them alternately point-up and point-down. As the wedges get thinner, the shape they form straightens out into a rectangle. Its height is the radius r, and its width is half the circumference, π · r. Multiply height by width and you get r · πr = πr². That's the whole trick — the "squared" comes from area scaling with the radius twice over, and π is inherited from the circle's roundness.

Worked example

You're ordering a pizza with a 30 cm diameter. How much pizza are you actually getting? First halve the diameter to get the radius: r = 30 / 2 = 15 cm. Then:

A = π · 15² = 225π ≈ 706.858347 cm²

That's more than 700 square centimetres of pizza. Notice that doubling the radius doesn't double the area — it quadruples it. A 30 cm pizza has four times the food of a 15 cm one, which is worth remembering next time two smalls look cheaper than one large.

Area from the diameter

If you only know the diameter d, halve it first: r = d / 2, then apply A = πr². You can also fold that into a single formula:

A = π · (d / 2)² = π · d² / 4

Area from the circumference

Sometimes you've measured the distance around a circle instead of across it — say, a tree trunk or a barrel. From the circumference C, recover the radius with r = C / (2π), then square and multiply as usual:

A = π · (C / 2π)² = C² / (4π)

The calculator above handles all three cases — just pick what you know.

Common mistakes

  • Radius vs diameter. The single most common slip. The diameter goes all the way across; the radius is half of that. Plug a diameter into πr² by accident and your area comes out four times too big.
  • Forgetting to square. πr² is not π · r. The exponent is doing real work.
  • Square units. Area is always in square units — cm², m², in². If your radius is in centimetres, your area is in square centimetres, not centimetres.
  • Rounding π too early. Using 3.14 is fine for a rough estimate, but for precise work keep more digits (or leave the answer as a multiple of π, like 225π).

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