Circle Area Calculator

A circle's area depends on one measurement only, since every circle is the same shape at a different size. Pick whichever length is easiest to get. Across a pipe or a tabletop, that is often the diameter. Around a tree trunk or a column, a tape wrapped around the outside gives the circumference without any need to find the center.

Formula

A = π × r²

A

the area

π

pi, approximately 3.14159

r

the radius, from the center to the edge

Area from the radius

Square the radius, then multiply by π. A circle with a radius of 5 m covers π × 25 ≈ 78.54 m². Because the radius is squared, doubling it makes the circle four times larger, not two.

Area from the diameter

The diameter runs straight across through the center and is twice the radius. Either halve it and use the standard formula, or use the version below. A circle 14 inches across covers π × 196 ÷ 4 ≈ 153.94 square inches.

This is why a bigger pizza is often better value than it looks. A 16-inch pizza has about 201 square inches and a 12-inch pizza about 113, so the larger one holds roughly 1.78 times as much despite being only a third wider.

• A = π × d² ÷ 4

Area from the circumference

Circumference is the distance around the circle. Dividing its square by 4π gives the area directly. A trunk measuring 31.4 inches around has a cross-section of 31.4² ÷ (4 × π) ≈ 78.46 square inches. Pull the tape snug but level, because a slanted wrap reads long and inflates the area.

• A = C² ÷ (4 × π)

Radius and circumference from area

The formulas also run backward. To get a radius from a known area, divide the area by π and take the square root, so an area of 100 gives a radius of about 5.64. Multiply that radius by 2π to get a circumference of about 35.45. For part of a circle, the semicircle area calculator covers half circles, and a quarter circle is simply one quarter of the full area.

Frequently asked questions