Area of a Circle Calculator

The area of a circle formula

The area of a circle is the amount of flat surface inside its edge. It depends only on the radius, the distance from the centre to any point on the circle.

A = π × r²π ≈ 3.14159265, r is the radius.

Because the radius is squared, area grows much faster than size: doubling the radius makes the area four times larger, and tripling it makes the area nine times larger.

If you know the diameter d (twice the radius) or the circumference C instead, two equivalent forms save a step:

A = π × d² ÷ 4

A = C² ÷ (4 × π)

How to use the calculator

1. Type the radius into the Circle radius box. It starts at 3 so you can see a result straight away.
2. Choose the unit beside it: mm, cm, dm, m, km, in, ft, yd or mile.
3. Press Calculate area. The answer comes in the same unit, squared, and is rounded to six decimals.

If you only have the diameter, halve it before entering. If you have the circumference, divide it by 2π to get the radius, or use the circumference calculator for the reverse direction.

Worked examples

From a radius. A round table has a radius of 3 cm in a scale model. A = π × 3² = π × 9 = 28.274334 cm².

From a diameter. A circular pond is 10 m across. The radius is 5 m, so A = π × 25 = 78.539816 m². Using the diameter form gives the same number: π × 10² ÷ 4 = π × 25.

Comparing two sizes. A 12 inch pizza has a radius of 6 in and an area of π × 36 = 113.097336 in². A 16 inch pizza has a radius of 8 in and an area of π × 64 = 201.061930 in². The larger pizza is only a third wider in diameter, yet it offers (16 ÷ 12)² = 1.78 times as much to eat.

From a circumference. A rope circle measures 20 cm around. Its area is 20² ÷ (4π) = 400 ÷ 12.566371 = 31.830989 cm².

Radius to area lookup table

Areas for whole-number radii, in square units of whatever unit the radius uses.

Common mistakes

• Using the diameter as the radius. This inflates the area by a factor of four. Always check which one you measured.
• Forgetting to square. Multiplying π by r instead of r² gives something closer to half a circumference.
• Mixing up units. If the radius is in centimeters the answer is in square centimeters. To change it into another unit, use the area unit converter; square meters are not 100 square centimeters, they are 10,000.
• Rounding π too early. Using 3.14 for a large circle leaves a visible error: for r = 7 m, 3.14 gives 153.86 m² while the exact value is 153.94 m².

Practical uses

• Landscaping: seed, turf or mulch for a round flower bed or lawn.
• Pipes and ducts: the cross-section of a round pipe decides how much fluid it can carry. A pipe with a 25 mm inner radius has a cross-section of 1,963.5 mm².
• Cooking and baking: scaling a recipe from one round tin to another by area rather than by diameter.
• Manufacturing: material needed to cut round plates, lids and gaskets.

A slice of a circle is a sector; its area is a fraction of the full disc, available in the sector area calculator. For several shapes in one place, try the general area calculator.