Enter a circle's radius, diameter, or area and the Circumference Calculator works out all the missing values for you. Fill in any one field — circumference, diameter, radius, or area — and the other three update automatically using the formulas C = 2πR and A = πR².
Circumference
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Radius
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Diameter
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Area
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The circumference is the total distance around the outside edge of a circle — essentially its perimeter. It is always proportional to the diameter, linked by the constant π (pi ≈ 3.14159). For a circle with radius R, the circumference is C = 2πR.
The two most common forms are C = 2πR (using radius) and C = πD (using diameter). Both are equivalent because the diameter D equals 2R. Pi (π) is approximately 3.14159265.
Measure or identify the radius (distance from center to edge) or diameter (distance across the circle). Then apply C = 2πR or C = πD. For example, a circle with radius 14 cm has a circumference of 2 × π × 14 ≈ 87.96 cm.
Rearrange the formula C = πD to get D = C ÷ π. Simply divide the circumference by pi (≈ 3.14159) to obtain the diameter. For example, a circumference of 87.96 cm gives a diameter of about 28 cm.
Use the formula R = C ÷ (2π). Divide the circumference by 2π (approximately 6.28318) to get the radius. For instance, C = 87.96 cm gives R = 87.96 ÷ 6.28318 ≈ 14 cm.
First find the radius using R = C ÷ (2π), then calculate the area with A = πR². Alternatively, the combined formula is A = C² ÷ (4π). For C = 87.96 cm, the area is approximately 615.75 cm².
Wrap a flexible measuring tape or a piece of string around the outside of the circular object and note the length — that is the circumference. You can then enter that value into this calculator to find the radius, diameter, and area.
The ancient Greek mathematician Eratosthenes estimated Earth's circumference around 240 BC. By measuring the angle of the Sun's shadow in two cities (Alexandria and Syene) on the same day, he calculated Earth's circumference to be roughly 40,000 km — remarkably close to the modern value of about 40,075 km.