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Circle & Annulus Calculator

Calculate circle properties from any one measurement, or compute an annulus (ring) from inner and outer radii.

Circle formulas

AreaA = πr2
CircumferenceC = 2πr = πd
Diameterd = 2r
Radius from arear = √Aπ
Radius from circumferencer = C2π
Annulus (ring) areaA = π(R2 − r2)

Where r = radius, d = diameter, R = outer radius of a ring, π ≈ 3.14159

Worked examples

  1. A pizza has a radius of 7 inches. Find its area and circumference.

    1. A = π × 72 = 49π
    2. C = 2 × π × 7 = 14π

    Answer: A ≈ 153.94 in², C ≈ 43.98 in

  2. A circle has a circumference of 31.4 cm. Find the radius and area.

    1. r = 31.42π ≈ 4.997 cm
    2. A = π × 4.9972

    Answer: r ≈ 5.00 cm, A ≈ 78.46 cm²

  3. A ring has an outer radius of 10 cm and an inner radius of 6 cm. Find its area.

    1. A = π(102 − 62) = π(100 − 36) = 64π

    Answer: A ≈ 201.06 cm²

Tips & common mistakes

  • Using the diameter in πr² is the most common mistake — halve it first.
  • Doubling the radius doubles the circumference but quadruples the area.