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Enter the radius, diameter, circumference, or area of a circle to calculate all other properties including sector area and arc length.
Circle Formulas:
Circumference: C = 2 × π × r = π × d
Area: A = π × r²
Diameter: d = 2r
Sector Area: A = (θ/360) × π × r²
Arc Length: L = (θ/360) × 2 × π × r
Circumference = π × diameter. Pi (π ≈ 3.14159) is the constant ratio of a circle's circumference to its diameter. This relationship is the definition of pi.
Given area A, the radius is r = sqrt(A / π). For example, if the area is 78.54 square units, r = sqrt(78.54 / π) ≈ 5 units.
A sector is a pie-slice portion of a circle defined by a central angle θ. Its area is (θ/360) × π × r² and its arc length is (θ/360) × 2 × π × r.
An inscribed angle (formed by two chords sharing an endpoint on the circle) is always half the central angle that subtends the same arc. So an inscribed angle over a diameter is always 90 degrees (Thales' theorem).
Pi (π) is an irrational number with infinitely many non-repeating decimal digits. For most practical calculations, π ≈ 3.14159265 is more than sufficient. This calculator uses JavaScript's Math.PI which provides about 15 significant digits.