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Circumference

Circle Circumference

Understand C = 2πr = πd, when to use each form, and how to handle semicircles and arcs.

Formulas

Standard Forms

C = 2πr

C = πd

Use π ≈ 3.14 or 22/7 unless exact form is preferred.

Semicircle Perimeter

P = ½C + d = πr + 2r

Remember to add the diameter for semicircle boundary length.

Examples

Given radius: r = 3 cm → C = 2πr = 2 × π × 3 = 6π ≈ 18.84 cm
Given diameter: d = 10 cm → C = πd = 10π ≈ 31.4 cm
Semicircle perimeter: P = ½(2πr) + d = πr + 2r

Common Pitfalls

• Forgetting the 2 in C = 2πr and using C = πr.
• Confusing radius with diameter in formulas.
• Mixing linear units (cm) with area units (cm²).

Practice & Tools

Circle Calculator

Compute circumference from radius/diameter.

Method: C = 2πr or C = πd
Related: unit conversion, rounding π

Open Circle Calculator

Practice Problems

Reinforce circumference concepts with targeted questions.