All calculatorsCircumference Calculator
Convert between a circle’s circumference (C), diameter (D), and radius (r) using C = πD and C = 2πr. Includes unit support, quick picks, optional step-by-step, and a small visual.
Background
Circumference is the distance around a circle. Diameter goes straight across through the center, and radius is half the diameter. These are always related: D = 2r, C = πD, and C = 2πr.
How to use this calculator
- Select which value you know: C, D, or r.
- Enter that value.
- Pick a unit and click Calculate.
- Enable Step-by-step to see the exact formula used.
How this calculator works
- From circumference: D = C/π, r = C/(2π)
- From diameter: C = πD, r = D/2
- From radius: C = 2πr, D = 2r
Formula & Equation Used
Circumference: C = πD = 2πr
Diameter–radius: D = 2r
Example Problem & Step-by-Step Solution
Example 1 — find diameter and radius from circumference
Given C = 31.4 cm, find D and r.
- Use D = C/π and r = C/(2π).
- D = 31.4 / π ≈ 9.99 cm
- r = 31.4 / (2π) ≈ 4.995 cm
Example 2 — find circumference and radius from diameter
Given D = 8 in, find C and r.
- Use C = πD and r = D/2.
- C = π·8 ≈ 25.133 in
- r = 8/2 = 4 in
Example 3 — find circumference and diameter from radius
Given r = 2 m, find C and D.
- Use C = 2πr and D = 2r.
- C = 2π·2 ≈ 12.566 m
- D = 2·2 = 4 m
Frequently Asked Questions
Q: Do I need to convert units first?
Only if you want a different unit. Otherwise, keep one unit selected and your answers will be in that same unit.
Q: Why does π show up?
For every circle, the ratio C/D is constant — that constant is π.
Q: Can these values be negative?
No. Real circle measurements must be positive, so the calculator flags non-positive inputs.
