circumference to radius calculator

Enter a circle's circumference to instantly calculate radius, diameter, and area.

How to convert circumference to radius

If you know a circle's circumference and need its radius, the conversion is straightforward. The radius is simply the circumference divided by 2π. This calculator does that instantly and also shows extra values like diameter and area for convenience.

Key formula:
r = C / (2π)
where:

r = radius
C = circumference
π ≈ 3.14159265359

Why this circle formula works

By definition, the circumference of a circle is:

C = 2πr

To solve for radius, divide both sides by 2π:

r = C / (2π)

This relationship is one of the most common geometry formulas used in school math, engineering calculations, manufacturing measurements, and construction planning.

Step-by-step manual example

Example: circumference = 50 cm

Start with the formula: r = C / (2π)
Substitute: r = 50 / (2 × 3.14159)
Compute denominator: 2π ≈ 6.28318
Final radius: r ≈ 7.96 cm

So a circle with a circumference of 50 cm has a radius of about 7.96 cm.

Quick reference values

C = 6.2832 → r = 1
C = 12.5664 → r = 2
C = 31.4159 → r = 5
C = 62.8319 → r = 10
C = 314.1593 → r = 50

Related circle conversions

When working with circles, you often need more than one conversion. Here are the most useful relationships:

Diameter from radius: d = 2r
Radius from diameter: r = d/2
Circumference from radius: C = 2πr
Area from radius: A = πr²
Radius from area: r = √(A/π)

Common mistakes to avoid

Forgetting the 2 in 2π. Using C/π gives diameter, not radius.
Mixing units. Keep all measurements in the same unit system.
Rounding too early. Keep extra decimal places during intermediate calculations.
Using negative values. Circumference should be a positive number in real geometry contexts.

Tip: If you accidentally calculate diameter first, just divide by 2 to get radius.

Where this calculator is useful

This circumference to radius tool is practical in many real-world situations:

Designing circular parts, pipes, lids, and wheels
Estimating dimensions for round tables, gardens, and patios
School homework and exam practice for circle geometry
CAD drafting, 3D modeling, and manufacturing tolerances
Construction layouts involving circular arcs and boundaries

FAQ

What is the radius if I only know circumference?

Use r = C / (2π). Enter the circumference in the calculator above and it computes radius instantly.

Is circumference the same as perimeter?

Circumference is the perimeter specifically for circles. The terms are related, but "circumference" is the precise circle term.

Can I use inches, feet, meters, or centimeters?

Yes. The formula works with any unit. Radius comes out in the same unit as circumference.

Does this tool also give diameter and area?

Yes. After calculating radius, the tool also displays diameter and area so you can continue your geometry work faster.

Final takeaway

The circumference-to-radius conversion is simple and reliable: divide by 2π. Use the calculator at the top of this page for accurate results with customizable precision, whether you're solving a math problem or working on a practical design task.