Quick answer
Radius = circumference ÷ 2π. A circumference of 6.2832 (2π) gives a radius of 1.
Enter the circumference. The calculator returns the radius.
Related tools: Circumference Calculator: Circumference of a circle. Radius Calculator: Radius of a circle from diameter, circumference or area. Circumference to Diameter Calculator: Convert a circle's circumference to its diameter.
How to use the Circumference to Radius Calculator
- Enter circumference (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Circumference | A number | > 0 |
Formula and method
Formula
r = C ÷ 2π
IEEE-754 double precision; shown to at most 6 decimal places.
Direct application of the circle relationships.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Circumference = 6.283185307179586.
| Result | Value |
|---|---|
| Circumference to Radius | 1 |
Example 2
Inputs: Circumference = 20.
| Result | Value |
|---|---|
| Circumference to Radius | 3.183099 |
The first line is the headline result (circumference to Radius). IEEE-754 double precision; shown to at most 6 decimal places.
Reasoning
C = 2πr, so r = C ÷ 2π. A running track with a 400 m inner lap has radius 63.66 m if it were a circle. The radius leads to the area A = πr².
Practical uses
Work out the radius of a pulley, wheel or circular planter from a measured circumference. Keep the unit consistent. The value must be positive.
Radius from a distance around
r = C ÷ 2π. A 400 m running track lap corresponds to a circle of radius about 63.66 m. A circumference of 50 gives r ≈ 7.9577.
Divide by 2π (about 6.2832), not π, or the answer will be double.
How the result changes with circumference
Holding every other input at the first worked example, this table changes only circumference. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Circumference | Circumference to Radius |
|---|---|
| 3.142 | 0.500065 |
| 6.283 | 0.999971 |
| 12.57 | 2.000578 |
| 25.13 | 3.999564 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Circumference: entering "0" shows "Circumference must be greater than 0." beside that field and no result.
Choosing between the Circumference to Radius Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Circumference Calculator](/math/circumference/) | i know the and value | Circumference |
| [Radius Calculator](/math/radius-calculator/) | i know the and value | Radius |
| [Circumference to Diameter Calculator](/math/circumference-to-diameter/) | circumference | Circumference to Diameter |
| [Diameter to Radius Calculator](/math/diameter-to-radius/) | diameter | Diameter to Radius |
| [Triangle Calculator](/math/triangle-calculator/) | side a, side b and side c | Area |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Value must be positive
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for circumference to confirm this.
Frequently asked questions
What radius gives a circumference of 100?
A circumference of 100 gives r = 100 ÷ 2π ≈ 15.92.
How do I find the area from circumference?
Find r = C ÷ 2π and then A = πr², which simplifies to C² ÷ 4π.
Is radius half the diameter?
Yes. The radius is half the diameter, so a 9 cm diameter is a 4.5 cm radius.
What radius does a circumference of 50 give?
50 ÷ 2π ≈ 7.9577.
Why divide by 2π?
Because C = 2πr, so r = C ÷ 2π.
What does the Circumference to Radius Calculator calculate?
Convert a circle's circumference to its radius. It returns Circumference to Radius.
What formula does the Circumference to Radius Calculator use?
r = C ÷ 2π. Direct application of the circle relationships.
What do I need to enter in the circumference to Radius Calculator?
You enter Circumference.
What is an example of a circumference to Radius result?
With circumference 6.283185307179586, the circumference to Radius is 1.
Related calculators
- Circumference Calculator — Circumference of a circle.
- Radius Calculator — Radius of a circle from diameter, circumference or area.
- Circumference to Diameter Calculator — Convert a circle's circumference to its diameter.
- Diameter to Radius Calculator — Convert a circle's diameter to its radius.
- Triangle Calculator — Area, perimeter, angles and type of a triangle from its three sides.
- Circle Calculator — Radius, diameter, circumference and area of a circle from any one of them.
- Endpoint Calculator — Other endpoint of a segment from its midpoint and one endpoint.
- Perimeter Calculator — Perimeter of common shapes.
- Rational or Irrational Calculator — Whether the k-th root of a whole number is rational.
Sources
- Standard Euclidean geometry formulas (e.g. NIST Digital Library of Mathematical Functions §4, CRC Standard Mathematical Tables)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.