Quick answer
Circumference = 2πr = πd. A circle of radius 1 has a circumference of 6.283185, a diameter of 2 and an area of 3.141593.
Choose whether you know the radius, diameter, circumference or area, and enter it. The calculator returns the circumference and the other measurements.
Related tools: Area of a Circle Calculator: Area of a circle from its radius, diameter or circumference. Circle Diameter Calculator: Diameter of a circle from radius, circumference or area. Circle Calculator: Radius, diameter, circumference and area of a circle from any one of them.
How to use the Circumference Calculator
- Choose i know the: Radius, Diameter, Circumference and Area.
- Enter value (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| I know the | Choose one: Radius; Diameter; Circumference; Area | Starts at Radius |
| Value | A number | > 0 |
Formula and method
Formula
d = 2r; C = 2πr; A = πr²
IEEE-754 double precision; shown to at most 6 decimal places.
Every quantity is derived from the radius: r = d/2 = C/2π = √(A/π).
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: I know the = Radius; Value = 1.
| Result | Value |
|---|---|
| Circumference | 6.283185 |
| Radius | 1 |
| Diameter | 2 |
| Area | 3.141593 |
Example 2
Inputs: I know the = Diameter; Value = 10.
| Result | Value |
|---|---|
| Circumference | 31.415927 |
| Radius | 5 |
| Diameter | 10 |
| Area | 78.539816 |
The first line is the headline result (circumference). Below it the circumference Calculator lists radius, diameter and area, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
From circumference to diameter
d = C ÷ π. A belt of length 62.83 cm around a circular pulley means a diameter of about 20 cm. That inverse step is the most common use: wrapping a tape measure round a tree or pipe and dividing by π gives its diameter.
Units and π
The answer is in the same unit as the input. π ≈ 3.14159; 22/7 is a rough approximation with an error of about 0.04%.
How the result changes with value
Holding every other input at the first worked example, this table changes only value. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Value | Circumference | Radius | Diameter |
|---|---|---|---|
| 0.5 | 3.141593 | 0.5 | 1 |
| 1 | 6.283185 | 1 | 2 |
| 2 | 12.566371 | 2 | 4 |
| 4 | 25.132741 | 4 | 8 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Value: entering "0" shows "Value must be greater than 0." beside that field and no result.
Choosing between the Circumference 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 |
|---|---|---|
| [Area of a Circle Calculator](/math/area-of-a-circle/) | i know the and value | Area |
| [Circle Diameter Calculator](/math/circle-diameter/) | i know the and value | Diameter |
| [Circle Calculator](/math/circle-calculator/) | i know the and value | Area |
| [Radius Calculator](/math/radius-calculator/) | i know the and value | Radius |
| [Circumference to Diameter Calculator](/math/circumference-to-diameter/) | circumference | Circumference to Diameter |
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 value to confirm this.
Frequently asked questions
What is the circumference of a circle with diameter 10?
It is 10π, which is about 31.416 units.
Is circumference the same as perimeter?
Circumference is the perimeter of a circle.
How do I find the radius from the circumference?
Divide the circumference by 2π to get the radius.
What does the Circumference Calculator calculate?
Circumference of a circle. It returns Circumference, Radius, Diameter and Area.
What formula does the Circumference Calculator use?
d = 2r; C = 2πr; A = πr². Every quantity is derived from the radius: r = d/2 = C/2π = √(A/π).
What does the “I know the” option change?
It sets how the circumference is worked out. The choices are Radius, Diameter, Circumference and Area.
What is an example of a circumference result?
With i know the Radius and value 1, the circumference is 6.283185.
Related calculators
- Area of a Circle Calculator — Area of a circle from its radius, diameter or circumference.
- Circle Diameter Calculator — Diameter of a circle from radius, circumference or area.
- Circle Calculator — Radius, diameter, circumference and area of a circle from any one of them.
- Radius Calculator — Radius of a circle from diameter, circumference or area.
- Circumference to Diameter Calculator — Convert a circle's circumference to its diameter.
- Circumference to Radius Calculator — Convert a circle's circumference to its radius.
- Triangle Calculator — Area, perimeter, angles and type of a triangle from its three sides.
- Rectangular Prism Volume Calculator — Volume of a rectangular prism (box).
- Midpoint Calculator — Midpoint of a line segment.
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.