Circumference Calculator

By Bogna Szyk and Mateusz Mucha
Last updated: Sep 08, 2020

If you need to solve some geometry exercises, this circumference calculator is the page for you. It is a tool specifically created to find the diameter, circumference and area of any circle. Read on to learn:

  • what the definition of circumference is
  • how to find the circumference of a circle
  • how to convert circumference into diameter

As is the case with all of our tools, the circumference calculator works in all directions - it is also a circumference to diameter calculator, and can be used to convert circumference to radius, circumference to area, radius to circumference, radius to diameter (duh!), radius to area, diameter to circumference, diameter to radius (yes, again with the rocket science), diameter to area, area to circumference, area to diameter or area to radius.

If you want to draw a circle on the Cartesian plane, you might find this equation of a circle calculator useful.

Definition of circumference

The circumference of a circle is the linear distance of a circle's edge. It is the same as the perimeter of a geometric figure, but the term 'perimeter' is used exclusively for polygons.

Circumference is often misspelled as circumfrence.

Formula for circumference

The following equation describes the relation between the circumference and the radius R of a circle:

C = 2πR

Where π is a constant approximately equal to 3.14159265...

💡 It is impossible to find the exact value of π. It is an irrational number, so we typically use approximations such as 3.14 or 22/7. If you're interested in this topic, go ahead and take a look at the first million digits of π!

A similarly simple formula determines the relationship between the area of a circle and its radius:

A = π * R²

How to find the circumference of a circle

  1. Determine the radius of a circle. Let's assume it's equal to 14 cm.
  2. Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm.
  3. You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm².
  4. Finally, you can find the diameter - it is simply double the radius: D = 2 * R = 2 * 14 = 28 cm.
  5. Use our circumference calculator to find the radius when you only have the circumference or area of a circle.

If you wish to calculate the properties of a three-dimensional solid, such as a sphere, cylinder or cone, it's best to use our volume calculator.

Circumference to diameter

You have probably noticed that, since diameter is twice the radius, the proportion between the circumference and the diameter is equal to π:

C/D = 2πR / 2R = π

This proportion (circumference to diameter) is the definition of the constant pi. It is used in many areas, such as physics and mathematics. For example, you can find it in the centrifugal force calculator.

Bogna Szyk and Mateusz Mucha