Circumference Calculator

By Bogna Szyk and Mateusz Mucha
Last updated: Sep 12, 2021

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.

FAQ

How to find the circumference of a circle?

To calculate the circumference, you need the radius of the circle:

  1. Multiply the radius by 2 to get the diameter.
  2. Multiply the result by π, or 3.14 for an estimation.
  3. That's it; you found the circumference of the circle.

Or you can use the circle's diameter:

  1. Multiply the diameter by π, or 3.14.
  2. The result is the circle's circumference.

What is the circumference of a circle?

The circumference of a circle is the linear distance of the circle's edge. It is equivalent to the perimeter of a geometric shape, although that term perimeter is only used for polygons.

Who calculated the circumference of the earth first?

The first person to calculate the Earth's circumference was Eratosthenes, a Greek mathematician, in 240 B.C. He discovered that objects in a city on the Northern Tropic do not throw a shadow at noon on the summer solstice, but they do in a more northerly location. Knowing this, and the distance between the locations, he succeeded in calculating the Earth's circumference.

How do I find the diameter from the circumference?

If you want to find the diameter from the circumference of a circle, follow these steps:

  1. Divide the circumference by π, or 3.14 for an estimation.
  2. And that's it; you have the circle's diameter.

How to find the area of a circle from the circumference?

To find the area of a circle from the circumference, follow these steps:

  1. Divide the circumference by π.
  2. Divide the result by 2 to get the circle's radius.
  3. Multiply the radius by itself to get its square.
  4. Multiply the square by π, or 3.14 for an estimation.
  5. You found the circle's area from the circumference.

How do I find the radius from the circumference?

To find the radius from the circumference of a circle, you have to do the following:

  1. Divide the circumference by π, or 3.14 for an estimation. The result is the circle's diameter.
  2. Divide the diameter by 2.
  3. There you go, you found the circle's radius.

How to measure the circumference?

  • Calculate the circumference as 2 ⨉ radius ⨉ π.
  • Calculate the circumference as diameter ⨉ π.
  • Wrap a string around the object and measure the length of it.
  • Use Omni's circumference calculator.

What is the formula for the circumference?

The formula for the circumference, if the circle's radius is given, is:

  • 2 ⨉ radius ⨉ π

Or if the circle's circumference is given:

  • Circumference ⨉ π

You can estimate π as 3.14.

What is the circumference of a circle with a radius of 1 meter?

To calculate the circumference of a circle with a radius of 1 meter, simply follow these steps:

  1. Multiply the radius by 2 to get the diameter of 2 meters.
  2. Multiply the result by π, or 3.14 for an estimation.
  3. And there you go; the circumference of a circle with a radius of 1 meter is 6.28 meters.

How do I find the circumference of a cylinder?

To find the circumference of a cylinder, you have to be aware that a cylinder's cross-section is a circle. If you know the cylinder's radius:

  1. Multiply the radius by 2 to get the diameter.
  2. Multiply the result by π, or 3.14 for an estimation.
  3. That's it; you found the circumference of the cylinder.

Or you can use the cylinder's diameter:

  1. Multiply the diameter by π, or 3.14.
  2. The result is the cylinder's circumference.

How do I find the area of a circle with a circumference of 1 meter?

If you want to find the area of a circle with a circumference of 1 meter, do the following:

  1. Divide the circumference by π. This is the circle's diameter, in this case, 31.8 centimeters.
  2. Divide by 2. This result is the circle's radius of 15.9 centimeters.
  3. Multiply the radius with itself, getting the square, in our case 256 cm².
  4. Multiply by π, or 3.14 for an estimation.
  5. That's it; a circle with a circumference of 1 meter has an area of 795.78 cm².

How to find the radius of a circle with a circumference of 10 centimeters?

To find the radius of a circle with a circumference of 10 centimeters, you have to do the following:

  1. Divide the circumference by π, or 3.14 for an estimation. The result is the circle's diameter, 3.18 centimeters.
  2. Divide the diameter by 2.
  3. And there you go, the radius of a circle with a circumference of 10 centimeters is 1.59 centimeters.

What is the unit of the circumference of a circle?

Since a circle's circumference is the linear distance of the circle's edge, it describes a length. Therefore, the most common units of a circle's circumference are millimeter, centimeter, meter for the metric system, and inch, feet, and yard for the imperial system.

Bogna Szyk and Mateusz Mucha
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