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Circumference Calculator

Created by Bogna Szyk and Mateusz Mucha
Reviewed by Jack Bowater
Last updated: Jan 30, 2024


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; and
  • 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.

How to use the circumference calculator

The following instructions will help you get the best use out of our circumference calculator:

  1. Enter either the radius or the diameter of the circle. Ensure you're using the right units before entering the values.

  2. The circle's circumference and area appear instantly in their fields. You can change their units if you desire.

For example, a circle with a 5 cm radius will have a 10 cm diameter and a 31.4159 cm circumference. The calculator also gives the area of this circle to be 78.5398 cm².

We can also use the calculator in reverse — i.e., to find the radius of a circle from its circumference. For instance, providing a circumference of 44 cm tells us that the circle has a radius of 7.00282 cm and a diameter of 14.00563 cm.

Please continue reading to learn more about the circumference of a circle, its formula, and the definition of pi (π).

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.

Circumference calculation is important for determining the hoop stress on any rotationally symmetrical object. Find out more with our hoop stress 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.

🔎 If you're interested in the relationship between the circumference and other variables, you can take a look at our circumference to diameter and circumference and area of a circle calculators.

Making the circumference calculator

As our celebrated veterans, Bogna and Mateusz are experts at creating user-friendly scientific tools that solve day-to-day problems. The idea for creating this calculator began to take root when Mateusz realized that tires with larger circumferences traveled further per revolution, thus improving his cycling speed. Now, this circumference calculator helps Mateusz and his cycling pals pick the right tires for them.

We strive to ensure the accuracy and reliability of our content. A trained expert reviews each tool, and then a native speaker proofreads it. If you'd like to learn more about our quality standards, please visit our Editorial Policies page.

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 diameter is given:

  • Diameter × 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
Circle shape marked with radius (r) and circumference (c). Also shows formulas for the circumference and area of a circle
Radius (r)
in
Diameter
in
Circumference (c)
in
Area
in²
Check out 11 similar circle calculators ⭕
Arc lengthArea of a circleCircle calc: find c, d, a, r… 8 more
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