Circumference Calculator

Circumference is the linear distance around the edge of a circle, or the boundary length of a circle. It is analogous to the perimeter of a geometric shape, but the term 'perimeter' is exclusively used for polygons, while 'circumference' is used for circles. Circumference is a fundamental concept in geometry and is important in many practical applications, such as calculating the distance traveled by a wheel in one rotation or measuring the size of circular objects.

The formula for calculating the circumference of a circle is straightforward:

Circumference = 2 × π × Radius

Or using the diameter:

Circumference = π × Diameter

Where π (Pi) is a mathematical constant approximately equal to 3.14159265359. π is an irrational number that cannot be precisely represented with finite digits, so we typically use 3.14 or 22/7 as approximations in calculations.

The formula for the area of a circle is:

Area = π × Radius²

Our circumference calculator is very easy to use:

1. Enter any one value among the four inputs (radius, diameter, circumference, or area)
2. The calculator will instantly compute and display the other three values
3. You can change the input value at any time, and the results will update in real-time
4. Calculation details are shown below to help you understand the process

For example, if you enter a radius of 5 cm, the calculator will show: a diameter of 10 cm, a circumference of approximately 31.42 cm, and an area of approximately 78.54 square cm.

The ratio of a circle's circumference to its diameter is exactly equal to π:

Circumference/Diameter = π

This relationship is one of the definitions of π and forms the basis of many mathematical and physical formulas. No matter the size of the circle, the ratio of circumference to diameter is always π, which is an important property of circles.

Let's say a circle has a radius of 7 meters.

1. Diameter = 2 × 7 = 14 meters
2. Circumference = 2 × π × 7 ≈ 43.98 meters
3. Area = π × 7² = π × 49 ≈ 153.94 square meters

Assume a circle has a circumference of 60 centimeters.

1. Diameter = 60 ÷ π ≈ 19.1 centimeters
2. Radius = 19.1 ÷ 2 ≈ 9.55 centimeters

Determine which value you know - radius, diameter, circumference, or area - and enter it in the corresponding input field.

After entering a value, the calculator automatically computes and displays the other three values. All results update in real-time.

Check the calculation steps section to understand the detailed process of deriving other values from your input.

You can try entering different values or switch input types (from radius to circumference, etc.) to see how the results change.