Understanding the Properties of a Circle

A circle is a fundamental shape in geometry, defined as the set of all points in a plane that are at a fixed distance from a central point. Understanding its properties—radius, diameter, circumference, and area—is essential in mathematics, physics, engineering, and design.

Key Terms and Formulas

Radius (r)

The radius is the distance from the center of the circle to any point on its boundary. It is the foundational measurement from which all others can be derived.

Diameter (d)

The diameter is the length of a straight line passing through the center of the circle and connecting two points on the boundary. It is always exactly twice the length of the radius.

Circumference (C)

The circumference is the distance around the outside of the circle. It is the circle's perimeter. The ratio of a circle's circumference to its diameter is always the constant Pi (π), which is approximately 3.14159.

Area (A)

The area of a circle is the total space it occupies in a two-dimensional plane. It is calculated using the radius and Pi. For calculations involving other 2D shapes, you can use our general Area Calculator.

How to Use This Circle Calculator

This tool is designed for flexibility. Instead of needing to know the radius, you can start with any of the four main properties:

1. Select the property you know (Radius, Diameter, Circumference, or Area) using the radio buttons.
2. Enter the known value into the corresponding input field.
3. Click "Calculate" to see all four properties computed instantly.

This is particularly useful when you need to find the radius from the area of a circular plot of land, or determine the diameter of a pipe from its circumference. The circle is also the basis for 3D shapes like cylinders and spheres; you can explore their properties with our Volume Calculator.

For more tools related to geometry and algebra, check out our complete collection of Math calculators.