Circle Calculator
Calculate radius, diameter, circumference, and area of a circle
Circle Properties
Understanding Circles: Formulas and Applications
Our Circle Calculator helps you explore the fundamental properties of circles quickly and accurately. A circle is a fundamental shape in geometry, defined as the set of all points in a plane that are equidistant from a central point.
Did you know? The ratio of a circle’s circumference to its diameter is always constant, and this constant is known as Pi (π), approximately 3.14159!
How to Use the Circle Calculator
To use the calculator, select the property you know about the circle and enter its value:
- Radius (r): The distance from the center of the circle to any point on its boundary.
- Diameter (d): The distance across the circle passing through its center (twice the radius).
- Circumference (C): The distance around the circle.
- Area (A): The amount of two-dimensional space enclosed by the circle.
Input your known value, click “Calculate Circle,” and get all other properties instantly!
Key Circle Formulas
Here are the essential formulas used in our calculator:
- Radius (r):
- From Diameter: \(r = d / 2\)
- From Circumference: \(r = C / (2\pi)\)
- From Area: \(r = \sqrt{A / \pi}\)
- Diameter (d):
- From Radius: \(d = 2r\)
- From Circumference: \(d = C / \pi\)
- From Area: \(d = 2\sqrt{A / \pi}\)
- Circumference (C):
- From Radius: \(C = 2\pi r\)
- From Diameter: \(C = \pi d\)
- From Area: \(C = 2\sqrt{A\pi}\)
- Area (A):
- From Radius: \(A = \pi r^2\)
- From Diameter: \(A = \pi (d/2)^2\)
- From Circumference: \(A = C^2 / (4\pi)\)
Practical Applications of Circles
Circles are ubiquitous in daily life and various scientific and engineering disciplines:
- Engineering & Architecture: Designing wheels, gears, pipes, and circular structures.
- Physics: Describing orbits of planets, wave propagation, and circular motion.
- Computer Graphics: Rendering circular objects and creating rounded shapes.
- Art & Design: Used in patterns, logos, and visual compositions.
- Everyday Objects: Clocks, coins, plates, and many other common items.
Our Circle Calculator simplifies these calculations, making it easier to understand and apply circular geometry.