Circle Calculator
Inputs
Enter a value (Radius, Diameter, Circumference, or Area) to solve the complete circle.
About Circle Properties
A circle is a simple yet fundamental shape in geometry, defined as the set of all points in a plane that are at a given distance from a center point.
Circles define many natural and man-made objects, from planets and raindrops to wheels and gears. Understanding how to calculate their properties is essential in fields ranging from engineering to graphic design.
Definitions & Formulas
Here are the key components of a circle and the formulas to calculate them:
Radius (r)
The distance from the center of the circle to any point on its edge.
r = d / 2r = C / (2π)Diameter (d)
The distance across the circle through the center. It is twice the radius.
d = 2rCircumference (C)
The distance around the boundary of the circle (the perimeter).
C = 2πrC = πdArea (A)
The amount of space occupied by the circle.
A = πr²What is Pi (π)?
Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter. It equals approximately 3.14159.
No matter how large or small a circle is, if you divide its circumference by its diameter, you will always get π. It is an irrational number, meaning its decimal representation goes on forever without repeating.
Example Calculations
Example 1: Finding Area from Radius
If a circle has a radius of 5 cm:
- Formula: A = πr²
- Calculation: 3.14159 × 5² = 3.14159 × 25
- Result: 78.54 cm²
Example 2: Finding Radius from Circumference
If a circle has a circumference of 31.4 meters:
- Formula: r = C / (2π)
- Calculation: 31.4 / (2 × 3.14159) = 31.4 / 6.283
- Result: 5 meters
Frequently Asked Questions
Does this calculator use 3.14 or full Pi?
This calculator uses the full precision of Pi (Math.PI in JavaScript) for the most accurate results, rather than the simplified 3.14.
What units should I use?
You can use any unit of length (cm, inches, meters, feet). The result will be in the same unit (e.g., if you enter radius in inches, area will be in square inches).
How do I find the diameter from the area?
First, find the radius using r = √(A/π), then multiply by 2 to get the diameter. Our calculator does this automatically for you!