Circle Calculator

Circle Formulas

A circle is a two-dimensional shape where all points are equidistant from a central point. The distance from the center to any point on the circle is called the radius.

Key Measurements

• Radius (r): Distance from center to edge
• Diameter (d): Distance across the circle through the center
• Circumference (C): The perimeter or distance around the circle
• Area (A): The space enclosed by the circle

Circle Formulas

Diameter Formula

d = 2r

Circumference Formulas

C = 2 * Pi * r
C = Pi * d

Area Formula

A = Pi * r^2

Reverse Formulas

From Diameter:   r = d / 2
From Circumference:   r = C / (2 * Pi)
From Area:   r = sqrt(A / Pi)

What is Pi?

Pi (represented by the Greek letter "Pi") is a mathematical constant approximately equal to 3.14159265359. It represents the ratio of a circle's circumference to its diameter and is the same for all circles, regardless of size.

Example Calculations

Example 1: From Radius

Given radius = 5 units:

Diameter = 2 * 5 = 10 units
Circumference = 2 * Pi * 5 = 31.416 units
Area = Pi * 5^2 = Pi * 25 = 78.54 square units

Example 2: From Diameter

Given diameter = 14 units:

Radius = 14 / 2 = 7 units
Circumference = Pi * 14 = 43.98 units
Area = Pi * 7^2 = 153.94 square units

Example 3: From Area

Given area = 100 square units:

Radius = sqrt(100 / Pi) = sqrt(31.83) = 5.64 units
Diameter = 2 * 5.64 = 11.28 units
Circumference = 2 * Pi * 5.64 = 35.45 units

Applications

Construction

Calculating material needed for circular structures, pools, gardens, and foundations.

Engineering

Designing wheels, gears, pipes, and other circular components.

Daily Life

Measuring pizza sizes, determining fence length for circular areas, calculating paint needed for circular surfaces.

Related Shapes

• Sphere: A 3D circle (all points equidistant from center in 3D space)
• Ellipse: A stretched circle with two focal points
• Semicircle: Half of a circle