Circle Area Calculator

Calculate the area, circumference, and diameter of a circle. Enter either the radius or diameter to get instant results with step-by-step calculations.

r d = 2r C = 2πr center

Circle Formulas:

Area: A = πr²
Circumference: C = 2πr
Diameter: d = 2r
Radius from Area: r = √(A/π)

Examples

Example 1: From Radius

Given: Radius = 5 cm

Solution:

A = π × 5² = 25π ≈ 78.54 cm²

C = 2π × 5 ≈ 31.42 cm

d = 2 × 5 = 10 cm

Example 2: From Diameter

Given: Diameter = 12 in

Solution:

r = 12/2 = 6 in

A = π × 6² = 36π ≈ 113.10 in²

C = 2π × 6 ≈ 37.70 in

Example 3: From Circumference

Given: C = 31.42 m

Solution:

r = C/(2π) = 31.42/(2π) ≈ 5 m

A = π × 5² ≈ 78.54 m²

d = 10 m

Example 4: Unit Circle

Given: Radius = 1 unit

Solution:

A = π × 1² = π ≈ 3.14159 sq units

C = 2π × 1 = 2π ≈ 6.283 units

Example 5: Real World - Pizza

Given: Pizza diameter = 16 in

Solution:

r = 8 in, A = π × 64 ≈ 201.06 in²

Pizza area ≈ 201 square inches

About Circle Calculations

What is a Circle?

A circle is a 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 Circle Properties

Property Formula Description
Radius (r) r Distance from center to edge
Diameter (d) d = 2r Distance across circle through center
Area (A) A = πr² Space inside the circle
Circumference (C) C = 2πr = πd Distance around the circle

About Pi (π)

Pi is a mathematical constant approximately equal to 3.14159. It represents the ratio of a circle's circumference to its diameter and is an irrational number with infinite decimal places.

Practical Applications

  • Calculating land area for circular gardens or pools
  • Determining material needed for circular constructions
  • Engineering: pipes, wheels, gears
  • Food industry: pizza sizes, cake pans
  • Sports: running tracks, circular fields