Circle Formula Calculator

Calculate radius, diameter, circumference, and area of a circle with complete formulas

Calculate Circle Properties

Select which measurement you have

Enter a positive value

Circle Properties

Radius (r)
0 cm
r = d/2
Diameter (d)
0 cm
d = 2r
Circumference (c)
0 cm
c = 2πr
Area (A)
0 cm²
A = πr²

Formulas Used

Radius to Diameter: d = 2r
Diameter to Radius: r = d/2
Circumference: c = 2πr = πd
Area: A = πr² = πd²/4
π (pi) ≈ 3.14159265359

Example Calculation

Pizza Circle Example

Problem: A pizza has a radius of 6 inches. Find its diameter, circumference, and area.

Given: Radius (r) = 6 inches

Solution

Diameter: d = 2r = 2 × 6 = 12 inches

Circumference: c = 2πr = 2 × π × 6 = 37.699 inches

Area: A = πr² = π × 6² = π × 36 = 113.097 square inches

Circle Properties

r

Radius

Distance from center to edge

Half of the diameter

d

Diameter

Distance across the circle

Twice the radius

c

Circumference

Distance around the circle

Perimeter of the circle

A

Area

Space inside the circle

Measured in square units

Circle Formulas

Basic Relationships
d = 2r
r = d/2
Circumference
c = 2πr
c = πd
Area
A = πr²
A = πd²/4
π (Pi)
π ≈ 3.14159...

Understanding Circle Formulas

What is a Circle?

A circle is a perfectly round shape where every point on the edge is exactly the same distance from the center. This distance is called the radius, and it's fundamental to all circle calculations.

Key Components

  • Center: The exact middle point of the circle
  • Radius: Distance from center to any point on the circle
  • Diameter: Distance across the circle through the center
  • Circumference: Distance around the outside of the circle

Formula Applications

Real-World Uses

  • • Calculating pizza area for pricing
  • • Designing circular gardens or pools
  • • Engineering wheel and tire specifications
  • • Architecture and construction planning
  • • Sports field design (running tracks, etc.)

Why π (Pi)?

Pi (π) is the ratio of a circle's circumference to its diameter. This ratio is the same for all circles, approximately 3.14159. It's an irrational number, meaning its decimal representation never ends or repeats.

From Radius

d = 2r
c = 2πr
A = πr²

From Diameter

r = d/2
c = πd
A = πd²/4

From Area

r = √(A/π)
d = 2√(A/π)
c = 2√(πA)