Circle Measurements Calculator

Calculate radius, diameter, circumference, and area of a circle from any given measurement

Calculate Circle Measurements

Select the measurement you know

Enter a positive value to calculate other measurements

Circle Measurement Results

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

Example Calculation

Garden Circle Example

Problem: A circular garden has a radius of 5 meters.

Find: Diameter, circumference, and area of the garden.

Solution

Given: Radius (r) = 5 m

Diameter: d = 2r = 2 × 5 = 10 m

Circumference: c = 2πr = 2 × π × 5 ≈ 31.416 m

Area: A = πr² = π × 5² ≈ 78.540 m²

Circle Formulas

From Radius (r)

Diameter: d = 2r
Circumference: c = 2πr
Area: A = πr²

From Diameter (d)

Radius: r = d/2
Circumference: c = πd
Area: A = π(d/2)²

From Circumference (c)

Radius: r = c/(2π)
Diameter: d = c/π
Area: A = c²/(4π)

From Area (A)

Radius: r = √(A/π)
Diameter: d = 2√(A/π)
Circumference: c = 2√(πA)

Circle Facts

π (Pi) is approximately 3.14159265359

A circle has 360 degrees or 2π radians

The ratio of circumference to diameter is always π

Circles have the largest area for a given perimeter

All points on a circle are equidistant from the center

Understanding Circle Measurements

What are Circle Measurements?

Circle measurements are the fundamental properties that define a circle: radius, diameter, circumference, and area. These measurements are interconnected, meaning if you know one, you can calculate all the others using mathematical formulas.

Key Definitions

  • Radius: Distance from center to edge
  • Diameter: Distance across circle through center
  • Circumference: Distance around the circle
  • Area: Space inside the circle

Real-World Applications

  • Architecture and construction planning
  • Garden and landscape design
  • Manufacturing and engineering
  • Sports field and track design
  • Material calculation and cost estimation

Fun Fact: The value of π was first calculated by ancient mathematicians like Archimedes around 250 BC using geometric methods!

Mathematical Relationships

Basic Formulas

r = d / 2
d = 2r
c = 2πr = πd
A = πr² = π(d/2)²

Derived Formulas

r = c / (2π)
r = √(A / π)
d = c / π
c = 2√(πA)