Circle Calculator

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Input Values

Please provide any value below to calculate the other properties of a circle.

Radius (r)

Diameter (d)

Circumference (C)

Area (A)

Circle Visualization

r = 5

d = 10

Properties

Formulas

Applications

Circle Properties

Radius (r): 5

Diameter (d): 10

Circumference (C): 31.416

Area (A): 78.54

π Approximation: 3.1416

Circumference Formula: C = 2πr = πd

Area Formula: A = πr² = πd²/4

Diameter Formula: d = 2r = C/π

Radius Formula: r = d/2 = C/(2π)

π Definition: π = C/d ≈ 3.14159

Engineering: Calculate material requirements for circular objects

Construction: Determine dimensions for circular structures

Education: Learn geometric properties and relationships

Design: Create visually appealing circular layouts

Calculation Steps

Given: Radius r = 5

Diameter d = 2 × r = 2 × 5 = 10

Circumference C = 2 × π × r = 2 × 3.1416 × 5 ≈ 31.416

Area A = π × r² = 3.1416 × 5² ≈ 78.54

About Circles

Circle Properties

A circle is a simple closed shape consisting of all points in a plane that are at a given distance from a given point, the center.

The distance between any point of the circle and the center is called the radius. The diameter is twice the radius.

Historical Significance

The circle has been known since before the beginning of recorded history. Natural circles would have been observed, such as the Moon, Sun, and a short plant stalk blowing in the wind on sand, which forms a circle shape in the sand.

The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible.