Circle Calculator

Calculate radius, diameter, circumference, area, sector area, and arc length of a circle from any known value.

Inputs

Known Value

Value

Sector Angle (degrees)

Tab to move between fields

Results

Area

78.54

Circumference31.42

Radius5

Diameter10

Sector Area78.54

Arc Length31.42

Area of a circle

1.Square the radius
$r^2$
Area scales with the square of a length, not the length itself — doubling the radius quadruples the area. This step is where that relationship enters.
2.Multiply by π
$A = pi * r^2$
π is the fixed ratio between a circle's circumference and its diameter. It converts the squared radius — the area of a square on the radius — into the area of the circle itself.

Archimedes proved that a circle's area equals that of a right triangle whose height is the radius and whose base is the circumference, and bounded π between 3+10/71 and 3+1/7 by comparing inscribed and circumscribed 96-gons.

Archimedes, Measurement of a Circle, Propositions 1 and 3·c. 250 BCE

How to Use This Calculator

Enter any single known circle measurement — radius, diameter, circumference, or area — and all others are derived.
Key relationships: diameter = 2r; circumference = 2πr; area = πr².
For a circular sector, enter the central angle (in degrees) to get sector area and arc length.
Sector area = (θ/360) × πr²; arc length = (θ/360) × 2πr.
The pie chart visualizes the sector vs. remaining arc, which is useful for checking proportional reasoning.
All inputs must be positive; radius and diameter inputs override each other — enter only one at a time.

How the result changes with Value

Value	Area
10,000	314,159,265.36
35,000	3,848,451,000.65
65,000	13,273,228,961.42
90,000	25,446,900,494.08

What each input means

Known Value: Calculation mode to use.
Value: The input value.

How this is calculated

Formula

A = πr², C = 2πr

Worked example, using the default values

Identify Input Parameters
Known Value = 0, Value = 5, Sector Angle (degrees) = 360 = 3 input(s) provided
Calculate Area
Area
78.5398 = 78.5398
Calculate Circumference
Circumference
31.4159 = 31.4159
Calculate Radius
Radius
5 = 5