Circle Area Calculator
Calculate the area of a circle from radius, diameter, or circumference. Get exact answers in terms of π and decimal approximations.
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Frequently Asked Questions
What is the area of a circle?
The area of a circle is the total space enclosed within its boundary. It represents the 2-dimensional surface inside the circle.
What is the formula for the area of a circle?
A = πr², where r is the radius and π ≈ 3.14159. The area is proportional to the square of the radius.
How do you find area from diameter?
First find the radius (r = d/2), then use A = πr². Alternatively, use A = π(d/2)² = πd²/4.
How do you find area from circumference?
First find the radius using r = C/(2π), then calculate A = πr². This gives A = C²/(4π).
Why does area use radius squared?
Area is a 2-dimensional measurement, so the radius must be squared. This makes area grow much faster than circumference as the radius increases.
What are practical uses of circle area?
Circle area is used for calculating pizza sizes, land plots, coverage areas, material requirements for circular objects, and many engineering applications.
How does doubling the radius affect the area?
Doubling the radius quadruples the area because area depends on r². If r becomes 2r, then area becomes π(2r)² = 4πr² = 4 times the original area.
What units is area measured in?
Area is measured in square units (e.g., square meters, square feet, square inches) corresponding to whatever unit the radius is measured in.