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Circle Area Calculator

Find a circle's area from its radius or diameter — A = πr².

Privacy: your files never leave your device. All processing happens locally in your browser.

How to use

  1. 1.Pick radius or diameter with the toggle, then type your value in any unit you like.
  2. 2.Read the circle area instantly below, shown with the worked A = πr² formula.
  3. 3.Check the extra figures too — radius, diameter (2r), and circumference (2πr).

About Circle Area Calculator

The area of a circle is πr², where r is the radius. This circle area calculator returns that value the instant you type a number, and it also shows the diameter (d = 2r) and the circumference (C = 2πr) so you can read every measurement of the circle from a single input. Switch the toggle to enter a diameter instead, and the tool halves it to the radius (r = d ÷ 2) before applying the same formula.

Why πr²? A circle can be sliced into many thin wedges and rearranged into a shape that approaches a rectangle of height r and width πr (half the circumference). The rectangle's area, r × πr, is πr² — and that is exactly the circle's area. The radius is the distance from the center to the edge; the diameter is the full width across the center, so d = 2r and r = d/2. Because the radius is squared, doubling it makes the area four times larger, not twice.

What is π? Pi is the constant ratio of a circle's circumference to its diameter, about 3.14159. It is irrational, so its decimals never end or repeat. This calculator uses your device's full-precision value of π (JavaScript's Math.PI, accurate to about 15 digits), which is far more precise than the classroom shortcuts 3.14 or 22/7, so your results are as exact as floating-point math allows.

The tool guards the edge cases for you. A radius or diameter of 0 gives an area of exactly 0 (a single point). Negative values are rejected, because a radius is a length and cannot be negative. Non-numeric text is flagged instead of producing a wrong answer, and an unrealistically huge value that overflows is caught rather than shown as a broken number.

Where is this useful? Find the area of a circular table, rug, pizza, garden bed, or pool; size a round pipe or duct cross-section; work out material for a circular sign or gasket; or check geometry and physics homework. Keep your units consistent — enter the radius in centimeters and the area comes out in square centimeters; use meters and you get square meters. The tool never converts units, so the numbers stay pure π · r².

A quick worked example: with r = 5, the area is π × 5² = 25π ≈ 78.54 square units, the diameter is 10, and the circumference is 10π ≈ 31.42. Everything runs locally in your browser — nothing is uploaded — so results are instant and private.

Frequently asked questions

What is the formula for the area of a circle?
The area of a circle is A = πr², where r is the radius and π ≈ 3.14159. Multiply the radius by itself, then by π. For example, a radius of 5 gives 25π ≈ 78.54 square units. If you only know the diameter d, first halve it: r = d ÷ 2.
How do I find the area of a circle from the diameter?
Halve the diameter to get the radius (r = d ÷ 2), then use A = πr². You can also write it directly as A = π(d/2)² = πd² ÷ 4. This calculator does it for you — just switch the toggle to 'diameter' and type the value; it converts to the radius automatically before computing the area.
What value of π does this calculator use?
It uses your device's full-precision π (about 3.14159265358979), not the rounded 3.14 or 22/7 used in class. That means results are accurate to roughly 15 significant digits, so the area is as exact as standard floating-point math allows.
What is the difference between radius and diameter?
The radius is the distance from the center of the circle to its edge; the diameter is the full distance across the circle through the center. They are related by d = 2r, so the diameter is always twice the radius. The area formula uses the radius, so a given diameter must be halved first.
What units does the circle area come out in?
It is unit-agnostic. Enter the radius or diameter in any single unit and the area is that unit squared: centimeters give square centimeters, meters give square meters, inches give square inches. The tool does not convert units, so keep everything in one consistent unit.

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