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Circle Area Calculator

Calculate the area of a circle with π times radius squared. Includes the formula, a worked example, and how circumference relates to area.


Calculate area of circle

Formula

textarea=pitimesr2\\text{area} = \\pi \\times r^2

Where r is the radius of the circle.

Worked example

Calculate the area of a circle with radius 5 cm:

textarea=pitimes52=pitimes25approx3.1416times25=78.54textcm2\\text{area} = \\pi \\times 5^2 = \\pi \\times 25 \\approx 3.1416 \\times 25 = 78.54 \\text{ cm}^2

Result: 78.54 cm²

How to use

  1. Enter the radius of the circle
  2. Click "Calculate" to see the area

Related formulas

  • Circumference: 2pir2 \\pi r
  • Diameter: 2r2r
  • Area from diameter: fracpid24\\frac{\\pi d^2}{4}

Common use cases

  • Calculating land area
  • Design and manufacturing
  • Physics and engineering
  • Architecture and construction
  • Graphics and design

FAQ

What is π (pi)? Pi is the ratio of a circle's circumference to its diameter, approximately 3.14159265.

Can I calculate the area of a semicircle? Yes, divide the full circle area by 2.

How do I find the radius from the area? r=sqrtfractextareapir = \\sqrt{\\frac{\\text{area}}{\\pi}}

What units should I use? Any consistent unit (meters, feet, inches, etc.). The area will be in square units.

Is the formula accurate? Yes, it's mathematically exact. Use sufficient precision for π in your calculations.

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