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Area of a Circle Calculator

How to Find the Area of a Circle

The area of a circle is calculated using the formula A = pi r squared, where r is the radius. Enter any known circle measurement and this calculator derives the area automatically with a step-by-step solution showing the formula substitution.

Circle Measurement

Enter one known value to compute all circle properties

Details: Distance from center to edge

Distance from the center to the edge (half the diameter)

Arc & Sector (Optional)

Enter a central angle to also calculate arc length, sector area, segment area, and chord length

Leave empty to skip arc/sector calculations

Circle Calculation Tips

Click to show tips

Try an Example

Pick a scenario to see how the calculator works, then adjust the values

Unit Circle

The fundamental circle with radius 1, used throughout mathematics.

Key values: Radius = 1 · Area = 3.14 · Circumference = 6.28

Pizza (12-inch)

A standard 12-inch diameter pizza for area and slice calculations.

Key values: Diameter = 12 in · Area = 113.1 sq in · 45-degree slice

Circular Garden

A garden bed with a 5-meter radius for landscaping calculations.

Key values: Radius = 5 m · Area = 78.54 sq m · Circumference = 31.42 m

Documentation

This calculator is also known as Area of a Circle Calculator.

Read the complete guide

Understanding A = pi r squared

The formula A = pi r squared tells us that the area of a circle equals pi (approximately 3.14159) multiplied by the radius squared. The squaring is crucial: it means area grows quadratically with radius. Doubling the radius quadruples the area.

Common Input Conversions

How to find area from different known values:

CategoryValue
From radiusA = pi r squared
From diameterA = pi (d/2) squared = pi d squared / 4
From circumferenceA = C squared / (4 pi)

Examples

Student Homework

Find the area of a circle with radius 5 cm.

A = pi x 5 squared = pi x 25 = 78.54 square cm.

Key takeaway: Always check whether the problem gives you the radius or diameter before applying the formula.

Tips for Area Calculations

Avoid common mistakes:

  • Always use radius, not diameter, in A = pi r squared
  • Remember that pi r squared means pi times (r squared), not (pi times r) squared
  • Use Math.PI or a full-precision value for pi, not 3.14
  • Area is always in square units (cm squared, m squared, etc.)

Frequently Asked Questions about Area of a Circle Calculator

What is the formula for the area of a circle?

The formula is A = pi r squared, where r is the radius. If you have the diameter d, use A = pi d squared / 4.

Why does doubling the radius quadruple the area?

Because area depends on r squared. If r becomes 2r, the area becomes pi (2r) squared = 4 pi r squared, which is 4 times the original area.

How do I find the area if I only know the circumference?

Use A = C squared / (4 pi). First square the circumference, then divide by 4 pi. For example, if C = 31.42, then A = 31.42 squared / (4 pi) = 78.54.

Specialized Calculators

Choose from 4 specialized versions of this calculator, each optimized for specific use cases and calculation methods.

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