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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
This calculator is also known as Area of a Circle Calculator.
Read the complete guideUnderstanding 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:
| Category | Value |
|---|---|
| From radius | A = pi r squared |
| From diameter | A = pi (d/2) squared = pi d squared / 4 |
| From circumference | A = 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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4 CalculatorsRelated Calculators
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