Area of a Circle
Calculate the exact area of a circle given its radius or diameter. Get instant step-by-step solutions — completely free, no signup required.
Free Area of a Circle Calculator
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About Area of a Circle
Calculate the exact area of a circle given its radius or diameter. Geometry explores the properties and relationships of shapes, sizes, and dimensions. From basic triangles to 3D solids, geometric formulas are used in engineering, architecture, and physics.
Our Area of a Circle calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any area of a circle expression and receive a complete, verified solution with every step shown.
Area of a Circle Formula
A = πr²
The area of a circle equals π multiplied by the radius squared. If you are given the diameter, halve it first. Leave the answer in terms of π for an exact value, or multiply by 3.14159 for a decimal approximation, and always give square units.
Worked Example
Find the area of a circle with diameter 10 m
- Radius = 10 ÷ 2 = 5 m
- A = π × 5²
- A = 25π m²
- Decimal: 25 × 3.14159 ≈ 78.54 m²
Answer: 25π ≈ 78.54 m²
Common Mistakes to Avoid
- Using the diameter in place of the radius, which makes the answer four times too big.
- Computing (πr)² instead of π·r².
- Writing linear units instead of square units.
How to Use the Area of a Circle Calculator
- 1
Type your Area of a Circle problem into the input field above
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Press Enter or click the Solve button to run the calculation
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Review the step-by-step solution that appears below the input
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Check the breakdown of each operation to understand the method
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Try a different problem to practice and build your understanding
Frequently Asked Questions
What is the Area of a Circle formula?
A = πr². The area of a circle equals π multiplied by the radius squared. If you are given the diameter, halve it first. Leave the answer in terms of π for an exact value, or multiply by 3.14159 for a decimal approximation, and always give square units.
Can you show a worked Area of a Circle example?
Find the area of a circle with diameter 10 m: Radius = 10 ÷ 2 = 5 m; A = π × 5²; A = 25π m²; Decimal: 25 × 3.14159 ≈ 78.54 m². Answer: 25π ≈ 78.54 m².
Is this Area of a Circle calculator free to use?
Yes — the Area of a Circle calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.
Can I use this for Area of a Circle homework and exam practice?
Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.