Area of a Circle Calculator

Our Area of a Circle Calculator helps you find the area of any circle from its radius, diameter, circumference, or even the area itself. It provides complete circle analysis with step-by-step calculations, unit support, and an interactive results panel.

What is the Area of a Circle?

The area of a circle is the total space enclosed within its circumference. It represents the two-dimensional region inside the circle, measured in square units such as square centimeters (cm²) or square inches (in²). Unlike polygons, a circle's area depends on the mathematical constant pi (π), approximately 3.14159.

Area of a Circle Formulas

Using Radius

The standard formula uses the radius (distance from center to edge):

A = πr²

Where A is the area, π (pi) is approximately 3.14159265, and r is the radius.

Using Diameter

When you know the diameter, divide it by 2 to get the radius:

A = π(d/2)² = πd²/4

Using Circumference

When you only know the circumference (distance around the circle):

A = C²/(4π)

Finding Radius from Area

To reverse-calculate the radius when you know the area:

r = √(A/π)

How to Use the Calculator

Select input type: Choose whether you know the radius, diameter, circumference, or area.
Enter the value: Input your measurement as a positive number.
Choose a unit (optional): Select from mm, cm, m, km, inches, feet, yards, or miles.
Set precision: Choose decimal places from 2 to 10 for accuracy.
Read results instantly: View the area, radius, diameter, and circumference with step-by-step calculations.

Example Calculations

Example 1: Pizza Area

A 12-inch pizza has a diameter of 12 inches. What is its area?

Radius = 12/2 = 6 inches
A = π × 6² = π × 36 = 113.10 square inches

Example 2: Circular Garden

A circular flower bed has a radius of 2.5 meters. What area does it cover?

A = π × 2.5² = π × 6.25 = 19.63 square meters

Example 3: From Circumference

A tree trunk has a circumference of 1.5 meters. What is its cross-sectional area?

Radius = 1.5/(2π) = 0.239 m
A = π × 0.239² = 0.179 square meters

Related Circle and Geometry Calculators

For more circle-related calculations, explore our Circle Calculator to compute all circle properties from any single value, the Circle Sector Calculator for sector area and arc length, and the Arc Length Calculator for measuring curved distances on a circle. For a comprehensive shape tool, use our Area Calculator covering rectangles, triangles, trapezoids, and more.

Frequently Asked Questions

What is the formula for the area of a circle?

The area of a circle is A = πr², where A is the area, π (pi) is approximately 3.14159, and r is the radius of the circle. You can also use A = π(d/2)² using the diameter, or A = C²/(4π) using the circumference.

How do you find the area of a circle from the diameter?

Divide the diameter by 2 to get the radius, then use A = πr². Alternatively, use the direct formula A = π(d/2)² = πd²/4. For example, a circle with diameter 10 has area = π × 25 = 78.54 square units.

What is the relationship between radius, diameter, and circumference?

The diameter is twice the radius (d = 2r). The circumference equals π × diameter (C = πd) or 2π × radius (C = 2πr). Knowing any one value lets you calculate all other circle properties.

Can you find the radius if you know the area?

Yes. Rearrange A = πr² to get r = √(A/π). Divide the area by π, then take the square root. For example, if area = 100 square units, r = √(100/π) = √31.83 = 5.64 units.

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