Circle Area Calculator

A tool to calculate area of rectangle and also support various units.


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Understanding Circle

A comprehensive guide to calculate area of circle with the help of the radius and diameter.

What is a Circle?

In mathematics, a circle is a simple, closed shape defined as the set of all points in a plane that are equidistant from a central point. This central point is called the center of the circle, and the distance from the center to any point on the circle is the radius.

Here's a more detailed breakdown:
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Center: The fixed point around which all points on the circle are equidistant.
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Radius: The distance from the center of the circle to any point on its circumference.
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Diameter: The longest straight-line distance across the circle, passing through the center. It's twice the length of the radius.
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Circumference: The total distance around the circle, also known as its perimeter.
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Semicircle: Half of a circle, created by dividing the circle along its diameter.

What is the Area of a Circle?

The area of a circle is the measure of the space enclosed within its boundary. A circle is a perfectly round shape defined by its radius (the distance from the center to any point on the boundary) or its diameter (the distance across the circle through the center, which is twice the radius). Calculating the area of a circle is fundamental in geometry and has applications in fields such as engineering, architecture, and physics.

The area of a circle can be calculated using either the radius or the diameter. In this blog, we’ll explore both methods, provide the formulas, and illustrate each with an example using a radius of 5 meters and a diameter of 10 centimeters.

Methods to Calculate the Area of a Circle

Here, we have defined total two ways to calculate area of circle, You can go with any one from above circle area calculator based on your given values.

1. Using the Radius

The most common method to calculate the area of a circle is by using its radius. The formula is:

\( \text{Area} = {\text{π × Radius²}}\)

Where π (pi) is a mathematical constant approximately equal to 3.14159. The unit of area is in square units (e.g., square meters, square inches), depending on the unit of the radius.

Example: Calculate the area of a circle with a radius of 5 meters.

\( \text{Area} = {\text{π × Radius²}}\)

\( \text{Area} = {\text{π × 5²}}\)

\( \text{Area} = {\text{3.14159 × 25}}\)

\( \text{Area} \approx 78.54 \) square meters

So, the area of the circle is 78.54 square meters.

2. Using the Diameter

If the diameter of the circle is known, you can calculate the area by first finding the radius and then applying the area formula. The relationships are:

\( Radius = \frac{Diameter }{2} \)

Area = \( π × ( \frac{Diameter }{2})^2 \)

This method is useful when the diameter is given instead of the radius.

Example: Calculate the area of a circle with a diameter of 10 centimeters:
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Calculate the radius:

\( Radius = \frac{10 }{2} \)

\( Radius = 5 \) centimeters

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Apply the area formula:

Area = \( π × ( \frac{10 }{2})^2 \)

Area = \( 3.14159 × {5²} \)

Area = \( 3.14159 × {5²} \)

Area \( \approx 78.54 \) square centimeters

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So, the area of the circle is approximately 78.54 square centimeters.