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## Circle Area Calculator

Circle area calculator is an online tool that is used to calculate the area of a circle.

The circle calculator can calculate:

• Area of circle

• Radius of circle

• Diameter of circle

• Circumference of circle

It is a free online utility that helps you find a circular area. It can be used by students, teachers, engineers, and tutors without any restrictions. Students can use this tool to solve their geometry problems related to a circle.

Teachers can use it to check if the answers of students are correct for the specific circle problems.

In this post, we will cover circle definition, how to use circle area calculator, how to find area of a circle, area of circle formula, few examples of circle area calculation, and a lot more.

## How did the circle area calculator work?

If you are looking for a tool that can calculate the area of a circle without wasting your time, you are in the right place. The area of a circle calculator is the best tool to get the circle area by inputting the radius or the diameter.

To use this calculator, follow the steps below:

• Choose the value for which you want to solve the equation of the circle. i.e., area, radius, etc.

• Select the set of given values from the drop-down list.

• Enter the required values in the given input boxes.

• Use the button to perform the calculation.

In the resulting pan on the right side, you will get the results of the calculation along with the formula and all steps involved in the calculation. Did you get what you were looking for? Geometry problems include various topics that students have to cover.

After calculating the area of a circle, you can also calculate the sector of a circle using our sector area calculator.

## What is a circle?

A circle is a shape where the distance from the center to the edge of the circle is always the same. Every circle has a center, which is a point that lies at the center of the circle.

Khan Academy Geometrically, a circle can be defined as, “A shape consisting of all points in a plane that are a given distance from a given point, the center; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. ” Wikipedia

**Radius:** The distance from the center of the circle to its boundary is called the radius of the the circle. It is denoted by r.

**Diameter**: A distance or line from the center of the circle that touches the boundary of the circle on two sides is called the diameter of the circle. It is denoted by d. The diameter is exactly double than the radius.

**Circumference**: The distance around the circle is called the circumference of the circle. It is denoted by C.

## Circle area formula - Circle calc: find a

The formula for area of a circle is very simple to interpret and use. If we take the square of the radius of the circle and multiply it with pi (π), we will get the circle area. In fact, the area of a circle is pi r squared.

The area of a circle formula can be expressed as:

**A = π r ^{2}**

Where:

**A** represents the area of the circle,

**r** is the radius of the circle,

and **π** is the mathematical constant valuing **13.1415.**

## The diameter of circle formula - Circle calc: find d

Diameter of a circle can be calculated by multiplying the radius of the circle with 2.

The formula for the diameter of the circle can be written as:

**D = 2 r**

In this equation, D is the diameter of the circle while r is the radius of the circle.

## Circumference of circle formula - Circle calc: find c

If we multiply the radius of the circle with **pi (π)** and **2**, we will get the circumference of the circle.

The formula for the circumference of a circle can be written as:

**C = 2 π r**

In this equation, **C** is the circumference of the circle while **r** is the radius of the circle.

## How to calculate the area of a circle?

The surface area of a circle calculator above can be used to calculate the area of a circle with much comfort.

However, if you need to find the circle area manually, you can follow the below steps:

• Determine the radius of the circle and write it down.

• Write down the area of circle formula.

• Substitute the values in the formula and calculate the area.

Let’s go try this method by using an example.

### Example:

If the radius of a circle is **20 cm**, find the area of that circle?

**Solution:**

**Step 1**: Determine the radius of the circle and write it down.

**r = 20 cm**

**Step 2:**

Write down the area of circle formula.

**A = π r ^{2}**

**Step 3**:

Substitute the values in the formula and calculate the area.

**A = 3.1415 × 202 **

**A = 1256.6 cm ^{2} **

So, the area of the circle with a **20 cm** radius will be **1256.6 cm2**.

## Circle area – Real-world example

John is constructing a house for which he has to insert a pipe in the ground. The radius of the pipe is 6 cm. How wide the hole should John dig in to insert the pipe through it?

Solution:

**Step 1:**

Write it down the radius of the pipe.

**r = 6 cm**

**Step 2:**

Write down the area of circle formula.

**A = π r ^{2}**

**Step 3:**

Substitute the values in the formula and calculate the area.

**A = 3.1415 × 6 ^{2} **

**A = 113 cm ^{2}**

So, John has to dig a **113 cm ^{2}** wide hole in the ground to get the pipe in the ground.

## FAQs

### What is the area of a circle?

The area of a circle can be determined by squaring the radius of the circle and multiplying it with π.

**A = π r ^{2}**

### How do you calculate area of a circle?

You can calculate the area of the circle by multiplying the squared radius r2 of the circle with π. Here’s how you can calculate the area of the circle. **A = π r ^{2}**

### What's the area of a 9 inch circle?

9-inch circle means that the diameter of the circle is 9 inches. You can calculate the area of a 9 inch circle as:

• Divide the diameter by 2 to get the radius

**r = d/2 = 9/2**

**r = 4.5 inch**

• Use the circle area formula to find the area.

**A = π r ^{2}**

**A = 3.1415 × 4.5 ^{2}**

**A = 63.62 sq. inch**

### What is the area of a 12 inch circle?

If the diameter of a circle is 12 inches, it means its radius is 6 inches. Use the circle area formula to find the area.

**A = π r ^{2}**

**A = 3.1415 × 6 ^{2}**

**A = 113 sq. inch**

### How do I find the radius of a circle from the area?

If the circle is known, you can find the radius of a circle by using the circle area equation.

Suppose, the area of a circle is **25 cm ^{2}**.

**A = π r ^{2}**

**25 = 3.1415 × r ^{2}**

**r2 = 25/3.1415**

**r ^{2} = 7.95**

Take square root on both sides to get the radius.

**r = 2.82 cm**

**References:**

A manual of greek mathematics | source by HEATH THOMAS L (2003)

Area of a circle explained | source by Wikipedia.com

Circumference and area of a circle - Perimeter and area - National 4 Application of Maths | BBC.CO.UK