## Calculator Use:

To use this calculator, follow the steps below:

• Choose the value which you want to calculate. i.e., area, radius, etc.

• Select the value you have from the drop-down list.

• Enter the required values in the given input boxes.

• Press the **calculate **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.

## What is the area of a circle?

We know that the amount of space covered by a flat surface or piece of land or an object is called its area. We also know that a circle is the set of all those points in a plane whose distance from the fixed point remains constant. The fixed point is called the **centre** of the circle and the constant distance is known as the **radius** of the circle. The line segment passing through the centre of a circle and having its endpoints on the circle is called the **diameter** of the circle.

So, **the space occupied by a circle is called its area.**

Before we move to learn about the formula for finding the area of a circle, it is important to know about the number π ( pi ).

We know that the circumference of a circle is in a constant ratio to its diameter. This constant is denoted by the Greek letter π which is read as “pie”. This constant π is not a rational number. Therefore, it cannot be written as a terminating or a non-terminating decimal. The value of π correct to 2 places of decimal is 3.14 and in fractions it is $\frac{22}{7}$.

## What is the formula for the area of a circle?

The area of a circle having a radius ‘r’ (The distance from the centre to a point on the boundary) is given by πr^{2} where π = $\frac{22}{7}$ or 3.14 (approx.)

Let us understand it through an example. Suppose we have a circle that has a radius of 7 cm. Its area will be given by –

Area = πr^{2} = $\frac{22}{7}$ x 7 x 7 = 154 cm^{2}

Now, what is instead of the radius we are given the diameter of a circle, how do we calculate the area?

We know that in a circle, the radius is half of the diameter. Mathematically,

r = $\frac{d}{2}$, where ‘d’ is the diameter and ‘r’ is the radius.

So, we half the given diameter and obtain the radius.

## Circumference of a Circle

**Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. **This is the length we would obtain if we open the circle and make a straight line from it.

### What is the formula for the circumference of a circle?

The formula for the circumference of a circle is given by –

Circumference of a Circle = 2πr, where

r = Radius of the circle

Now, what is instead of the radius we are given the diameter of a circle, how do we calculate the circumference?

Since, diameter ( d ) = 2 x radius, we substitute 2r = d in the above equation to get,

Circumference of a Circle = πd, where

d = Diameter of the circle

## How to use the circle area calculator for finding the area of a circle?

Using the circle area calculators is very simple and it helps you verify your results within seconds. Let us see how we can calculate the area and circumference of a circle using this calculator.

Not only the area and the circumference, but we can also find out other values of a circle such as a radius or a diameter. Let us take an example.

### Finding the area of a circle when we know its diameter

Suppose we are required to find the area of a circle having a diameter of 4 cm.

Let us first find the value of the same using the formula. We will have,

Here diameter (d) = 4 cm

By the relation between radius and diameter, we have, r = $\frac{d}{2}$

Hence r = $\frac{4}{2}$ = 2 cm

Now, area of this circle = = πr^{2} = $\frac{22}{7}$ x 2 x 2 = **12.57 cm ^{2}**

How would we check the result using the area calculator? We would do so by using the below-stated steps –

**Step 1 – **In the “ Enter information “ section of the circle area calculator, we will have to select “ area “ as that is what we are required to find. Below is a snapshot of what the drop options would look like –

**Step 2 –** Once we have selected the area as the option, we will now move to choose the selection of the “ Given “ option. Since we have been given the diameter of the circle, we would choose the same. Below is a snapshot of what the drop options would look like –

**Step 3 – **Now, we would enter the value of the diameter that has been given to us in the “ diameter “ section that has been given to us. Below is a snapshot of what the box for entering the value of the diameter would look like –

**Step 4 –** the last step would be to click on the “ calculate “ button. As soon as we do that we can see the result on the right hand side of the entries that we made in the previous steps. Below is a snapshot of what the result would look like.

Let us take another example.

## Finding the radius of a circle when we know its circumference

Suppose we want to find the radius of the circle having a circumference of 50 cm.

Let us first find the value of the same using the formula. We will have,

Here circumference = 50 cm

Now, we know that

Circumference of a Circle = 2πr, where

r = Radius of the circle

Therefore,

Circumference of a Circle = 2πr = 50

⇒ πr = 25

⇒ r = $\frac{25}{\pi} = \frac{25×7}{22}$ = 7.954 = 7.96 cm (approx.)

Now, let us find the same using the circle area calculator.

We would do so by using the below-stated steps –

**Step 1 – **In the “ Enter information “ section of the circle area calculator, we will have to select “ radius “ as that is what we are required to find. Below is a snapshot of what the drop options would look like –

**Step 2 –** Once we have selected the radius as the option, we will now move to choose the selection of the “ Given “ option. Since we have been given the circumference of the circle, we would choose the same. Below is a snapshot of what the drop options would look like –

**Step 3 – **Now, we would enter the value of the circumference that has been given to us in the “ circumference “ section that has been given to us. Below is a snapshot of what the box for entering the value of the circumference would look like –

**Step 4 –** The last step would be to click on the “ calculate “ button. As soon as we do that we can see the result on the right hand side of the entries that we made in the previous steps. Below is a snapshot of what the result would look like.

We can clearly see that only do we get the answer we also get to know the formula used as well as the steps involved in the calculation. This not only helps us to verify our answers but also helps us in having getting to learn more about the concepts related to the area of the circle and other dimensions related to it.