Geometry Calculators

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Programmers and Teachers:

# Area of a Circle Calculator

Get unlimited calculations here.

## Lesson on Area of a Circle

#### Lesson Contents

### How to Calculate the Area of a Circle by Hand

We can easily hand calculate the area of a circle by using the area formula. The formula for the area of a circle is given as:**A = πr ^{2}**

Where

*A*is the area and

*r*is the radius.

If we do not know the radius but know some other dimension of the circle, we can easily convert it to radius before applying the area formula. Here are the conversions for diameter and circumference:

r = ^{d}⁄_{2}

r = ^{C}⁄_{2π}

Where *r* is the radius, *d* is the diameter, and *C* is the circumference.

### Uses for Circle Area Calculations

In real-world applications, there are countless uses for knowing how to calculate the area of a circle. Here are some examples:

- Calculating the sectional density of a projectile.
- Calculating the mass of a cylindrical object with a known density.
- Calculating airflow properties through the nozzle of a jet or rocket engine.
- Calculating how much water can flow through a pipe.
- Calculating how far a ball will fly when drag is acting on it.

## How the Calculator Works

The calculator on this page is written in the programming language *JavaScript* (JS). The JavaScript function *area* runs in your device’s internet browser JS engine when an input change is detected. This allows the area to be calculated nearly instantly.

The first step in the calculator’s routine is to check the input unit. If the unit is diameter or circumference, it converts the size input to radius using the same conversion formulas given above. If the unit is radius, the size input is left alone and the calculator moves forward.

Then, the area of the circle is calculated using the same area formula given above. The raw area output is rounded to the fourth decimal place and displayed in the answer area as the final area of your circle.