A circle is one of the first few shapes we learn as a child. In math, it is defined as a round figure that comes with no corners or edges. The space it occupies is called its area. There is a formula for manually calculating the area of a circle, but you can use our free online Circle Area Calculator if you need a quick answer or to double-check your work. It's easy as pi!

## How to Use the Circle Area Calculator

Our free online Circle Area Calculator has the following parts:

- Area field
- Diameter field
- Circumference field
- Solve Area button beside each of the above fields
- Clear All button

What's great about our calculator is you only have to enter one value to get all the other values. Let's say you are given the diameter of a circle. Your task is to find its circumference and area.

Here are the steps:

- Click CLEAR ALL to reset the calculator.
- Input the value into the diameter field.
- Click the SOLVE OTHERS button next to the diameter field.
- The area and circumference fields will automatically populate.
- Click the CLEAR ALL button again to calculate a new value.

This same process applies if you only have the circumference and area values.

## Important Terms

It's nice to have a tool that you can use whenever you need it. At the same time, it's good to understand exactly how it works so you can still calculate your values even when you're offline. Some important terms you'll need to remember are:

- Circumference: the circle's perimeter or the circle's length if it were straightened out into a line.
- Diameter: the length of the line between any two points on the edge of the circle, passing through its center.
- Radius: the length of the line that extends from the center of the circle to any point on its edge. It is equivalent to one-half of the diameter
- Pi (π): a mathematical constant that represents a circle's circumference-to-diameter ratio.

## Calculating the Area of a Circle

When solving for a circle's area, you'll end up working with different values depending on what the math problem is asking you. The formula you use will, therefore, change according to those values. But one thing always remains the same: pi. Pi is an irrational number that has infinite values. It just keeps on going. However, the majority of us stop at 3.1416, or even better, 3.14.

### Formula #1

A = π r2

You'll need to provide the radius.

### Formula #2

A = C2 / 4π

You'll need to provide the circumference.

### Formula #3

A = (π/4) × D2

You'll need to provide the diameter.

## Why Measure Circle Area?

If you wonder why you have to learn how to calculate the area of a circle, let's start with history. In the 16th century, German mathematician Johannes Kepler measured the areas of planetary orbits as they rounded the sun. When Mars seemed to suddenly reverse its course, Kepler calculated circle areas to create just the right miniature circles, also known as epicycles, to predict planetary paths.

Fast forward a few hundred years. Engineers use a circle's symmetrical properties to design rockets, athletic tracks, Ferris wheels, bicycles, and more. Without the scientific formulas used to determine such properties, it would be impossible to create many of those with safety and precision. The importance of the circle has more than proven itself in various applications over time.

So that's why we learn to measure a circle's area. You may not need the formula every day of your life, but we wouldn't have all the modern conveniences we enjoy today without it.