# Equation of a Circle Calculator

Writing an **equation** of a circle using different parameters like **coordinates**, radius, and others can spin your head. Doesn’t matter how much **proficiency** you have in Geometry, you will still find **complications**. But you can get it **done** through a simple approach using the **Equation of a circle calculator**.

Using this online Maths calculator, you can get the equation of a circle in all its three major types. It means that this calculator will show you the standard, **general**, and parametric equations of a **circle** using your given input. So, you won’t have to worry whether you need a general **equation** or a parametric equation for practical mathematics. Want to **learn** about it more? Keep reading!

**Table of Contents**

## What is the equation of a circle?

To learn about the **equation** of a circle and its different types, you need to understand what is a circle **first**. A circle is a geometrical **two-dimensional** round figure on the **surface** of which all points have the same distance from a **fixed** point called the **center of a circle**.

The equation of a circle is a **specific** algebraic expression that **shows** whether the given points can be part of the circumference of a circle or not. If a point **fulfills** the equation of a **circle**, it **means** that the point will be located on the **circumference**.

Depending on the **type** of coordinates given, an **equation** of a circle can be written in three different types. These types are described **briefly** here in the following section.

### Standard Equation of a Circle

It is the basic equation of the circle that describes the points located on the circumference of the circle. Here is how to write the standard equation of a circle.

(x - A)^{2}+ (y - B)^{2}= r^{2}

Here, A & B are the coordinates of the center of a circle while “r” is the radius of that circle.

## General Equation of a circle

Another type of **equation** of a circle is the general type. It is not used **mostly** because it is a complicated **process** to get information from this equation. But you can easily convert a general equation of motion to its **standard** form. Here is how you can **write** the general equation of a **circle**.

x^{2}+ ax + y^{2}+ by + c = 0

In this equation, “**a**”, “**b**”, and “ **c**” are three different **coefficients** that will depend on the **coordinates** of the circle.

## Parametric Equation of a circle

The third and last **type** of equation of a circle is called the **parametric equation** because of its dependence on the **angle** of that **circle**. As the word **parameter** refers to theta that is used to **represent** the measurement of an **angle**, that’s why it is called a parametric equation of a circle/ Here is how we can write this equation of a **circle**.

x = rcosθ +^{x}0

y = rsinθ +^{y}0

In the above equations, “r” refers to the radius of the circle while “^{x}0” and “^{y}0” are the coordinates of the circle. Similarly, “θ” refers to the angle of the circle.

## Equation of a circle formula

Till now, you have **got** an **idea** about the equation of a circle and its **types**. Let us now share a formula using which you **can** write a standard equation of a circle.

(x - A)^{2}+ (y - B)^{2}= r^{2}

You only have to put the coordinates of the center of the circle and **solve** the above basic **Mathematical operations**. In the end, you will get a resultant equation that we call **an equation** of a circle.

### How to find the equation of a circle?

To let you understand how to calculate the equation of a circle, we have solved an example here. The following example shows how to write and solve a standard equation of a circle using the given coordinates.

**Example 1:**

Write an equation of a circle when the coordinates of the center of that circle are (2, 7) and the radius is 6.

**Solution:**

As we know,

(x - A)^{2}+ (y - B)^{2}= r^{2}

Also, we have been given the values of r, A, and B. So, we have to put those values in the above equation.

(x - 2)^{2}+ (y - 7)^{2}= (6)^{2}

x^{2}-4x +4 + y^{2}-14y +49 = 36

By solving the above equation, we have found the final output.

x^{2}-4x + y^{2}-14y +17 = 0

### How to use the equation of a circle calculator?

If you are facing complications in writing an equation of a circle, you should use this tool by Calculator’s Bag. This calculator will not only show you the standard form of the equation but also the final output when the equation will be converted to other types. Here are the steps you need to follow for using this tool.

- Insert the “x” and “y” coordinates of the center of the circle
- Put the value of the radius
- This calculator will automatically show the standard form of the equation of that circle

### FAQ | Equation of a Circle Calculator

**What is the equation for a circle in the standard form calculator?**

In the standard form, an equation of a circle will be written as:

(x - A)^{2}+ (y - B)^{2}= r^{2}

**What is the practical application of the equation of a circle in real life? **

These equations are normally used to design round tracks for sports, round building blocks, and Ferris wheels.

**Why is the circle theorem important? **

Circle theorems are important because we can easily find the missing values of a circle including angles without using multiple tools.

**What is the purpose of the equation of a circle? **

The equation of a circle defines the entire properties of a circle including the points feasibility on its circumference.

**How do you find the missing angle of a circle? **

Using the parametric equation of a circle, we can find the missing angles of a circle. We can also use a protector to do this practice if we don’t want to solve the equation.