# Polar to Rectangular Coordinates Calculator

In Mathematics, two **coordinate** systems are considered to be the **most** important to **show** the location of different points. Conversion of **position** from one coordinate system to the other is a **common** task. But you can’t do this **unless** you have a strong concept about these systems and **know** the relationship between these systems.

Do you want to **learn** about Polar to Rectangular coordinate conversion? Don’t you know how to **convert** coordinates from one system to the other? If you are finding it difficult, you can **use** this **Polar to Rectangular coordinates calculator**. This online free tool has been designed for this purpose **only**. You can use this maths calculator just by inserting the values of **polar** coordinates to get them **converted** to a rectangular system.

**Table of Contents**

## Polar to Rectangular Coordinates Definition

Polar coordinates and **rectangular** coordinates are two major systems used in **graphical** mathematics. These are particularly used to **show** the position of any object with reference to some **coordinates/axes**.

In a rectangular coordinate system, the reference **axes** are represented by the “**x**” and “**y**” axes. It means that every **point** shown in this system will have two coordinates related to the **x** and **y** axes.

On the other **side**, the Polar coordinate system involves “**𝝷**” and “**r**” as its reference **axes**. As both systems are used for the same purpose, so, we can interconvert coordinates from **one** system to another.

## How to convert Polar coordinates to Rectangular coordinates?

Like all other **conversions**, this conversion also has a particular **formula** that you need to follow. Here is the **relationship** through which we can find the coordinates of a **point** in rectangular coordinates using polar coordinates.

x = r cos𝝷

y = r sin𝝷

**No doubt**, it seems to be simple to perform this conversion. But you won’t be **able** to do so unless you **know** the values of **cos𝝷** and **sin𝝷**. Here is an example for proper **clarification** of the concept.

**Example 1:**

Convert the following polar coordinate system to rectangular coordinates if the value for 𝝷 is 30 degrees and for r is 12

**Solution:**

As we know,

x = r cos𝝷

So,

x = 12 cos30

x = 10.392

Similarly, we can find the values of y as,

y = r sin𝝷

So,

y = 12 sin30

y = 6

### How to use the Polar to Rectangular coordinates calculator?

If you don’t know the **values** of trigonometric functions, you can use this tool by Calculator’s Bag. This online maths calculator has been designed for this purpose. It will automatically **perform** all calculations and show you the final output.

- Insert the values of “𝝷”
- Enter the value of “r”
- This calculator will automatically show the values of rectangular coordinates instantly

### FAQ | Perpendicular Line Calculator

**How do you go from polar to rectangular?**

To go from polar to rectangular coordinates, we need to follow these particular relations,

x = r cos𝝷

y = r sin𝝷

**What is the relation between the polar form and the rectangular form of a complex function?**

There are different approaches to writing a complex number in polar form and in rectangular form. So, there is no fixed relationship unless we know the values of the coordinates.

**What is the difference between polar and rectangular?**

The polar coordinate system belongs to angle and diagonal values while the same coordinates are converted to an x-y system in a rectangular coordinate system.

**What is the rectangular and polar form of complex numbers? **

A complex number is written in rectangular form as z = a + bi while a complex number is written in polar form as,

r = √x^{2}+ y^{2}

𝝷 = tan^{-1}(y/x)

**What is the rectangular form used for? **

It is used to represent the location of any point in the x-y coordinate system.