θ-coordinate

# 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.

## 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 = √x2 + y2

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.