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# Rectangular to Polar Calculator

Rectangular coordinates, or cartesian coordinates, come in the form (x,y), points are identified by their distances from the x and y axes. Polar coordinates, on the other hand, come in the form (r,θ), points are identified by their angle on the unit circle and their distance from the origin.

## What is Rectangular to Polar Calculator?

'**Rectangular to Polar Calculator**' is an online tool that helps to convert rectangular to polar coordinates. Online Rectangular to Polar Calculator helps you to convert rectangular to polar coordinates in a few seconds.

### Rectangular to Polar Calculator

## How to Use Rectangular to Polar Calculator?

Please follow the below steps to convert rectangular to polar coordinates:

**Step 1:**Enter the rectangular coordinates(x,y) in the given input boxes.**Step 2:**Click on the**"Calculate"**button to convert rectangular to polar coordinates.**Step 3:**Click on the**"Reset"**button to clear the fields and enter the different values.

## How to Find Rectangular to Polar Calculator?

Rectangular coordinates are expressed as (x,y) while polar coordinates are expressed as (r, θ).

Converting rectangular to polar coordinates means expressing the rectangular coordinates in the form of polar coordinates.

The formula's for converting rectangular coordinates to polar coordinates:

r = √(x^{2} + y^{2}), θ = tan^{-1}(y / x)

Here, (x, y) are rectangular coordinates and (r, θ) are polar coordinates.

**Solved Examples on Rectangular to Polar Calculator**

**Example 1:**

Convert rectangular coordinates(5, 6) into polar coordinates and verify it using the online rectangular to polar** **calculator.

**Solution:**

Given: x = 5, y = 6

To convert rectangular to polar coordinates,

r = √(x^{2} + y^{2})

= √(5^{2} + 6^{2})

= √(25 + 36)

r = 7.81

θ = tan^{-1}(y / x)

= tan^{-1}(6 / 5)

= tan^{-1}(1.2)

θ = 50.19°

Therefore, polar coordinates (r, θ) = (7.81, 50.19°)

**Example 2:**

Convert rectangular coordinates(7, 8) into polar coordinates and verify it using the online rectangular to polar** **calculator.

**Solution:**

Given: x = 7, y = 8

To convert rectangular to polar coordinates,

r = √(x^{2} + y^{2})

= √(7^{2} + 8^{2})

= √(49 + 64)

r = 10.63

θ = tan^{-1}(y / x)

= tan^{-1}(8 / 7)

= tan^{-1}(1.14)

θ = 48.79°

Therefore, polar coordinates (r, θ) = (10.63, 48.79°)

**Example 3:**

Convert rectangular coordinates(3, 6) into polar coordinates and verify it using the online rectangular to polar** **calculator.

**Solution:**

Given: x = 3, y = 6

To convert rectangular to polar coordinates,

r = √(x^{2} + y^{2})

= √(3^{2} + 6^{2})

= √(9 + 36)

r = 6.7

θ = tan^{-1}(y / x)

= tan^{-1}(6 / 3)

= tan^{-1}(2)

θ = 63.43°

Therefore, polar coordinates (r, θ) = (6.7, 63.43°)

Similarly, you can use the online rectangular to polar** **calculator to convert rectangular to polar coordinates for the following:

- Convert rectangular coordinates(11,15) into polar coordinates
- Convert rectangular coordinates(7, 9) into polar coordinates

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