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# cart2pol

Transform Cartesian coordinates to polar or cylindrical

## Syntax

• ``````[theta,rho] = cart2pol(x,y)``````
example
• ``````[theta,rho,z] = cart2pol(x,y,z)``````
example

## Description

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``````[theta,rho] = cart2pol(x,y)``` transforms corresponding elements of the two-dimensional Cartesian coordinate arrays `x` and `y` into polar coordinates `theta` and `rho`.```

example

``````[theta,rho,z] = cart2pol(x,y,z)``` transforms three-dimensional Cartesian coordinate arrays `x`, `y`, and `z` into cylindrical coordinates `theta`, `rho`, and `z`.```

## Examples

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Convert the Cartesian coordinates defined by corresponding entries in matrices `x` and `y` to polar coordinates `theta` and `rho`.

```x = [5 3.5355 0 -10] ```
```x = 5.0000 3.5355 0 -10.0000 ```
```y = [0 3.5355 10 0] ```
```y = 0 3.5355 10.0000 0 ```
```[theta,rho] = cart2pol(x,y) ```
```theta = 0 0.7854 1.5708 3.1416 rho = 5.0000 5.0000 10.0000 10.0000 ```

Convert the three-dimensional Cartesian coordinates defined by corresponding entries in the matrices `x`, `y`, and `z` to cylindrical coordinates `theta`, `rho`, and `z`.

```x = [1 2.1213 0 -5]' ```
```x = 1.0000 2.1213 0 -5.0000 ```
```y = [0 2.1213 4 0]' ```
```y = 0 2.1213 4.0000 0 ```
```z = [7 8 9 10]' ```
```z = 7 8 9 10 ```
```[theta,rho,z] = cart2pol(x,y,z) ```
```theta = 0 0.7854 1.5708 3.1416 rho = 1.0000 3.0000 4.0000 5.0000 z = 7 8 9 10 ```

## Input Arguments

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Cartesian coordinates, specified as scalars, vectors, matrices, or multidimensional arrays. `x`, `y`, and `z` must be the same size, or any of them can be scalar.

Data Types: `single` | `double`

## Output Arguments

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Angular coordinate, returned as an array. `theta` is the counterclockwise angle in the x-y plane measured in radians from the positive x-axis.

Radial coordinate, returned as an array. `rho` is the distance from the origin to a point in the x-y plane.

Elevation coordinate, returned as an array. `z` is the height above the x-y plane.

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### Tall Array Support

This function fully supports tall arrays. For more information, see Tall Arrays.

### Algorithms

The mapping from two-dimensional Cartesian coordinates to polar coordinates, and from three-dimensional Cartesian coordinates to cylindrical coordinates is