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# Convert between Polar and Cartesian Coordinates

## Cartesian and Polar coordinate converting

In the Cartesian system the coordinates are perpendicular to one another with the same unit length on both axes.

Cartesian coordinates in the figure below: (2,3) A Polar coordinate system is determined by a fixed point, a origin or pole, and a zero direction or axis. Each point is determined by an angle and a distance relative to the zero axis and the origin.

Polar coordinates in the figure above: (3.6, 56.31)

Polar coordinates can be calculated from Cartesian coordinates like

r = (x2 + y2)1/2                            (1)

where

r = distance from origin to the point

x = Cartesian x-coordinate

y = Cartesian y-coordinate

θ = atan(y / x)

= tan-1(y / x)                          (2)

where

θ = angle relative to the zero axis (degrees)

Cartesian coordinates can be calculated from Polar coordinates like

x = r cos(θ)                           (3)

y = r sin(θ)                           (4)

x

y

r

θ (degrees)

## Related Topics

• Mathematics - Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more

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## Citation

• Engineering ToolBox, (2009). Convert between Polar and Cartesian Coordinates. [online] Available at: https://www.engineeringtoolbox.com/converting-cartesian-polar-coordinates-d_1347.html [Accessed Day Mo. Year].

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