# Rectangular and Polar Conversion Tool

The rectangular and Polar Conversion tool is used to convert the phasor quantity in the polar coordinates to the rectangular coordinates(or cartesian coordinates) and vice versa. They are the two forms of representing the phasor quantity.

## How to use the conversion Calculator?

- Select the conversion you need, that is select either rectangular to polar form or Polar to rectangular form.
- Enter the inputs for the corresponding conversion.
- Select your choice of the phase angle: in degrees or radians.
- Press the convert button to see the conversion result.

In the rectangular coordinate system, a phasor can be divided into two components, represented as *a + jb*. The two components are the horizontal component or real part and a vertical component or imaginary part.

Whereas in a polar coordinate system, the phasor is represented as *Z = E ∠± ϕ*. Here *E* is the magnitude of the phasor and *ϕ* is the angle made by the phasor with respect to the reference axis.

For detailed understanding of the concept, learn the Mathematical representation of phasor in Complex form.

## Rectangular to Polar Conversion

Let Z be the phasor quantity. In rectangular form, it can be written as, *Z = a + jb*.

It is converted into polar form, represented as *Z = E ∠± ϕ*.

where, E is the magnitude given by,

ϕ is the phasor angle given by,

The final conversion result would be,

## Polar and Rectangular form conversion

Again, let us consider Z as the phasor quantity. In polar form, it is given by *Z = E ∠± ϕ*.

It has to be converted into the rectangular form, *Z = a + jb*.

The real part and imaginary part is determined as, *a = E cosϕ* and *b = E sinϕ *.

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