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Polar fom and Rectangular form conversion Calculator

by | Last updated Jul 28, 2021 | Electrical Tools

Polar form and rectangular form are the two forms of representing the phasor quantity. The conversion calculator given in this section is used to convert the polar form to the rectangular form and vice versa.

In the rectangular form, 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 polar form, the phasor is represented as Z = E \angle \pm \phi. Here E is the magnitude of the phasor and \phi is the angle made by the phasor with respect to the reference axis.

For detail understanding of the concept, learn 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 \angle \pm \phi

where, E is the magnitude given by,

    \[ E = \sqrt{a^2 + b^2} \]

\phi is the phasor angle given by,

    \[ \phi = tan^{-1} \frac{b}{a} \]

The final conversion result would be, a + jb = E \angle \pm \phi

How to use the conversion Calculator? 

  1. Enter the values of the real(a) and imaginary part(b) of the rectagular form in the respective input fields.
  2. Select your choice, wheher you need the phase angle output in degrees or radians.
  3. Press the convert button to see the conversion result.

Polar and Rectangular form conversion

Again, let us consider Z as the phasor quantity. In polar form, it is given by Z = E \angle \pm \phi

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

The real part and imaginary part of the rectangular form is determined as, a = E cos \phi and b = E sin \phi

How to use the conversion Calculator? 

  1. Enter the values of the maginutde and phase angle of the polar form in the respective input fields.
  2. Select wheher the phase angle input you have entered is in degrees or radians.
  3. Press the convert button to see the conversion result.

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