# Polar to Exponential Form Conversion Calculator

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This polar to exponential form conversion calculator converts a number in polar form to its equivalent value in exponential form.

Polar, or phasor, forms of numbers take on the format, amplitude < phase. The phase is specified in degrees.

Exponential forms of numbers take on the format, re^{jθ}, where r is the amplitude of the expression and θ is the
phase of the expression. The amplitude r must be expressed in absolute value form. R cannot be a negative number. θ (theta) must be expressed
in unit radians. Unlike the polar form, which is expressed in unit degrees, a complex exponential number is expressed in unit radians.

Polar forms of numbers can be converted into their exponential equivalents relatively easily. The amplitude of the polar form is the direct amplitude of the exponential form. So no conversion is necessary for the amplitude. The phase of the polar form must only be converted into its equivalent in radian value. So this is the only conversion that really needs to take place. Degrees from the polar form needs to be converted into radians in the exponential form.

So, for example, let's take the expression in polar form, 15 < 70°. We want to convert this into its equivalent exponential form.
So, to do this, we take the formula and plug in the values, giving us, exponential form= 15e^{j1.22}. 70° is 1.22 in radian form.

And that's all that's required in order to convert from polar form to exponential form.

Usually, in electronics, polar forms are used in express components in AC circuit analysis. For example, if you are doing AC circuit analysis, one of the things that is required to do this is to convert the circuit from the time domain to the frequency domain, so that the circuit can be analyzed in the frequency domain. Therefore, the power source of the circuit is converted from the expression in the time domain to its expression in the frequency domain. In the frequency domain, the power source is expressed in polar form. So in situations like these, you will encounter numbers in polar form. This calculator can be useful in expressing this polar form to another form, like rectangular form.

Since the only 2 components of a number expressed in polar form are the amplitude and the phase of the signal, these are the only
2 inputs required for the calculator to compute the equivalent number in exponential form.

Related Resources

Rectangular to Polar Form Conversion Calculator

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