Rectangular to Polar Form Conversion Calculator


Rectangular to polar form formula


Rectangular to polar form conversion example

Enter the Real Number
Enter the Imaginary Number   j

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

Rectangular forms of numbers take on the format, rectangular number= x + jy, where x and y are numbers. The x is the real number of the expression and the y represents the imaginary number of the expression.

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

Rectangular forms of numbers can be converted into their polar form equivalents by the formula, Polar amplitude= √ x2 + y2 , where x and y represent the real and imaginary numbers of the expression in rectangular form. This finds the amplitude of the polar expression.

To find the phase of the polar form, the formula to do so is, phase= arctan(y/x), where y is the imaginary number and x is the real number. This calculator computes the phase in degrees, not in radians.

So, for example, let's take the expression in rectangular form, 31 + 75j. We want to convert this into its equivalent polar form. So, to do this, we take the formula and plug in the values, giving us for the amplitude, amplitude = √ 312 + 752 = 81.15. For the phase, we plug the numbers into the formula, giving us for the phase, phase= arctan(75/31)= 67.54°.

And that's all that's required in order to convert from rectangular form to polar 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 need to convert numbers into their polar forms.

Since the only 2 components of a number expressed in rectangular form are the real number and the imaginary number, these are the only 2 inputs required for the calculator to compute the equivalent number in polar form.

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