Select a circuit to calculate magnitude and phase with. Use an electronic circuit with a resistor and an inductor in series. Use a series resistor with a value of 20 Ohms and an inductor with a value of 2 Henries. For this example, calculate the real and reactive reactance at a frequency of 20 Hertz.
Calculate the real component of the impedance of the series circuit. Remember that resistors are the only components that have a real component. Also remember that a resistor's impedance doesn't vary with frequency. So conclude that the real component of the series circuit is equal to 20 Ohms, the value of the resistor in the circuit.
Calculate the reactive component of the impedance of the series circuit. Remember that reactive components are components whose impedance depends on the frequency. Because the inductive reactance of an inductor is frequency dependent, it is the only reactive component of the impedance of the circuit. Remember that the inductive reactance is equal to the product of 6.28 times the frequency times the inductor value. For this example, the inductive reactance is 25.12 Ohms since 6.28 times 20 times 2 is 25.12.
Calculate the magnitude of the series impedance. Square the real component and then square the reactive component. Sum these results together. Next take the square root of this sum. For this example, from step 1, the real component is 20 Ohms. The square of 20 is 400. From step 2, the reactive component is 25.12 ohms. The square of 25.12 is 631. The sum of these squares is 1031, since 400 plus 631 is 1031. The square root of 1031 is 32.1. So square root of the sum of the squares of the real and reactive component is 32.1 Ohms. Or in other words, the magnitude of the impedance of this series circuit is 32.1 Ohms at a frequency of 20 Hertz.
Calculate the phase of the series impedance. Divide the impedance of the reactive component by the impedance of the real component. Then take the arctangent of this division. The result will be the phase of the series impedance at the specified frequency. For this example, divide 25.12, the reactive component, by 20, the real component, to obtain 1.26. Next take the arctangent of 1.26. Use the arctangent function on your calculator. The arctangent of 1.26 is 51.6 degrees. So the phase of the series impedance circuit is 51.6 degrees at a frequency of 20 Hertz.