Impedance Calculator
Magnitude and phase — they do not simply add.
Work out Impedance. Magnitude and phase — they do not simply add. Shows the working, not just the answer.
Impedance magnitude
153.198 Ω
-86.26° phase · Capacitive — current leads the voltage
Impedance combines resistance and reactance, but not by adding them — they are 90° apart, so the magnitude is the hypotenuse √(R² + X²) and the phase angle is the arctangent of X over R. The two reactances subtract because they are 180° apart from each other: inductive current lags the voltage and capacitive current leads it. Whichever wins sets the character of the circuit, and when they cancel exactly you are at resonance. The power factor is the cosine of the phase angle, and it is what decides how much of the apparent power does real work. A phase angle of 60° means a power factor of 0.5 — the supply carries twice the current needed to deliver the actual power.
How the Impedance Calculator works
Series RLC impedance at any frequency, with the phase angle, both reactances and the power factor. Resistance and reactance are 90° apart, so the magnitude is a hypotenuse rather than a sum.
Also known as: rlc impedance at frequency · phase angle of a circuit · why does impedance change with frequency · reactance and resistance combined
Frequently asked questions
How do you calculate impedance?
The magnitude is √(R² + X²) where X is the net reactance, and the phase angle is arctan(X/R). The two components are 90° apart, which is why they combine as a hypotenuse rather than adding.
Why do inductive and capacitive reactance subtract?
Because they are 180° apart from each other. Inductive current lags the voltage and capacitive current leads it, so they oppose directly and whichever is larger sets the circuit's character.
What does the phase angle tell me?
Whether current leads or lags voltage, and by how much. Positive means inductive with current lagging; negative means capacitive with current leading; zero means resonance.
What is the power factor?
The cosine of the phase angle, and the share of apparent power that does real work. A power factor of 0.5 means the supply carries twice the current needed for the actual power delivered.
Why does impedance depend on frequency?
Because both reactances do, in opposite directions — inductive reactance rises with frequency and capacitive falls. That frequency dependence is what makes filters possible.
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