About the Impedance Calculator
The AC Circuit Impedance Calculator finds the total opposition an AC circuit presents to current flow by combining a resistance value with a net reactance value. Anyone designing or troubleshooting an AC circuit, whether it is a speaker crossover, a motor start circuit, or an RF filter, needs this number to predict how much current a given voltage will actually produce. Because reactance shifts current out of phase with voltage while resistance does not, the two cannot simply be added together, which is exactly what this tool handles correctly.
How It Works
Enter the circuit's resistance in ohms and its net reactance in ohms, where net reactance is inductive reactance minus capacitive reactance and can be entered as a negative number if capacitance dominates. The calculator combines the two using a right-triangle relationship, since resistance and reactance act at 90 degrees to each other in the complex impedance plane, then reports both the impedance magnitude and the phase angle between voltage and current.
Formula & Methodology
To work this by hand, square the resistance and the net reactance separately, add them, and take the square root for the impedance magnitude in ohms. For the phase angle, take the arctangent of reactance over resistance (using atan2 so the sign and quadrant stay correct even when resistance is zero or reactance is negative), then convert the radian result to degrees.
Examples
Default 100 ohm resistor with 75 ohm net reactance
With resistance at 100 ohms and net reactance at 75 ohms, impedance works out to sqrt(100^2 + 75^2) = sqrt(15,625) = 125 ohms, with a phase angle of about 36.87 degrees, meaning current lags voltage by that amount.
Capacitor-dominated circuit
With resistance at 50 ohms and net reactance at -30 ohms, capacitive reactance exceeding inductive, impedance is sqrt(50^2 + 30^2) = sqrt(3,400), about 58.31 ohms, and the phase angle comes out to roughly -30.96 degrees, showing current leading voltage.
Advantages
- Avoids the error of simply adding resistance and reactance, which overstates impedance for any circuit that isn't purely resistive.
- Reports both the impedance magnitude and the phase angle in one calculation, saving a separate trigonometric step.
- Accepts negative reactance directly, so capacitive-dominated circuits don't need special-case handling.
Common Mistakes
- Adding R and X arithmetically instead of combining them as perpendicular components, which overstates impedance.
- Mixing up the sign convention for reactance, entering capacitive reactance as positive when it should reduce the net reactance value.
- Forgetting that reactance is frequency-dependent and reusing an old reactance figure after the circuit's operating frequency has changed.
Edge Cases to Watch For
- A negative net reactance, meaning capacitive reactance exceeds inductive reactance, produces a negative phase angle, indicating current leads voltage rather than lagging it.
- If net reactance is entered as zero, the circuit is purely resistive, impedance equals resistance exactly, and the phase angle is zero degrees.
- Reactance itself depends on frequency, rising for inductors and falling for capacitors as frequency changes, so the result is only valid at the single frequency used to calculate the reactance value entered.
Common Use Cases
- Electronics students verifying textbook AC circuit problems involving resistors, inductors, and capacitors in series.
- Audio and RF technicians checking impedance for speakers, antennas, or filter networks.
- Electricians diagnosing why a motor or AC-powered device draws more or less current than its resistance alone would suggest.