Impedance Calculator
The impedance and phase angle of a resistor, inductor and capacitor in series or in parallel at a frequency, with the inductive and capacitive reactance and the resonant frequency.
Result…
How it's calculated
ω = 2πf · XL = ωL · XC = 1 ÷ (ωC) Series: Z = R + j(XL − XC), |Z| = √(R² + (XL − XC)²), φ = atan((XL − XC) ÷ R) Parallel: Y = 1/R + j(ωC − 1/(ωL)), |Z| = 1 ÷ |Y|, φ = −atan(B ÷ G) Resonance: f0 = 1 ÷ (2π√(LC))
Impedance is the AC version of resistance: how much a circuit opposes an alternating current, in ohms, together with a phase angle that says how far the current is shifted from the voltage. An inductor's reactance XL = 2πfL rises with frequency; a capacitor's reactance XC = 1/(2πfC) falls with it. In series the reactances subtract and add to the resistance at right angles, so |Z| = √(R² + (XL − XC)²). In parallel it is easier to add admittances (1 divided by each part's impedance) and turn the total back into ohms. At the resonant frequency f0 = 1/(2π√(LC)) the two reactances are equal: a series circuit falls to just R, and a parallel one rises to just R (or to infinity with no resistor). A positive phase means inductive, a negative one capacitive.
Your numbers, step by step
About the Impedance calculator
This impedance calculator finds how strongly a resistor, inductor and capacitor together oppose an alternating current at one frequency. Choose series or parallel, enter the frequency in Hz, kHz or MHz, the resistance in ohms, the inductance in H, mH or µH and the capacitance in F, µF, nF or pF; leave out any part the circuit does not have. You get the impedance magnitude in ohms, the phase angle, the inductive reactance XL = 2πfL, the capacitive reactance XC = 1/(2πfC), the resistive and reactive parts, and the resonant frequency where XL equals XC. A chart shows how the impedance changes across the frequency range. Students checking homework, hobbyists building filters and engineers sizing a circuit can follow every step with their own numbers.
How to use it
- Pick the “Connection”: “Series RLC” if the parts are in one line, or “Parallel RLC” if each part sits across the same two points.
- Enter the “Frequency” and choose its unit.
- Enter “Resistance R”, “Inductance L” and “Capacitance C” with their units. Use 0 or leave blank for any part that is missing.
- Read the impedance and phase angle. A positive phase means the circuit is inductive; a negative one means it is capacitive.
- Check the resonant frequency to see whether you are above or below the point where the reactances cancel.
Worked example
A 100 Ω resistor, a 10 mH inductor and a 1 µF capacitor in series at 1 kHz. ω = 2π × 1,000 = 6,283.19 rad/s. XL = 6,283.19 × 0.01 = 62.83 Ω and XC = 1 ÷ (6,283.19 × 0.000001) = 159.15 Ω. The reactive part is 62.83 − 159.15 = −96.32 Ω, so |Z| = √(100² + 96.32²) = 138.85 Ω at a phase of −43.93°: the circuit is capacitive. The resonant frequency is 1 ÷ (2π√(0.01 × 0.000001)) = 1,591.5 Hz. The same three parts in parallel give 72.02 Ω at +43.93°.
Updated
Questions people ask
How do I calculate the impedance of a series RLC circuit?
Work out XL = 2πfL and XC = 1/(2πfC), subtract them to get the net reactance, then |Z| = √(R² + (XL − XC)²). The phase angle is atan((XL − XC) ÷ R).
How is parallel impedance different from series?
In parallel you add admittances instead: 1/R for the resistor and ωC − 1/(ωL) for the reactive parts. The impedance is 1 divided by the size of that total. At resonance a parallel circuit has its highest impedance, while a series one has its lowest.
What does a negative phase angle mean?
The capacitor's reactance is bigger than the inductor's at that frequency, so the circuit behaves like a capacitor and the current leads the voltage. A positive angle means it behaves like an inductor and the current lags.
What is a common mistake with impedance?
Adding resistance and reactance as plain numbers. They are at right angles, so 100 Ω of resistance and 100 Ω of reactance make about 141 Ω, not 200 Ω. Mixing up mH and µH, or µF and nF, is the other frequent slip.
How do I get the current once I know the impedance?
Divide the AC voltage by |Z|, the same way you use resistance in the Ohm's law calculator. For the capacitor itself, the capacitance calculator works out C from plate size and spacing.
How accurate is this for a real circuit?
It treats the parts as ideal. Real inductors have winding resistance and real capacitors have leakage and tolerance, so near resonance a measured circuit can differ a lot. Measure the finished circuit before relying on it.