| Case | Inputs | Rectangular Z (ohm) | |Z| (ohm) | Phase (deg) |
|---|---|---|---|---|
| Series RL | f=1000 Hz, R=100 ohm, L=10 mH | 100 + j62.83 | 118.10 | 32.14 |
| Series RC | f=60 Hz, R=220 ohm, C=10 µF | 220 − j265.26 | 344.62 | -50.33 |
| Series RLC | f=1000 Hz, R=47 ohm, L=5 mH, C=1 µF | 47 − j127.74 | 136.11 | -69.80 |
| Parallel RC | f=1000 Hz, R=1 kohm, C=0.1 µF | 716.96 − j450.48 | 846.73 | -32.14 |
| Parallel RL | f=1000 Hz, R=100 ohm, L=10 mH | 28.30 + j45.05 | 53.20 | 57.86 |
Impedance is a complex quantity: Z = R + jX. Magnitude and angle are:
- |Z| = √(R² + X²)
- θ = atan2(X, R) (degrees)
- ω = 2πf
- XL = ωL
- XC = 1/(ωC)
- Series: Z = R + j(XL − XC)
- Parallel: compute admittance Y = G + jB, then Z = 1/Y
- Parallel terms: G = 1/R, B = ωC − 1/(ωL)
Sign convention: inductors contribute positive X in Z, capacitors contribute negative X in Z.
- Select a calculation mode (series, parallel, rectangular input, or V/I).
- Enter the required values and choose units for each input.
- Click Calculate Impedance to show results above the form.
- Use Download CSV or Download PDF to export.
- Change the output unit to scale results for readability.
This short guide explains how impedance is computed and applied.
Impedance basics in AC circuits
Impedance (Z) combines resistance and reactance into one complex value. In audio, RF, and power electronics, matching Z reduces reflections and wasted power. This calculator reports Z in rectangular form (R + jX), plus magnitude and phase so you can compare components and networks quickly. Engineers also describe Z as AC opposition, shown as a magnitude and angle.
Why frequency changes everything
Reactance depends on frequency. Inductive reactance increases linearly with frequency, while capacitive reactance falls as frequency rises. That is why a 10 mH coil looks small at 50 Hz but significant at 10 kHz. Always enter the operating frequency, not a generic “test” value.
Typical component ranges and results
Common lab values produce practical impedances: R from 1 Ω to 1 MΩ, L from 1 µH to 10 H, and C from 10 pF to 10,000 µF. At 1 kHz, a 1 µF capacitor has about 159 Ω of reactance, while a 10 mH inductor has about 62.8 Ω.
Series networks: adding effects
In series circuits, the same current flows through each element, so impedances add directly. The real part stays R, and the imaginary part becomes XL − XC. Series RLC is useful for modeling coil resistance, capacitor ESR, and narrow‑band resonant branches.
Parallel networks: using admittance
Parallel circuits share voltage, so it is easier to work with admittance Y = G + jB. Conductance G equals 1/R, and susceptance B combines capacitive and inductive terms. This tool converts Y back to Z, giving a realistic equivalent for shunt components and loads. At high frequency, small capacitors can dominate susceptance and shift phase.
Resonance and phase behavior
At resonance, XL and XC cancel and X approaches zero in a series RLC, so Z is nearly purely resistive and phase is near 0°. Below resonance, capacitive behavior dominates (negative phase). Above resonance, inductive behavior dominates (positive phase).
Output units and scaling
Results can be shown in ohms, kilo‑ohms, or mega‑ohms. Scaling does not change physics; it just improves readability. For sensors and RC filters, kΩ is often convenient. For insulation and leakage checks, MΩ keeps numbers compact.
Where Z calculations are used
Impedance checks appear in loudspeaker crossover design, transformer and motor models, filter tuning, transmission line terminations, and test bench measurements. When you know Z, you can estimate current draw, voltage drop, power factor, and whether a source can drive a load safely.
What does j mean in impedance?
j is the imaginary unit used in electrical engineering. It marks the reactive part of impedance. Positive jX indicates inductive behavior, while negative jX indicates capacitive behavior.
Why can my impedance be negative?
The magnitude |Z| is never negative. Only the imaginary part X can be negative when capacitive reactance dominates. The sign tells whether current leads or lags voltage.
Do I need RMS values for the V/I mode?
Yes, use consistent magnitudes such as Vrms and Arms. If you use peak values for both, the ratio still works, but mixing peak with RMS will distort |Z|.
What is the difference between series and parallel RLC?
Series RLC adds impedances directly and models elements in one current path. Parallel RLC uses admittance because elements share voltage. The same R, L, and C can produce very different Z at a given frequency.
How do I interpret the phase angle?
A positive angle means voltage leads current (inductive load). A negative angle means current leads voltage (capacitive load). An angle near 0° indicates mostly resistive behavior.
Why does the tool show conductance and susceptance?
Those values belong to admittance Y = G + jB, used for parallel networks. They help you see whether the parallel load is dominated by resistance (G) or reactive effects (B).
Can this help with impedance matching?
Yes. Compare your load Z to your source or line target (like 50 Ω). Then adjust R, L, or C to move the magnitude and phase toward the desired impedance at the operating frequency.