Calculator Inputs
Enter 0 to omit a component. The calculator supports flexible series or parallel RLC analysis.
Example Data Table
Example below uses a series circuit with R = 10 Ω, L = 10 mH, and C = 1 µF.
| Frequency (Hz) | XL (Ω) | XC (Ω) | |Z| (Ω) | Phase (°) | Behavior |
|---|---|---|---|---|---|
| 500 | 31.416 | 318.310 | 287.068 | -88.004 | Capacitive |
| 1591.55 | 100.000 | 100.000 | 10.000 | 0.000 | Resonant |
| 5000 | 314.159 | 31.831 | 282.505 | 87.971 | Inductive |
Formula Used
Angular frequency: ω = 2πf
Inductive reactance: XL = ωL
Capacitive reactance: XC = 1 / (ωC)
Series impedance: Z = R + j(XL - XC)
Parallel admittance: Y = 1/R + j(ωC - 1/(ωL))
Parallel impedance: Z = 1 / Y
Magnitude: |Z| = √(Re(Z)2 + Im(Z)2)
Phase angle: θ = tan-1(Im(Z) / Re(Z))
Resonant frequency: fr = 1 / (2π√LC)
Series quality factor: Q = ωrL / R
Parallel quality factor: Q = R√(C/L)
Bandwidth: BW = fr / Q
These equations assume ideal lumped components. Entering 0 removes a branch from the model, so the calculator can also represent simpler RL, RC, LC, or resistive cases.
How to Use This Calculator
- Select either a series or parallel RLC circuit model.
- Enter the resistance value in ohms.
- Enter inductance and choose the correct unit.
- Enter capacitance and choose the correct unit.
- Enter the operating frequency and its unit.
- Set sweep start, sweep end, and graph points.
- Click Calculate Impedance to display results.
- Review impedance, phase, resonance, bandwidth, and the Plotly graph.
- Download the calculation as CSV or PDF if needed.
Frequently Asked Questions
1. What does this calculator actually compute?
It calculates impedance magnitude, phase angle, inductive reactance, capacitive reactance, resonance, quality factor, bandwidth, and a full frequency-response graph for series or parallel RLC circuits.
2. Can I use it for RL or RC circuits?
Yes. Enter 0 for the missing component. The calculator then evaluates the remaining active elements and still plots impedance over the sweep range.
3. Why does impedance change with frequency?
Inductors and capacitors respond differently as frequency changes. Inductive reactance rises with frequency, while capacitive reactance falls, changing total opposition to current.
4. What does a positive phase angle mean?
A positive phase angle means the circuit behaves more inductively. Voltage leads current, and the imaginary part of impedance is positive.
5. What does a negative phase angle mean?
A negative phase angle means the circuit behaves more capacitively. Current leads voltage, and the imaginary part of impedance is negative.
6. What happens at resonance?
At resonance, inductive and capacitive effects cancel. In a series circuit, impedance becomes minimum. In a parallel circuit, impedance often becomes maximum.
7. Why is the graph sweep logarithmic?
A logarithmic sweep shows low and high frequencies clearly in one plot. It is especially helpful when resonance occurs within a wide frequency range.
8. When should I download CSV or PDF results?
Use CSV for spreadsheets, reports, and further numeric analysis. Use PDF when you need a clean snapshot for printing, sharing, or documentation.