Circuits and Passives
Model class: Exact lumped-element relationship
Complex impedance and reactance
Calculate series RLC reactance, complex impedance magnitude, and phase at one stated sinusoidal frequency.
Interactive engine
Start with the stated conditions.
Values stay in this browser. Choose a representative scenario, then calculate deliberately.
Example ready
Calculate to inspect the result.
The result will identify the direct answer, assumptions, and any warning that changes the next decision.
How much does each input matter?
Each row holds every other input fixed at its current value and moves one input by ±10%, using the same model as the main result. It identifies which input is the binding lever, not a full tolerance stack.
Assumptions to check
- The entered complex-impedance values represent the stated operating condition.
- This exact lumped-element relationship is evaluated in the declared lumped or first-pass model.
- A complex-impedance calculation is not a component qualification or safety approval.
What this complex-impedance calculation establishes
Calculate series RLC reactance, complex impedance magnitude, and phase at one stated sinusoidal frequency. The useful result is the stated electrical quantity and the decision it supports, not an unstated claim about a finished product. This engine keeps the governing relationship visible so an input, unit, condition, or model boundary can be reviewed before a value becomes a component or layout choice.
Inductive reactance is 2πfL, capacitive reactance is 1 divided by 2πfC, and the series imaginary term is their difference. Treat the number as a first-pass result for the declared operating point. When a source, load, temperature, frequency, waveform, component tolerance, or measurement condition changes, repeat the calculation at the relevant corner rather than assuming the nominal answer persists.
Worked decision context
At 1 kHz, 100 Ω in series with 10 mH gives 100 + j62.832 Ω, magnitude 118.10 Ω, and phase 32.14 degrees. That example verifies the equation and illustrates the scale of the result, but it does not select a part by itself. Compare the result with available values, ratings, tolerance bands, and the receiving circuit or physical environment before implementation.
Use the primary output to identify the binding constraint. If it leaves little margin, document which input dominates and use selected-part data, a higher-fidelity model, simulation, or measurement. This is especially important when a small numerical difference changes a thermal, timing, noise, or reliability decision.
Limits and validation handoff
It omits parasitics, distributed behavior, saturation, dielectric loss, and frequency dependence of component values. The calculation does not silently include omitted parasitics, installation conditions, manufacturing variation, or product policy. Those conditions can be decisive even when the arithmetic is exact for the selected model.
Record inputs, units, model assumptions, and the intended decision with the result. Verify the leading risk against the selected component data sheet and a representative measurement when the circuit has consequential energy, high voltage, safety, compliance, or reliability requirements.
Common mistakes
- Treating the complex-impedance result as a guaranteed operating limit rather than a first-pass exact lumped-element relationship estimate.
- Mixing a data-sheet value measured under one condition with this complex-impedance calculation performed at another.
- Selecting a component before checking the boundary this calculation names: it omits parasitics, distributed behavior, saturation, dielectric loss, and frequency dependence of component values.
Model limit and handoff
Keep the entered complex-impedance conditions with the calculation, then validate the binding limit using the selected component, physical implementation, and representative operating corner.
FAQs
Is this complex-impedance result sufficient to approve a design?
No. It applies exact lumped-element relationship reasoning to the entered complex-impedance values and names the checks that still need selected-part data, a higher-fidelity model, or measurement. It omits parasitics, distributed behavior, saturation, dielectric loss, and frequency dependence of component values.
What does this complex-impedance calculator assume that could make the result wrong?
Inductive reactance is 2πfL, capacitive reactance is 1 divided by 2πfC, and the series imaginary term is their difference. If the entered values do not match the real operating condition, the result no longer describes the actual circuit.
Where should this complex-impedance result go next?
Compare this complex-impedance result with Engineering notation and units, then use the stated next decision below the calculator to move from this first-pass number toward an implementation.