Impedance Calculator

Compute impedance, reactance, and phase angle for series or parallel RLC circuits at a given frequency.

Circuit Inputs

Practical Guide

Impedance Calculator: Understand Your Circuit, Not Just the Number

Use this impedance calculator to quickly estimate how resistors, inductors, and capacitors behave at a given frequency, then use this guide to interpret the results, avoid common mistakes, and design safer, more predictable circuits.

10–15 min read Updated 2025

Quick Start: Using the Impedance Calculator Safely

The calculator above lets you estimate impedance for common RLC circuits in either series or parallel form. Follow these steps to get a result that matches what your bench or simulation will show.

  1. 1 Select the circuit mode that matches your schematic: Series (same current path through R, L, C) or Parallel (same voltage across branches).
  2. 2 Choose what you want to solve for: impedance magnitude \( \lvert Z \rvert \), inductive reactance \( X_L \), capacitive reactance \( X_C \), or phase angle \( \varphi \).
  3. 3 Enter the frequency and verify the unit (Hz, kHz, or MHz). Impedance depends strongly on frequency, especially when inductors and capacitors are present.
  4. 4 Enter component values for R, L, and C in the units you actually have (Ω / kΩ / MΩ, H / mH / µH, F / µF / nF / pF). Leave a component at zero if it is not present.
  5. 5 Press Calculate. The main result row shows the chosen output, while the Quick Stats table summarizes equivalent resistance, reactance, magnitude, and phase.
  6. 6 Expand Calculation Steps to see the LaTeX equations, substitutions, and unit handling the tool used. Use this for reports, lab writeups, or code documentation.
  7. 7 Adjust frequency or component values to run “what-if” studies—watch how resonance, phase angle, and magnitude shift as you tune R, L, and C.

Tip: For audio or power applications, sweep the frequency range of interest (for example, 20 Hz–20 kHz or 45–65 Hz) rather than evaluating a single point.

Warning: The calculator assumes ideal components. Real parts have ESR, leakage, tolerance, and temperature dependence. Always compare against datasheets and derating guidelines.

Choosing Your Method: Series vs Parallel vs Reactance-Only

Most impedance questions fall into one of three patterns: a pure resistor network, a series RLC path, or a parallel RLC network. The calculator exposes these as modes and solve-for targets instead of separate tools.

Method A — Series Impedance \( Z = R + jX \)

Use when current flows through all elements in a single loop and you care about how voltage drops and phase shift behave across the path.

  • Matches typical small-signal models and textbook examples.
  • Easy to reason about: \( X = X_L – X_C \) and then \( Z = R + jX \).
  • Great for filters, snubbers, and many sensor circuits.
  • Does not directly model separate branches or bypass paths.
  • Can hide large current in L/C if you only look at magnitude.
\[ X_L = 2\pi f L,\quad X_C = \frac{1}{2\pi f C},\quad Z = R + j(X_L – X_C) \]

Method B — Parallel Impedance via Admittance

Use when all elements share the same voltage but carry different branch currents—classic for power distribution, bias networks, and shunt filters.

  • Matches how parallel RLC behaves in resonance and damping problems.
  • Makes it clear how conductance and susceptance add: \( Y = G + jB \).
  • Useful when comparing load impedances and source specs.
  • Math is slightly less intuitive than series form.
  • Requires working with admittance \( Y = 1/Z \) and then inverting.
\[ G = \frac{1}{R},\quad B = \omega C – \frac{1}{\omega L},\quad \lvert Z \rvert = \frac{1}{\sqrt{G^2 + B^2}} \]

Method C — Reactance-Only Spot Checks

Use when you just need inductive or capacitive reactance at a given frequency, without a full impedance calculation.

  • Perfect for sizing coupling capacitors or inductors.
  • Matches many “inductive reactance” or “capacitive reactance” homework and exam questions.
  • Very quick what-if analysis: double the frequency, see reactance change instantly.
  • Ignores resistance and losses completely.
  • Can be misleading if ESR or leakage dominates.
\[ X_L = 2\pi f L,\quad X_C = \frac{1}{2\pi f C} \]

What Moves the Impedance Number the Most

Impedance is not a fixed “property” of a component; it changes with frequency and topology. These are the main levers you can pull and what they typically do.

Frequency \( f \)

Inductors scale as \( X_L \propto f \), capacitors as \( X_C \propto 1/f \). Near resonance, small shifts in frequency dramatically change both magnitude and phase.

Resistance \( R \)

Increasing \( R \) raises \(\lvert Z \rvert\) in series circuits and lowers the Q factor in RLC networks. In parallel, a low \( R \) can dominate the combined impedance near resonance.

Inductance \( L \)

Larger \( L \) increases \( X_L \) and shifts resonant frequency down. At very low frequencies, the inductor may be almost a short; at high frequencies, almost an open circuit.

Capacitance \( C \)

Larger \( C \) decreases \( X_C \) and pushes resonance down. At very low frequencies, the capacitor behaves like an open; at high frequencies, it looks like a short.

Topology (Series vs Parallel)

In series, impedances add directly; in parallel, admittances add. A circuit that is “high impedance” in series form can behave as a “low impedance” load when recast in parallel.

Component Tolerances & ESR

Real parts rarely match their nameplate values. ESR, leakage, and tolerance can shift the actual impedance curve away from ideal predictions, especially near resonance.

Worked Examples with the Impedance Calculator

Example 1 — Series RLC at 1 kHz

  • Circuit: Series RLC
  • R: 50 Ω
  • L: 10 mH
  • C: 1 µF
  • Frequency: 1 kHz
  • Goal: Find \(\lvert Z \rvert\) and phase \( \varphi \).
1
Convert to base units: \( f = 1000~\text{Hz} \), \( L = 10\times10^{-3}~\text{H} \), \( C = 1\times10^{-6}~\text{F} \).
2
Compute reactances: \[ X_L = 2\pi f L,\quad X_C = \frac{1}{2\pi f C}. \] At 1 kHz, \( X_L \) is modest, \( X_C \) is large.
3
Net reactance: \[ X = X_L – X_C. \] The sign of \( X \) tells you whether the circuit is net inductive (positive) or capacitive (negative).
4
Impedance magnitude and phase: \[ \lvert Z \rvert = \sqrt{R^2 + X^2},\quad \varphi = \tan^{-1}\!\left(\frac{X}{R}\right). \] Entering these numbers into the calculator reproduces the same result step by step.

In the calculator, choose Series, set Solve For to \(\lvert Z \rvert\), enter R, L, C, and f, then inspect the Quick Stats table to see \( X \) and \( \varphi \) at the same time.

Example 2 — Parallel RLC Near 60 Hz

  • Circuit: Parallel RLC
  • R: 100 Ω
  • L: 50 mH
  • C: 47 µF
  • Frequency: 60 Hz
  • Goal: Estimate \(\lvert Z \rvert\) as seen by a source.
1
Convert to base units: \( f = 60~\text{Hz} \), \( L = 50\times10^{-3}~\text{H} \), \( C = 47\times10^{-6}~\text{F} \). Select Parallel mode in the calculator.
2
Compute admittance terms: \[ G = \frac{1}{R},\quad B_L = -\frac{1}{\omega L},\quad B_C = \omega C,\quad B = B_L + B_C. \]
3
Admittance magnitude and impedance: \[ \lvert Y \rvert = \sqrt{G^2 + B^2},\quad \lvert Z \rvert = \frac{1}{\lvert Y \rvert}. \] The calculator performs these steps internally and reports \( \lvert Z \rvert \) and phase.
4
Use the phase angle solve-for option to see whether the equivalent load looks slightly inductive or capacitive to the 60 Hz source.

Parallel networks can present very high or very low impedance around resonance. Always compare your calculation against the allowed load range of the driving source.

Common Layouts & Variations

Different circuit patterns produce very different impedance curves, even with similar component values. Use this table as a qualitative guide before you dig into detailed models.

ConfigurationTypical UseImpedance Behavior & Notes
Purely resistiveHeaters, simple loads, current-limiting resistors\( Z = R \) is constant with frequency (within component parasitics). Phase angle \(\varphi \approx 0^\circ\).
Series RLSnubbers, chokes, inrush limiting Magnitude rises with frequency as \( X_L \) grows. At low frequency, impedance is close to \( R \); at high frequency, inductor dominates and phase becomes inductive.
Series RCCoupling networks, simple high-pass filters At low frequency, capacitor looks open and \(\lvert Z \rvert\) is large; at high frequency, capacitor looks like a short and impedance approaches \( R \).
Series RLCBand-pass filters, tuned circuits Exhibits a sharp minimum of \(\lvert Z \rvert\) near resonance \[ f_0 \approx \frac{1}{2\pi\sqrt{LC}}. \] The resistor sets bandwidth and damping.
Parallel RLCNotch filters, tank circuits, line conditioning Exhibits a maximum of \(\lvert Z \rvert\) near resonance. Small changes in R, L, or C can significantly alter peak impedance and bandwidth.
Complex load (speaker, sensor, cable)Audio, instrumentation, high-speed links Impedance varies with frequency and sometimes temperature. Often modeled as an RLC network with additional parasitics; always compare calculator results with measured curves from datasheets.
  • Confirm whether elements are truly in series or parallel before choosing a mode.
  • Identify which components dominate impedance in your band of interest.
  • Check whether any resonance falls inside your operating bandwidth.
  • Use manufacturer models when accuracy is critical (filters, RF, medical equipment).

Specs, Logistics & Sanity Checks

An impedance calculator gives you ideal numbers. Turning those into a robust design means respecting datasheets, tolerances, and safety margins.

Key Specs to Watch

  • Voltage rating: ensure capacitors and inductors can withstand the AC peak and any transients.
  • Current rating: series impedance must survive continuous RMS and fault currents.
  • Frequency range: many components are specified only over a limited bandwidth.
  • Tolerance & drift: \( \pm 20\% \) parts can move resonance and phase more than you expect.

Practical Sanity Checks

  • Compare \(\lvert Z \rvert\) against the source’s recommended load range.
  • Verify that high-\( Q \) networks do not create dangerous overvoltages at resonance.
  • Check that impedance is not so low that it exceeds breaker or fuse limits.
  • For audio and RF, confirm that impedance mismatch is acceptable for the required power transfer.

Workflow Tips

  • Use the calculator early to size ballpark values for R, L, and C.
  • Refine the design in simulation (SPICE, MATLAB, etc.) using realistic models.
  • Measure impedance or transfer function on a prototype whenever possible.
  • Keep a record of calculator inputs alongside design revisions for traceability.

Treat the impedance calculator as a fast front-end to your design process, not as a substitute for simulations, lab measurements, and code compliance.

Frequently Asked Questions

What is electrical impedance in simple terms?
Impedance \( Z \) is the AC equivalent of resistance. It combines resistance and reactance into a complex quantity \( Z = R + jX \), capturing both how much a circuit resists current and how much it shifts the phase between voltage and current.
How is impedance different from resistance?
Resistance \( R \) is the part of impedance that dissipates power as heat and does not depend on frequency. Reactance \( X \) comes from inductors and capacitors and changes with frequency. Together they form impedance \( Z = R + jX \).
How do I know if my circuit is series or parallel for this calculator?
If current flows through R, L, and C in one continuous path, it is a series circuit. If they share the same two nodes and each branch has its own current, it is parallel. If the schematic is more complex, you may need to reduce it to an equivalent series or parallel form first.
Why does the calculator show a negative reactance or phase angle?
A negative reactance or negative phase angle means the circuit is net capacitive: current leads voltage. Positive reactance or phase angle indicates inductive behavior, where current lags voltage. This sign information is essential when designing filters and matching networks.
What frequency should I use in the impedance calculator?
Use the frequency at which the circuit will actually operate, or sweep across your band of interest. For mains applications, 50 or 60 Hz is typical; for audio it may be 20 Hz–20 kHz; for switching supplies it might be tens or hundreds of kilohertz.
Do I need to include parasitics like ESR or leakage in the calculation?
For rough sizing, ideal R, L, and C are usually fine. For precision work, RF, or high-power filters, parasitics can dominate behavior. In those cases, extend your model to include ESR, parallel resistance, and any known stray inductances or capacitances from datasheets or measurements.
Can impedance ever be lower than the resistor value in the circuit?
Yes. In some parallel networks and certain frequency ranges, the combined impedance can be lower than any single branch resistance. The calculator’s parallel mode shows this by computing the total admittance and then inverting it to find the equivalent impedance.
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