Impedance Calculator

Calculate AC impedance, reactance, phase angle, resonance, power factor, current, and circuit behavior for RC, RL, LC, and RLC circuits.

Calculator is for informational purposes only. Terms and Conditions

1

Choose what to solve for

Select the circuit type, connection, and target result.

Choose the components included in the ideal lumped-element AC circuit model.
Series adds impedances. Parallel adds admittances, then inverts to get total impedance.
Resonance solve modes require a circuit containing both L and C.
Presets only change units and example defaults, not the governing equations.
Enter R, L, C, and frequency to calculate total impedance.
2

Enter the known values

Fill in the visible fields. The calculator updates automatically.

Use the real resistance in the circuit. In real inductors, this may include winding resistance.
Inductance creates positive reactance. Its opposition increases as frequency increases.
Capacitance creates negative reactance. Its opposition decreases as frequency increases.
Frequency must be greater than zero for capacitor or inductor impedance calculations.
Optional. Enter RMS voltage to estimate RMS current, apparent power, real power, and reactive power.
Advanced Options
3

Circuit and phasor visual

The visual updates with the selected circuit and calculated impedance angle.

AC circuit diagram
Impedance phasor diagram
4

Solution

Live result, quick checks, warnings, and calculation steps.

Impedance Magnitude
Ω
Real-time result updates as you type.

Quick checks

  • Complex impedance
  • Phase angle
  • Net reactance
  • Inductive reactance
  • Capacitive reactance
  • Circuit behavior

Source, standards, and assumptions

Educational AC circuit model

  • Source/standard: Standard engineering formula or educational calculation method. No single governing code standard is required for this simplified calculation.
  • Calculation basis: Ideal sinusoidal steady-state AC circuit analysis using complex impedance.
  • Series circuits add impedance directly. Parallel circuits add branch admittance and invert the total.
  • This is a lumped-element AC circuit calculator, not a PCB trace, microstrip, stripline, differential pair, antenna, or transmission-line impedance calculator.
Show solution steps See known values, equations, substitutions, and interpretation
  1. Enter values to see the full solution steps and checks.
On this page

Calculator Guide

How to Use the Impedance Calculator

The Impedance Calculator above helps calculate AC circuit impedance for R, C, L, RC, RL, LC, and RLC circuits. Use it to find complex impedance, impedance magnitude, reactance, phase angle, power factor, resonance, and estimated current when RMS voltage is known.

Impedance is the total opposition to alternating current. Unlike simple DC resistance, AC impedance can include both a real part from resistance and an imaginary part from inductive or capacitive reactance. That is why the result is often shown as both rectangular form \(Z=R+jX\) and magnitude-angle form \(|Z|\angle\theta\).

Best for Ideal RC, RL, LC, and RLC AC circuit checks
Main result Complex impedance, magnitude, phase angle, and behavior
Most important input Frequency, because reactance changes directly with \(f\)

Quick Answer

To calculate impedance, choose the circuit type and connection, enter resistance, inductance, capacitance, and frequency, then read the impedance result in ohms. A positive phase angle means the circuit is more inductive; a negative phase angle means it is more capacitive; a phase angle near zero means it is mostly resistive or near resonance.

When not to rely on this simplified calculator

Do not use this calculator as a final model for PCB trace impedance, microstrip, stripline, differential pairs, transmission lines, antennas, cable characteristic impedance, or high-frequency layouts where parasitics dominate. Those problems require different electromagnetic or transmission-line models.

Inputs and Outputs Used by the Impedance Calculator

The calculator uses the values that define an ideal sinusoidal AC circuit. The required inputs depend on the selected circuit type and solve mode, but most impedance calculations need frequency plus at least one circuit element.

Common impedance calculator inputs and outputs
TypeValueWhat It MeansCommon Unit
InputResistance, \(R\)The real opposition to current. In real inductors or circuits, this may include winding resistance or series resistance.\(\Omega\), \(k\Omega\), \(M\Omega\)
InputInductance, \(L\)The inductor value that creates positive reactance. Inductive opposition increases as frequency increases.nH, \(\mu H\), mH, H
InputCapacitance, \(C\)The capacitor value that creates negative reactance. Capacitive opposition decreases as frequency increases.pF, nF, \(\mu F\), F
InputFrequency, \(f\)The sinusoidal AC frequency used to calculate inductive and capacitive reactance.Hz, kHz, MHz
Optional InputRMS Voltage, \(V_{rms}\)Used with impedance magnitude to estimate RMS current and apparent power.V, kV
OutputImpedance, \(Z\)The total AC opposition in complex form and magnitude-angle form.\(\Omega\)
OutputPhase angle, \(\theta\)The angle showing whether the circuit is inductive, capacitive, or mostly resistive.degrees or radians

Impedance mode

Use this mode to calculate \(Z\), \(|Z|\), phase angle, reactance, behavior, and optional current from known circuit values and frequency.

Resonant frequency mode

Use this mode for LC or RLC circuits when \(L\) and \(C\) are known and you need the ideal resonance frequency.

Capacitance for resonance

Use this mode when target frequency and inductance are known and you need the capacitor value for ideal resonance.

Inductance for resonance

Use this mode when target frequency and capacitance are known and you need the inductor value for ideal resonance.

If you are working specifically with an RC timing or filter problem, the RC Circuit Calculator may be a better next step after checking impedance.

Impedance Formula Used by the Calculator

For a series RLC circuit, total impedance is the real resistance plus the net imaginary reactance. The same component impedances are also used for parallel circuits, but parallel circuits are usually solved by adding admittances first.

Series RLC impedance

\[ Z=R+j(X_L-X_C) \]
\[ |Z|=\sqrt{R^2+(X_L-X_C)^2} \]

The rectangular form \(Z=R+jX\) is useful for circuit math. The magnitude \(|Z|\) is useful for estimating current from voltage.

Reactance formulas

\[ X_L=2\pi fL \]
\[ X_C=\frac{1}{2\pi fC} \]

Inductive reactance \(X_L\) rises with frequency. Capacitive reactance \(X_C\) falls with frequency.

Parallel impedance using admittance

\[ Y_{total}=Y_R+Y_L+Y_C \]
\[ Z_{total}=\frac{1}{Y_{total}} \]

Use this method for parallel AC circuits because branch admittances add directly. In simple terms, \(Y=1/Z\), so each branch is converted to admittance before the total is inverted back to impedance.

Phase angle, power factor, and current

\[ \theta=\tan^{-1}\left(\frac{X_L-X_C}{R}\right) \]
\[ PF=\cos(\theta) \qquad I_{rms}=\frac{V_{rms}}{|Z|} \]

Power factor comes from the impedance phase angle in an ideal sinusoidal AC circuit. RMS current is calculated from RMS voltage divided by impedance magnitude.

Resonant frequency and rearranged resonance formulas

\[ f_0=\frac{1}{2\pi\sqrt{LC}} \]
\[ C=\frac{1}{(2\pi f_0)^2L} \qquad L=\frac{1}{(2\pi f_0)^2C} \]

At ideal LC resonance, \(X_L=X_C\). For a dedicated resonance workflow, use the Resonant Frequency Calculator.

What the Variables Mean

Each variable must be entered with the correct unit scale. Reactance and impedance are both measured in ohms, but inductance and capacitance often use small engineering prefixes such as \(\mu H\), mH, pF, nF, and \(\mu F\).

\(Z\)

Total impedance in ohms. It can be written as complex impedance \(R+jX\) or as magnitude and phase \(|Z|\angle\theta\).

\(R\)

Resistance in ohms. It is the real part of impedance and does not change with frequency in the ideal model.

\(X_L\)

Inductive reactance in ohms. It is positive imaginary opposition and increases as frequency or inductance increases.

\(X_C\)

Capacitive reactance in ohms. It is negative imaginary opposition and decreases as frequency or capacitance increases.

\(f\)

Frequency in hertz. Use \(1\,kHz=1000\,Hz\) and \(1\,MHz=1,000,000\,Hz\).

\(\theta\)

Impedance phase angle. Positive usually means inductive behavior; negative usually means capacitive behavior.

How to Use the Calculator

Use the calculator by matching the circuit type to your components, selecting series or parallel, choosing the solve mode, and confirming the unit selectors before trusting the output.

1

Select the circuit type

Choose R, C, L, RC, RL, LC, or RLC. Only enter values for the components that are actually in the ideal circuit model.

2

Choose series or parallel

Use series when all components share the same current path. Use parallel when components are connected across the same two nodes.

3

Pick the solve mode

Most users solve for impedance. If you are tuning an LC or RLC circuit, use resonant frequency, capacitance for resonance, or inductance for resonance.

4

Check the answer

Review magnitude, complex impedance, phase angle, reactance, and circuit behavior. If voltage is entered, also check current and power values.

Which circuit type should you choose?

Choose RC for resistor-capacitor behavior, RL for resistor-inductor behavior, LC for ideal resonance or tank-circuit checks, and RLC when resistance, inductance, and capacitance all affect the AC response.

How to Interpret Impedance Results

An impedance result is more than one number. The magnitude tells how strongly the circuit opposes AC current, while the sign and size of the reactance explain whether the circuit behaves more like an inductor, capacitor, resistor, or resonant circuit.

What to do with \(|Z|\)

Use impedance magnitude to estimate current: \(I_{rms}=V_{rms}/|Z|\). Larger \(|Z|\) means less current for the same RMS voltage.

What changes the result most?

Frequency often dominates because \(X_L\) increases with \(f\) and \(X_C\) decreases with \(f\). A small frequency change can strongly affect LC and RLC circuits.

Sanity check

If a series RLC circuit is near resonance, \(X_L\) and \(X_C\) should nearly cancel, so \(|Z|\) should move closer to \(R\).

How to read common impedance result patterns
Result PatternLikely MeaningWhat to Check
\(X_L>X_C\)The circuit behaves more inductively.Frequency, inductance value, and whether the current should lag voltage.
\(X_C>X_L\)The circuit behaves more capacitively.Capacitance value, frequency unit, and whether the current should lead voltage.
\(X_L\approx X_C\)The circuit is near ideal resonance.Whether the result should be dominated by resistance, ESR, or loading.
\(|Z|\) is unexpectedly hugeCapacitance may be too small, frequency may be too low, or a unit may be wrong.pF vs nF vs \(\mu F\), Hz vs kHz vs MHz.

Input Checklist Before You Trust the Answer

Most impedance calculator mistakes come from unit scale errors, wrong circuit topology, or treating ideal component values as if they include real-world parasitic behavior.

Check the topology

Series and parallel RLC circuits are not solved the same way. Series circuits add impedance directly; parallel circuits add admittance.

Check frequency units

Entering \(1\) as Hz when you meant \(1\,kHz\) changes reactance by a factor of 1000.

Check small component prefixes

\(1\,\mu F=1000\,nF\), \(1\,mH=1000\,\mu H\), and \(1\,nF=1000\,pF\).

Check optional voltage

Use RMS voltage for AC current and power estimates. Do not enter peak voltage unless the calculator explicitly asks for it.

Worked Example: Series RLC Impedance

This example calculates impedance for a simple series RLC circuit. It shows the same logic used by the calculator: calculate reactance, subtract capacitive reactance from inductive reactance, then combine the result with resistance.

Given values

Resistance
\(R=50\,\Omega\)
Inductance
\(L=10\,mH=0.010\,H\)
Capacitance
\(C=1\,\mu F=0.000001\,F\)
Frequency
\(f=1\,kHz=1000\,Hz\)

Step 1: Calculate reactance

\[ X_L=2\pi(1000)(0.010)=62.832\,\Omega \]
\[ X_C=\frac{1}{2\pi(1000)(0.000001)}=159.155\,\Omega \]

Step 2: Calculate net reactance and impedance

\[ X=X_L-X_C=62.832-159.155=-96.323\,\Omega \]
\[ Z=50-j96.323\,\Omega \]

Step 3: Calculate magnitude and phase angle

\[ |Z|=\sqrt{50^2+(-96.323)^2}=108.527\,\Omega \]
\[ \theta=\tan^{-1}\left(\frac{-96.323}{50}\right)=-62.567^\circ \]

Final answer

The impedance is approximately \(Z=50-j96.323\,\Omega\), with magnitude \(|Z|=108.527\,\Omega\) and phase angle \(-62.567^\circ\). The negative phase angle is reasonable because capacitive reactance is larger than inductive reactance at this frequency.

How to Visualize Series RLC Impedance

A series RLC impedance triangle shows why impedance magnitude is calculated with the Pythagorean relationship. Resistance is the horizontal leg, net reactance is the vertical leg, and total impedance magnitude is the diagonal.

Reference Checks and Source Notes

There is no single “normal” impedance value because impedance depends on the selected components, frequency, circuit topology, and application. A reasonable reference check is to compare each reactance value against the resistance and ask which term should dominate.

Source note for complex impedance

For a deeper educational explanation of complex impedance and phasors, see MIT OpenCourseWare’s complex impedance and phasors notes. For practical AC circuit sign conventions, the All About Circuits series R, L, and C explanation shows how resistance, inductive reactance, and capacitive reactance combine in AC circuit impedance.

At low frequency

Capacitors often look like high impedance because \(X_C=1/(2\pi fC)\) becomes large when \(f\) is small.

At high frequency

Inductors often look like high impedance because \(X_L=2\pi fL\) grows as frequency increases.

Design Notes and Practical Ranges

Impedance design depends heavily on the circuit purpose. Audio, power, sensor, RF, filter, and resonance applications can all use impedance, but they do not share one universal target range.

Learning and homework

Use ideal \(R\), \(L\), and \(C\) values to understand complex impedance, phase angle, and resonance.

Early circuit design

Use the result to compare component values, frequency response trends, and rough current levels before selecting real parts.

Final hardware

Check ESR, ESL, tolerance, temperature, voltage rating, current rating, layout, manufacturer data, and measurement results.

Power applications

When impedance connects to AC power, current, or correction, the Power Factor Calculator can help interpret \(PF\), kW, kVA, and kVAR relationships.

Units and Conversions

The formulas use ohms, henries, farads, and hertz. The calculator may let you enter common engineering units, but the underlying math still converts to base units before calculating reactance.

Common unit conversions for impedance calculations
QuantityCommon UnitsConversion Reminder
FrequencyHz, kHz, MHz\(1\,kHz=10^3\,Hz\), \(1\,MHz=10^6\,Hz\)
InductancenH, \(\mu H\), mH, H\(1\,mH=10^{-3}\,H\), \(1\,\mu H=10^{-6}\,H\), \(1\,nH=10^{-9}\,H\)
CapacitancepF, nF, \(\mu F\), F\(1\,\mu F=10^{-6}\,F\), \(1\,nF=10^{-9}\,F\), \(1\,pF=10^{-12}\,F\)
Impedance\(m\Omega\), \(\Omega\), \(k\Omega\), \(M\Omega\)\(1\,k\Omega=1000\,\Omega\), \(1\,M\Omega=10^6\,\Omega\)

Hidden unit trap

The most common error is entering capacitor or inductor prefixes incorrectly. A \(1\,\mu F\) capacitor is 1000 times larger than a \(1\,nF\) capacitor, which makes capacitive reactance 1000 times smaller at the same frequency.

Frequency cannot be zero for most AC impedance checks

For capacitor and inductor impedance calculations, frequency must be greater than zero. At \(f=0\), an ideal capacitor behaves like an open circuit and an ideal inductor behaves like a short circuit in steady-state DC.

Impedance vs Resistance vs Reactance

Resistance, reactance, and impedance are related, but they are not interchangeable. Resistance is the real part, reactance is the frequency-dependent imaginary part, and impedance combines both into the total AC opposition.

Resistance

\(R\) is the real component of impedance. In the ideal model, it does not depend on frequency.

Reactance

\(X\) is the imaginary component caused by inductors and capacitors. It changes with frequency.

Impedance

\(Z\) combines resistance and reactance. It controls AC current magnitude and phase relationship.

Series vs parallel method

For series circuits, add component impedances directly. For parallel circuits, convert each branch to admittance, add the admittances, and then invert the result: \(Z_{total}=1/Y_{total}\).

AC impedance is not the same as characteristic impedance

This calculator estimates lumped-element AC impedance using \(R\), \(L\), \(C\), and frequency. Transmission-line characteristic impedance, PCB trace impedance, microstrip impedance, stripline impedance, and antenna matching depend on geometry, dielectric properties, propagation effects, and layout details.

Common Impedance Calculator Mistakes

The formula is straightforward, but the result can be badly wrong if the circuit setup, unit scale, or interpretation is wrong.

Do

  • Use RMS voltage when estimating AC current and apparent power.
  • Check whether the circuit is series or parallel before calculating.
  • Convert \(\mu H\), mH, pF, nF, and \(\mu F\) carefully.
  • Use the phase angle to interpret inductive or capacitive behavior.

Don’t

  • Do not treat impedance magnitude as the same thing as resistance.
  • Do not ignore the sign of \(X_L-X_C\).
  • Do not use the lumped-element result for PCB trace impedance.
  • Do not assume ideal parts match real measured parts at every frequency.

Troubleshooting Unrealistic Results

If the impedance result looks too high, too low, or inconsistent with your expectation, start with frequency and unit prefixes. Then check whether the circuit model matches the actual circuit.

Result is too high

Check whether capacitance is too small, frequency is too low, or a capacitor was entered as pF instead of nF or \(\mu F\).

Result is too low

Check for a resonance condition, missing series resistance, or entering mH as H by mistake.

Phase sign seems wrong

Recalculate \(X_L-X_C\). Positive net reactance is inductive; negative net reactance is capacitive.

Measured value disagrees

Real parts include ESR, ESL, tolerance, leakage, temperature effects, probes, leads, and layout parasitics.

Assumptions and Limitations

This calculator is best used for educational and preliminary AC circuit analysis. It assumes ideal sinusoidal steady-state behavior and lumped circuit elements unless real resistance is manually included.

Ideal components

The formulas assume ideal resistors, capacitors, and inductors unless you include real resistance values such as ESR or winding resistance.

Single frequency

The result applies at the entered frequency. Impedance can be very different at another frequency.

Lumped-element model

The calculator is not a full electromagnetic, RF layout, cable, antenna, or transmission-line solver.

Final design

For hardware selection, verify component datasheets, voltage and current ratings, temperature effects, tolerances, and field measurements.

Related Calculators and Engineering Tools

Use these related Turn2Engineering tools when impedance connects to filters, resonance, RMS voltage, capacitance, or AC power calculations.

Key Terms

These terms help connect the calculator inputs, formulas, and result interpretation.

Impedance

Total opposition to AC current, including resistance and reactance. It is measured in ohms.

Reactance

Frequency-dependent opposition from capacitors and inductors. Inductive reactance is positive; capacitive reactance is negative in complex impedance form.

Admittance

The reciprocal of impedance, written as \(Y=1/Z\). It is often used to solve parallel AC circuits.

Phase Angle

The angle between voltage and current in an AC circuit. It helps identify inductive or capacitive behavior.

Resonance

The condition where ideal inductive and capacitive reactance are equal in magnitude, so \(X_L=X_C\).

Power Factor

The cosine of the phase angle in an ideal sinusoidal circuit. It relates real power to apparent power.

Impedance Calculator FAQ

What does an impedance calculator calculate?

An impedance calculator estimates AC circuit impedance from resistance, inductance, capacitance, and frequency. Depending on the selected circuit, it can show complex impedance, impedance magnitude, phase angle, reactance, power factor, resonance behavior, and current when voltage is known.

What is the formula for series RLC impedance?

For an ideal series RLC circuit, impedance is \(Z=R+j(X_L-X_C)\), where \(X_L=2\pi fL\) and \(X_C=1/(2\pi fC)\). The magnitude is \(|Z|=\sqrt{R^2+(X_L-X_C)^2}\).

Why does impedance change with frequency?

Impedance changes with frequency because inductive reactance increases as frequency increases, while capacitive reactance decreases as frequency increases. The balance between those two reactances determines whether the circuit behaves more inductively, capacitively, or resistively.

What does a negative phase angle mean?

A negative phase angle usually means the circuit is more capacitive, so current leads voltage in the ideal sinusoidal model. This happens when capacitive reactance is larger than inductive reactance.

Can this calculator be used for PCB trace impedance?

No. This calculator is intended for ideal lumped-element AC circuits such as RC, RL, LC, and RLC circuits. PCB trace impedance, microstrip, stripline, antenna, cable, and transmission-line problems require different models.

Why is my measured impedance different from the calculator result?

Measured impedance can differ because real components include ESR, winding resistance, leakage, tolerance, temperature effects, parasitic inductance, parasitic capacitance, lead length, and layout effects. The calculator uses an ideal simplified AC circuit model.

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