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
Choose what to solve for
Select the circuit type, connection, and target result.
Enter the known values
Fill in the visible fields. The calculator updates automatically.
Circuit and phasor visual
The visual updates with the selected circuit and calculated impedance angle.
Solution
Live result, quick checks, warnings, and calculation steps.
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
- 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 \(|Z|\angle\theta\).
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.
| Type | Value | What It Means | Common Unit |
|---|---|---|---|
| Input | Resistance, \(R\) | The real opposition to current. In real inductors or circuits, this may include winding resistance or series resistance. | \(\Omega\), \(k\Omega\), \(M\Omega\) |
| Input | Inductance, \(L\) | The inductor value that creates positive reactance. Inductive opposition increases as frequency increases. | nH, \(\mu H\), mH, H |
| Input | Capacitance, \(C\) | The capacitor value that creates negative reactance. Capacitive opposition decreases as frequency increases. | pF, nF, \(\mu F\), F |
| Input | Frequency, \(f\) | The sinusoidal AC frequency used to calculate inductive and capacitive reactance. | Hz, kHz, MHz |
| Optional Input | RMS Voltage, \(V_{rms}\) | Used with impedance magnitude to estimate RMS current and apparent power. | V, kV |
| Output | Impedance, \(Z\) | The total AC opposition in complex form and magnitude-angle form. | \(\Omega\) |
| Output | Phase 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
The rectangular form \(Z=R+jX\) is useful for circuit math. The magnitude \(|Z|\) is useful for estimating current from voltage.
Reactance formulas
Inductive reactance \(X_L\) rises with frequency. Capacitive reactance \(X_C\) falls with frequency.
Parallel impedance using admittance
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
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
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.
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.
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.
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.
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 \(R\).
| Result Pattern | Likely Meaning | What 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 huge | Capacitance 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.
Step 1: Calculate reactance
Step 2: Calculate net reactance and impedance
Step 3: Calculate magnitude and phase angle
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.
Net reactance is \(X=X_L-X_C\). Positive net reactance points in the inductive direction, while negative net reactance points in the capacitive direction.
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.
| Quantity | Common Units | Conversion Reminder |
|---|---|---|
| Frequency | Hz, kHz, MHz | \(1\,kHz=10^3\,Hz\), \(1\,MHz=10^6\,Hz\) |
| Inductance | nH, \(\mu H\), mH, H | \(1\,mH=10^{-3}\,H\), \(1\,\mu H=10^{-6}\,H\), \(1\,nH=10^{-9}\,H\) |
| Capacitance | pF, 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.
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.