Impedance Calculator

Input mode:

Choose whether to enter reactance values directly or derive them from L, C, and frequency.

Direct reactance Components

Resistance:

Enter the real part of the series impedance.

ohm

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Reference voltage:

Optional. Use 0 when you only need impedance.

V RMS

Display precision:

Adjust output decimals without changing the calculation.

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A small alternating-current network can draw very different current at 100 Hz than it does at 10 kHz, even when the resistor value has not changed. The reason is that inductors and capacitors oppose changing current in ways that depend on frequency. Impedance is the AC quantity that brings the real resistance and the frequency-dependent reactance into one complex value.

Resistance and reactance both use ohms, but they do not describe the same kind of opposition. Resistance dissipates energy as heat and sits on the real axis of a phasor diagram. Reactance stores energy for part of the cycle and returns it later, so it appears on the imaginary axis. Inductive reactance is treated as positive in the usual series convention, while capacitive reactance is subtracted from it.

This difference matters whenever current size and timing both affect the decision. A filter may need a target corner or resonance region, a coil load may need a safe RMS current estimate, and a teaching example may need to show why component voltage drops can exceed the source voltage near resonance. The answer is not just a bigger or smaller ohm value; the sign of the net reactance tells whether current lags or leads the source voltage.

Resistance: The real series opposition, measured in ohms, that contributes to real power.
Reactance: The inductive or capacitive opposition that changes with frequency and affects phase.
Impedance magnitude: The vector length of resistance plus signed reactance, used with RMS voltage to estimate RMS current.
Phase angle: The angle between the impedance vector and the real axis. Current has the opposite angle in the ideal series model.

The most common reading mistake is to add the three visible ohm quantities as if they shared one straight number line. A circuit with 50 ohm resistance and 18 ohm net reactance has an impedance magnitude of about 53.141 ohm, not 68 ohm, because the real and reactive parts are at right angles.

Ideal series RLC impedance is a first-pass model. It is useful for comparison, education, and early sizing, but it does not include every real component effect. Equivalent series resistance, winding resistance, dielectric loss, heating, saturation, parasitic capacitance, and non-sinusoidal waveforms can all make a measured circuit differ from the ideal phasor result.

How to Use This Tool:

Choose the input path that matches the numbers you already know. Entered reactance values go straight into the series phasor model, while component values first become reactance from frequency, inductance, and capacitance.

Choose Direct reactance when Inductive reactance and Capacitive reactance are already known in ohms, or choose Components when the reactances should be derived from Frequency, Inductance, and Capacitance.
Use positive magnitudes for both XL and XC. The capacitive sign is applied during the calculation.
Enter Resistance in ohms. Use the real series resistance that belongs in the ideal model, not a measured total impedance value.
In Components mode, set each unit selector before judging the answer. A value such as 4.7 mH is equivalent to 0.0047 H, but entering 4.7 H changes the result by a factor of 1000.
Open Advanced only when you need current, power, or component-voltage estimates. Leave Reference voltage at 0 when the impedance result alone is enough.
Set Display precision to the number of decimals you want to read. Precision affects displayed values, copied tables, and downloads; it does not change the internal arithmetic.
Review Impedance Snapshot for the magnitude, rectangular form, phase angle, current angle, and power factor, then use Reactance Ledger when the sign or derived reactance looks surprising.
If a validation message appears, correct the named field. Direct reactance mode accepts zero or greater values, while component mode requires frequency, inductance, and capacitance greater than zero.
Check Impedance Phasor Map before using the result in a report. A vector above the zero line means inductive behavior; a vector below it means capacitive behavior.

Interpreting Results:

Start with the signed rectangular form. R + jX tells you both the real resistance and the net reactance that produced the magnitude. A positive j term means the inductor dominates the capacitor at the chosen frequency. A negative j term means capacitive reactance is larger.

How to read impedance calculator outputs
Output	Read it as	Verify before acting
`Impedance magnitude`	Total ideal opposition to sinusoidal RMS current.	Confirm the frequency, unit prefixes, and whether the model is series.
`Rectangular form`	Resistance plus signed net reactance.	Check that capacitive reactance was entered as a positive magnitude.
`Polar form`	Magnitude with the impedance voltage phase angle.	Use `Current angle` for current phase; it is the negative of the impedance angle.
`Circuit behavior`	Inductive, capacitive, resistive balance, or zero impedance from the sign and size of net reactance.	Near balance is sensitive to small changes in frequency or component tolerance.
`Power factor`	The ideal real-power fraction, calculated from `R / \|Z\|`.	A high value does not prove real parts are lossless or thermally safe.
`Reference voltage` rows	RMS current, real power, reactive power, apparent power, and ideal component voltage drops.	Use measured current or voltage when resonance, heating, or nonlinear behavior matters.

A low impedance magnitude can mean higher current, but it does not automatically mean a useful or safe operating point. Near resonance, the inductor and capacitor can exchange energy while the source sees a mostly resistive load. Individual component voltages can still be large, so check the voltage rows when you provide a nonzero RMS source voltage.

Use the phasor map as a sign check rather than a measurement instrument. It helps catch swapped units, an unintended capacitive result, or a direct-reactance entry where XC was typed as negative even though the field expects a positive magnitude.

Technical Details:

Series RLC impedance is built from phasor addition. The same current passes through the resistor, inductor, and capacitor, but the voltage contribution from each part has a different phase relation to that current. The resistor voltage is in phase, the inductor voltage leads by one quarter cycle, and the capacitor voltage lags by one quarter cycle.

The two reactive magnitudes oppose one another in the signed reactance term. Raising frequency increases inductive reactance and decreases capacitive reactance, so the same component set can move from capacitive to near-resistive to inductive behavior as frequency changes.

Formula Core:

Component inputs are first scaled into hertz, henries, and farads. Direct reactance inputs skip the component conversion and use the entered ohm magnitudes.

\begin{array}{lcl} ω & = & 2 π f \\ X_{L} & = & ω L \\ X_{C} & = & \frac{1}{ω C} \\ X & = & X_{L} - X_{C} \\ Z & = & R + j X \\ | Z | & = & \sqrt{R^{2} + X^{2}} \\ θ & = & atan2 (X, R) \end{array}

Here f is frequency, L is inductance, C is capacitance, R is resistance, X is signed net reactance, and theta is the impedance phase angle. For R = 50 ohm, XL = 30 ohm, and XC = 12 ohm, the net reactance is 18 ohm and the magnitude is sqrt(50^2 + 18^2) = 53.141 ohm.

Series RLC sign and phase behavior
Net reactance condition	Behavior label	Impedance angle	Current relation
`XL > XC`	`Inductive`	Positive	Current lags source voltage.
`XL ~= XC`	`Resistive balance`	Near zero	Voltage and current are effectively in phase.
`XL < XC`	`Capacitive`	Negative	Current leads source voltage.
`\|Z\| = 0`	`Zero impedance`	Zero	The entered ideal values have no opposition.

The near-balance test uses a small tolerance based on the impedance magnitude, with a floor of 0.000000001 ohm. This prevents tiny floating-point differences from turning an otherwise balanced example into an inductive or capacitive label.

Reference Voltage Estimates:

A nonzero RMS source voltage adds current and power estimates to the same phasor model.

\begin{array}{lcl} I_{RMS} & = & \frac{V_{RMS}}{| Z |} \\ P & = & I^{2} R \\ Q & = & I^{2} X \\ S & = & V I \\ power factor & = & \frac{R}{| Z |} \end{array}

Input boundaries used for impedance calculations
Input area	Accepted values	Boundary reason
`Resistance`	Zero or greater.	Negative resistance is outside this ideal passive series model.
`Direct reactance`	`Inductive reactance` and `Capacitive reactance` are zero or greater.	The fields are magnitudes; the signs are assigned by the series convention.
`Components`	`Frequency`, `Inductance`, and `Capacitance` are greater than zero.	Capacitive reactance divides by frequency and capacitance.
`Reference voltage`	Zero or greater.	Zero suppresses current and power estimates while keeping impedance available.
`Display precision`	Two to five decimal places.	Rounding changes presentation only.

Unit prefixes are converted before the equations run. The frequency choices scale to hertz, inductance choices scale to henries, and capacitance choices scale to farads, so equivalent values such as 0.47 uF and 470 nF produce the same capacitance term.

Worked Examples:

These examples use the same series sign convention as the calculator: inductive reactance is positive and capacitive reactance is entered as a positive magnitude that gets subtracted.

Known reactance values

With Direct reactance selected, Resistance = 50 ohm, Inductive reactance = 30 ohm, and Capacitive reactance = 12 ohm produce Net reactance X near +18 ohm. Impedance magnitude is about 53.141 ohm, Polar form is about 53.141 ohm angle +19.799 deg, and Circuit behavior is Inductive.

Component values at 1 kHz

In Components mode, Frequency = 1 kHz, Inductance = 4.7 mH, Capacitance = 0.47 uF, and Resistance = 50 ohm derive XL near 29.531 ohm and XC near 338.628 ohm. The net reactance is about -309.097 ohm, so the circuit reads Capacitive and current leads voltage.

Reference voltage check

Keeping the direct-reactance example and setting Reference voltage = 12 V RMS adds Current at reference voltage of about 0.2258 A. The power estimates are about 2.55 W real power, 0.918 VAR reactive power, and 2.71 VA apparent power.

Component-mode warning

Selecting Components with Capacitance = 0 produces the message Capacitance must be greater than zero. Entering the intended capacitor value, such as 470 nF, restores the impedance snapshot and phasor map.

FAQ:

Should capacitive reactance be typed as a negative number?

No. Enter Capacitive reactance as a positive magnitude. The calculation forms XL - XC, so a negative entry would double-flip the intended sign and trigger validation.

Why does the component result change when only frequency changes?

Frequency controls both reactance equations. Higher frequency raises XL and lowers XC, so the same inductor and capacitor can move from capacitive to balanced to inductive behavior.

What does a negative phase angle mean?

A negative impedance phase angle means the net reactance is capacitive. The displayed Current angle has the opposite sign, so current leads source voltage in the ideal series model.

Why do current and power rows disappear at zero voltage?

A Reference voltage of 0 tells the calculator to show impedance only. Enter a positive RMS voltage when you want estimated RMS current, power, and ideal component voltage drops.

Can this replace a bench impedance measurement?

No. It models ideal series RLC behavior from the entered values. Use a meter, analyzer, or circuit simulation when tolerances, parasitics, heating, saturation, losses, or non-sinusoidal waveforms may change the circuit.

Glossary:

Impedance: The complex AC opposition that combines resistance and signed reactance.
Reactance: Frequency-dependent opposition from inductance or capacitance.
Phasor: A rotating-vector representation that keeps magnitude and phase together for sinusoidal quantities.
Power factor: The ideal real-power fraction of apparent power, calculated here as resistance divided by impedance magnitude.
Resistive balance: A near-zero net reactance state where source voltage and current are effectively in phase.
RMS: Root mean square, the AC value convention used for current, voltage, and power estimates.

References:

23.12 RLC Series AC Circuits, OpenStax College Physics 2e.
15.3 RLC Series Circuits with AC, OpenStax University Physics Volume 2.
Series R, L, and C, All About Circuits Electronics Textbook.