Impedance Calculator
Calculate online series RLC impedance from resistance, reactance, or component values to check magnitude, phase, power factor, and current behavior.{{ summaryHeading }}
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Introduction:
Impedance is the alternating-current version of opposition to current flow. It combines resistance, which uses energy as heat or work, with reactance, which stores and returns energy in inductors and capacitors. The result is not only a size in ohms. It also has a phase angle that says whether current lines up with voltage, lags it, or leads it.
Series RLC impedance matters whenever a resistor, inductor, and capacitor share the same current path. Audio crossovers, simple filters, motor and relay coils, resonant experiments, sensor interfaces, and power-factor checks all depend on the same relationship. A circuit can have a modest resistance value and still draw little current if the net reactance is large at the frequency being used.
Frequency is the part that often makes the answer move. Inductive reactance rises with frequency, while capacitive reactance falls as frequency rises. At the point where those two reactances have the same magnitude, they cancel in the series model and the circuit looks mostly resistive. Away from that balance, the impedance vector tilts toward the inductive or capacitive side.
The important boundary is that impedance is a steady-state sinusoidal model. It helps estimate current, phase, power factor, and ideal voltage drops for a chosen frequency, but it does not capture every real component behavior. Lead resistance, inductor saturation, capacitor equivalent series resistance, tolerance, heating, and frequency-dependent losses can all move a measured circuit away from the ideal result.
Technical Details:
Series RLC analysis treats resistance as the real part of the impedance and net reactance as the imaginary part. The inductor contributes positive reactance. The capacitor contributes negative reactance. Because the same current flows through all three parts in a series path, the total impedance is the vector sum of those real and reactive terms.
Angular frequency links component values to reactance. Raising frequency increases the inductor term because the magnetic field resists faster current change. The same frequency increase lowers the capacitor term because the capacitor charges and discharges more easily within each cycle. That opposite frequency response is why a series RLC circuit can pass through a resistive balance point even when both L and C are present.
The impedance angle is the voltage angle relative to current in the usual impedance convention. A positive angle means the net reactance is inductive, so current lags source voltage. A negative angle means the net reactance is capacitive, so current leads source voltage. When the net reactance is zero, impedance magnitude equals resistance, phase is zero, and the ideal power factor is one.
| Condition | Impedance behavior | Phase reading | Current reading |
|---|---|---|---|
XL > XC |
Inductive | Positive impedance angle | Current lags source voltage |
XL = XC |
Resistive balance | Near zero degrees | Current and voltage are effectively in phase |
XL < XC |
Capacitive | Negative impedance angle | Current leads source voltage |
Power factor follows directly from the triangle. In this ideal series model, R / |Z| is the real-power fraction. If an RMS reference voltage is supplied, RMS current is V / |Z|. Real power is I^2R, reactive power is I^2X, and apparent power is VI. The sign of reactive power follows the same net-reactance sign, so a capacitive result produces negative reactive power in the exported calculation.
| Input group | Allowed values | Why it matters |
|---|---|---|
| Resistance and direct reactance mode | Resistance, inductive reactance, and capacitive reactance must be zero or greater | The direct mode expects positive magnitudes, then applies +jXL and -jXC internally |
| Component mode | Frequency, inductance, and capacitance must be greater than zero | Reactance formulas divide by frequency and capacitance, so zero would make the component model invalid |
| Reference voltage | Zero or greater | A value of zero leaves current, power, and component-voltage estimates inactive |
| Display precision | Two to five decimal places | Precision changes displayed formatting and exports, not the calculation path |
The ohm is used for resistance, reactance, and impedance. Hertz sets cycles per second, henry sets inductance, and farad sets capacitance. Unit prefixes only scale the entered values before the equations run, so 4.7 mH and 0.0047 H represent the same inductance in the model.
Everyday Use & Decision Guide:
Use direct reactance mode when you already know XL and XC from a datasheet, worksheet, simulator, or earlier calculation. Enter both reactance values as positive ohm magnitudes. The calculator applies the signs for a series circuit, so an inductor adds positive reactance and a capacitor subtracts from it.
Use component mode when you know the physical values instead. Set frequency first, then enter inductance and capacitance with their units. That mode is better for "what happens at this frequency?" checks because changing Hz, kHz, or MHz immediately changes both reactance terms and can move the circuit from capacitive to resistive to inductive behavior.
- Read the headline as magnitude plus phase. A result such as
58 ohm | +31 degis not the same as a plain 58 ohm resistor because the current phase has shifted. - Check Reactance Ledger when the sign surprises you. It shows
XL,XC, net reactance, and the reactive share of the total impedance. - Open Impedance Phasor Map when you want a quick visual check. Points above the horizontal axis are inductive, while points below it are capacitive.
- Add a nonzero reference voltage only when you want current, real power, reactive power, apparent power, and ideal component voltage estimates.
- Use Display precision for reporting. It changes the rounded text you see and export, not the underlying result.
The most common wrong reading is to treat magnitude as the whole answer. Magnitude tells you how much RMS current an ideal sinusoidal source would drive for a chosen voltage, but phase tells you whether that current leads or lags. A load with the same magnitude can have a very different power factor if the net reactance changes sign or grows relative to resistance.
For lab notes, homework checks, or design handoffs, start with Impedance Snapshot and then copy or download the table if the summary is enough. Use JSON when you need the normalized inputs and calculated values together. The table exports include CSV and DOCX, and the phasor chart can be saved as PNG, WebP, JPEG, or CSV.
Keep the result tied to one frequency and one ideal series model. If you are checking a real part, compare the calculated current or phase against measured data before changing hardware, especially near resonance where tolerances and losses can move the balance point.
Step-by-Step Guide:
- Choose
Direct reactance valuesif you already knowR,XL, andXC, or chooseComponent values and frequencyif you want reactance derived fromf,L, andC. - Enter resistance in ohms. Use the real series resistance you want represented, including any intentional resistor or known equivalent series resistance.
- For direct mode, enter inductive and capacitive reactance as positive ohm magnitudes. For component mode, enter frequency, inductance, and capacitance with the matching unit prefixes.
- Leave
Reference voltageat zero if you only need impedance. Set an RMS voltage if you also want current, power, and ideal component voltage estimates. - Read the summary badges for inductive, capacitive, or resistive balance behavior, then open Impedance Snapshot for rectangular form, polar form, power factor, and current angle.
- Use Reactance Ledger, Impedance Phasor Map, or JSON for deeper checking, visualization, and export.
Interpreting Results:
The headline combines two views of the same impedance: magnitude and phase. The summary line adds rectangular form, where the first number is resistance and the signed j term is net reactance. A positive j term means inductive behavior. A negative j term means capacitive behavior.
| Output | What it means | Common misread |
|---|---|---|
| Impedance magnitude | Total opposition to sinusoidal RMS current in the ideal series circuit | Treating it as a plain resistor value and ignoring phase |
| Rectangular form | Resistance plus signed net reactance, written as R +/- jX |
Entering capacitive reactance as negative even though the tool expects a positive magnitude |
| Polar form | Magnitude and voltage phase angle of the impedance | Forgetting that current angle is the negative of the impedance angle |
| Power factor | The ideal real-power fraction, calculated from resistance divided by impedance magnitude | Reading a high power factor as proof that a real component has no losses or tolerance error |
| Reactive share | The absolute net-reactance share of the impedance magnitude | Assuming inductive and capacitive parts both remain visible after they cancel |
| Reference-voltage rows | Current, real power, reactive power, apparent power, and ideal voltage drops for the RMS voltage entered | Treating those rows as measured power rather than ideal estimates from the chosen voltage |
The phasor chart plots resistance on the horizontal axis and net reactance on the vertical axis. The diagonal endpoint is the impedance vector. If the endpoint is close to the horizontal axis, the circuit is close to resistive balance. If it sits high above the axis, inductive reactance is dominating. If it sits below the axis, capacitive reactance is dominating.
The validation message appears before results when an input would make the model invalid. In component mode, frequency, inductance, and capacitance must all be greater than zero. In direct mode, the reactance fields can be zero, but not negative. Correct those inputs before comparing phase, current, or export data.
Worked Examples:
Direct reactance check
With the default direct values, R = 50 ohm, XL = 30 ohm, and XC = 12 ohm. Net reactance is +18 ohm, so the rectangular form is about 50 + j18 ohm. The magnitude is about 53.141 ohm, the impedance angle is about +19.80 deg, and the result is inductive because XL is greater than XC.
Component values near capacitive behavior
Set component mode to 1 kHz, 4.7 mH, 0.47 uF, and 50 ohm. The inductor contributes about 29.531 ohm, while the capacitor contributes about 338.628 ohm. Net reactance is therefore about -309.096 ohm, so the circuit is strongly capacitive at that frequency and the current leads the source voltage.
Adding a reference voltage
Keep the direct reactance example and set Reference voltage to 12 V RMS. The ideal RMS current is about 0.2258 A. Real power is about 2.55 W, reactive power is about 0.918 VAR, and apparent power is about 2.71 VA. Those values are useful for a first estimate, but they still assume the entered series values describe the real circuit at that frequency.
FAQ:
Should capacitive reactance be entered as a negative number?
No. Enter capacitive reactance as a positive magnitude. The series calculation applies it as negative reactance when it builds R + j(XL - XC).
Why does component mode require frequency, inductance, and capacitance to be greater than zero?
The formulas need all three values. Inductive reactance uses frequency and inductance, while capacitive reactance divides by frequency and capacitance. A zero value would make at least one derived reactance meaningless for this model.
Does a resistive balance result mean there is no inductor or capacitor effect?
It means the ideal net reactance is close to zero at the entered frequency. The inductor and capacitor can still have large individual reactances, but their series effects cancel in the total impedance.
Why can component voltage estimates exceed the source voltage?
In a series RLC circuit, inductor and capacitor voltage phasors point in opposite reactive directions. Near resonance, individual reactive voltage drops can be large even when their net reactive contribution is small.
Does the calculator measure a live circuit?
No. It calculates an ideal series RLC result from the values you enter and keeps the calculation, tables, chart, and exports in the browser. Use measured impedance or oscilloscope data when real component losses, tolerance, or heating matter.
Glossary:
- Impedance
- Total opposition to alternating current, combining resistance and reactance as a complex value.
- Reactance
- The frequency-dependent opposition from inductors and capacitors.
- Phasor
- A rotating-vector representation that tracks AC magnitude and phase.
- Power factor
- The real-power fraction of apparent power in the ideal model.
- Resonance
- The series condition where inductive and capacitive reactance cancel, leaving the circuit mostly resistive.
- RMS
- Root mean square, the standard effective value used for AC voltage and current calculations.