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Calculate the reactance or admittance magnitude of an inductor or capacitor at a specified frequency.
Enter your parameters below to calculate results.
The Reactance Calculator determines the reactance and admittance magnitude of an ideal capacitor or inductor at a specified frequency. Enter the frequency along with the capacitance or inductance to calculate how strongly the component opposes alternating current.
Capacitive reactance decreases as frequency or capacitance increases. Inductive reactance increases as frequency or inductance increases. Both reactance and resistance are measured in ohms, but they represent different parts of a component's impedance.
This calculator is useful for AC circuit analysis, filter design, oscillator and resonant-circuit calculations, impedance matching, signal coupling, power-factor networks, and estimating component behavior at a selected frequency.
| Input | Meaning | Typical Units |
|---|---|---|
| Frequency, f | The frequency of the sinusoidal AC signal. | Hz, kHz, MHz |
| Capacitance, C | The ideal capacitance used to calculate capacitive reactance and admittance. | F, µF, nF, pF |
| Inductance, L | The ideal inductance used to calculate inductive reactance and admittance. | H, mH, µH, nH |
| Output | Symbol | Unit |
|---|---|---|
| Capacitive reactance magnitude | |XC| | Ω |
| Inductive reactance magnitude | |XL| | Ω |
| Capacitive admittance magnitude | |YC| | S |
| Inductive admittance magnitude | |YL| | S |
Reactance is the frequency-dependent opposition to alternating current caused by energy storage in an electric or magnetic field. Capacitors produce capacitive reactance, while inductors produce inductive reactance. Reactance is represented by X and measured in ohms.
Unlike resistance, ideal reactance does not continuously dissipate energy as heat. An ideal capacitor or inductor stores energy during part of an AC cycle and returns it to the circuit during another part. Real components also have resistance and other losses.
| Quantity | Symbol | Meaning | Unit |
|---|---|---|---|
| Resistance | R | The real part of impedance, associated with energy dissipation. | Ω |
| Reactance | X | The imaginary part of impedance, associated with energy storage. | Ω |
| Impedance | Z | The total complex opposition to AC. | Ω |
| Admittance | Y | The reciprocal of impedance, describing how readily AC flows. | S |
| Conductance | G | The real part of admittance. | S |
| Susceptance | B | The imaginary part of admittance. | S |
Resistance affects both AC and DC. Reactance is associated with changing voltage or current and therefore depends on frequency. The claim that resistance affects only DC is incorrect.
Impedance is commonly written in rectangular form as:
Z = R + jX
The symbol j is the imaginary unit used in electrical engineering. It satisfies:
j2 = -1
Therefore, j is not equal to -1. Inductive reactance is represented by a positive imaginary term, while capacitive reactance is represented by a negative imaginary term.
The magnitude of capacitive reactance is:
|XC| = 1 / (2 × π × f × C)
Using angular frequency ω = 2πf:
|XC| = 1 / (ω × C)
Where:
The signed reactance of an ideal capacitor is negative:
XC = -1 / (ωC)
Many calculators display the positive magnitude |XC|. The negative sign appears when the result is expressed as a complex impedance: -j|XC|.
The inductive reactance of an ideal inductor is:
XL = 2 × π × f × L
Using angular frequency:
XL = ω × L
Where:
Inductive reactance is positive, so the impedance of an ideal inductor is jXL.
Admittance is the reciprocal of impedance:
Y = 1 / Z
For ideal reactive components, admittance is purely imaginary, and its imaginary part is called susceptance.
YC = jωC
|YC| = BC = 2 × π × f × C
YL = -j / (ωL)
|YL| = 1 / (2 × π × f × L)
Admittance and susceptance are measured in siemens, symbol S. For a pure capacitor or inductor, the admittance magnitude is the reciprocal of the reactance magnitude.
| Frequency Change | Capacitive Reactance | Inductive Reactance |
|---|---|---|
| Frequency doubles | Decreases to one-half | Doubles |
| Frequency is reduced by half | Doubles | Decreases to one-half |
| Frequency approaches 0 Hz | Approaches infinity for an ideal capacitor | Approaches 0 Ω for an ideal inductor |
| Component Value Change | Reactance Result |
|---|---|
| Capacitance doubles at fixed frequency | Capacitive reactance falls to one-half. |
| Capacitance is reduced by half | Capacitive reactance doubles. |
| Inductance doubles at fixed frequency | Inductive reactance doubles. |
| Inductance is reduced by half | Inductive reactance falls to one-half. |
Calculate the reactance of a 1 µF capacitor at 1 kHz.
|XC| = 1 / (2 × π × 1000 × 0.000001) = 159.155 Ω
The ideal capacitor impedance is approximately -j159.155 Ω. Its admittance magnitude is:
|YC| = 1 / 159.155 = 0.006283 S = 6.283 mS
Calculate the reactance of a 10 mH inductor at 1 kHz.
XL = 2 × π × 1000 × 0.01 = 62.832 Ω
The ideal inductor impedance is approximately j62.832 Ω. Its admittance magnitude is:
|YL| = 1 / 62.832 = 0.015915 S = 15.915 mS
| Inputs | Reactance Formula in Ohms |
|---|---|
| f in Hz, C in µF | |XC| = 159154.943 / (f × C) |
| f in kHz, C in µF | |XC| = 159.154943 / (f × C) |
| f in Hz, L in mH | XL = 0.006283185 × f × L |
| f in kHz, L in mH | XL = 6.283185 × f × L |
Use these shortcut forms only when the input units match the table. Otherwise, convert the frequency to hertz, capacitance to farads, and inductance to henries before applying the base formulas.
DC steady state corresponds to 0 Hz, but component behavior during switching is a transient rather than a steady-state reactance calculation.
| Ideal Component | Impedance Angle | Phase Relationship |
|---|---|---|
| Resistor | 0° | Voltage and current are in phase. |
| Inductor | +90° | Voltage leads current by 90°. |
| Capacitor | -90° | Current leads voltage by 90°. |
For a simple series circuit containing resistance and a net reactance:
Z = R + jX
The impedance magnitude is:
|Z| = √(R2 + X2)
The impedance phase angle is:
θ = arctan(X / R)
These formulas apply directly to the stated series form. Parallel circuits are often easier to analyze using admittance, since the conductance and susceptance of the branches add together.
In an ideal series LC circuit, the net reactance is:
X = XL + XC = ωL - 1 / (ωC)
At series resonance, the magnitudes of the inductive and capacitive reactances are equal, so the net reactance is zero:
f0 = 1 / (2 × π × √(L × C))
Real resonant circuits still contain resistance and loss, which determine current, bandwidth, and Q factor.
The calculator uses ideal component equations. Real components exhibit parasitic and frequency-dependent effects:
For high-frequency, high-current, precision, or resonant applications, use impedance curves, self-resonant frequency, ESR, Q factor, tolerance, and bias data from the component datasheet.
Reactance is measured in ohms, symbol Ω, just like resistance and impedance.
The negative sign represents the capacitor's -90° impedance phase. A calculator may show the positive magnitude, but the complex impedance is -j|XC|.
An ideal inductor has a +90° impedance phase, so its impedance is written as jXL.
In ideal DC steady state, a capacitor behaves as an open circuit. During charging, discharging, or switching, transient current can still flow.
An ideal inductor behaves as a short circuit in DC steady state. A real inductor still has winding resistance and may have current or core limits.
Reactance is the imaginary component associated with energy storage. Impedance combines resistance and reactance into one complex quantity.
Admittance is the reciprocal of impedance and is measured in siemens. It indicates how readily AC current flows for an applied voltage.
No. It calculates the ideal reactance or admittance at one frequency. Real impedance also depends on loss, parasitic elements, tolerance, temperature, bias, and construction.