Reactance Calculator Overview

The Reactance Calculator determines the reactance and admittance magnitude of an ideal capacitor or inductor at a specified frequency. Enter frequency together with 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.

Calculator Inputs

Calculator Outputs

What Is Reactance?

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.

Resistance, Reactance, Impedance, and Admittance

Resistance affects both AC and DC. Reactance is associated with changing voltage or current and therefore depends on frequency. The old statement that resistance affects only DC is incorrect.

Complex Impedance and the Imaginary Unit

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.

• Ideal resistor: Z_R = R

• Ideal inductor: Z_L = jωL

• Ideal capacitor: Z_C = 1 / (jωC) = -j / (ωC)

Capacitive Reactance Formula

The magnitude of capacitive reactance is:

|X_C| = 1 / (2 × π × f × C)

Using angular frequency ω = 2πf:

|X_C| = 1 / (ω × C)

Where:

• |X_C| = capacitive reactance magnitude in ohms

• f = frequency in hertz

• C = capacitance in farads

• ω = angular frequency in radians per second

The signed reactance of an ideal capacitor is negative:

X_C = -1 / (ωC)

Many calculators display the positive magnitude |X_C|. The negative sign appears when the result is placed into complex impedance as -j|X_C|.

Inductive Reactance Formula

The inductive reactance of an ideal inductor is:

X_L = 2 × π × f × L

Using angular frequency:

X_L = ω × L

Where:

• X_L = inductive reactance in ohms

• f = frequency in hertz

• L = inductance in henries

• ω = angular frequency in radians per second

Inductive reactance is positive, so the impedance of an ideal inductor is jX_L.

Admittance and Susceptance Formulas

Admittance is the reciprocal of impedance:

Y = 1 / Z

For ideal reactive components, admittance is purely imaginary and its imaginary part is called susceptance.

Capacitor Admittance

Y_C = jωC

|Y_C| = B_C = 2 × π × f × C

Inductor Admittance

Y_L = -j / (ωL)

|Y_L| = 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.

Reactance and Frequency

Capacitance and Inductance Trends

Capacitive Reactance Example

Calculate the reactance of a 1 µF capacitor at 1 kHz.

• f = 1000 Hz

• C = 1 µF = 0.000001 F

|X_C| = 1 / (2 × π × 1000 × 0.000001) = 159.155 Ω

The ideal capacitor impedance is approximately -j159.155 Ω. Its admittance magnitude is:

|Y_C| = 1 / 159.155 = 0.006283 S = 6.283 mS

Inductive Reactance Example

Calculate the reactance of a 10 mH inductor at 1 kHz.

• f = 1000 Hz

• L = 10 mH = 0.01 H

X_L = 2 × π × 1000 × 0.01 = 62.832 Ω

The ideal inductor impedance is approximately j62.832 Ω. Its admittance magnitude is:

|Y_L| = 1 / 62.832 = 0.015915 S = 15.915 mS

Convenient Unit Formulas

Use these shortcut forms only when the input units match the table. Otherwise, convert frequency to hertz, capacitance to farads, and inductance to henries before applying the base formulas.

Reactance at DC

DC steady state corresponds to 0 Hz, but component behavior during switching is a transient rather than a steady-state reactance calculation.

• An ideal capacitor has infinite reactance at 0 Hz and behaves as an open circuit after the transient has settled.

• An ideal inductor has zero reactance at 0 Hz and behaves as a short circuit after the transient has settled.

• A real capacitor has leakage, while a real inductor has winding resistance, so neither component is ideal at DC.

Voltage and Current Phase

Combining Resistance and Reactance

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 with admittance, where conductance and susceptance add by branch.

Inductive and Capacitive Reactance Together

In an ideal series LC circuit, the net reactance is:

X = X_L + X_C = 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.

Real Capacitors and Inductors

The calculator uses ideal component equations. Real components include parasitic and frequency-dependent effects:

• Capacitor ESR: equivalent series resistance causes loss and heating.

• Capacitor ESL: equivalent series inductance makes a capacitor appear inductive above self-resonance.

• Inductor winding resistance: copper resistance adds a real impedance component.

• Core loss: magnetic materials introduce frequency-dependent loss.

• Parasitic capacitance: an inductor may become capacitive above self-resonance.

• Component tolerance: actual capacitance or inductance may differ from the nominal value.

• Bias and temperature: component value and loss may change with operating conditions.

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.

How to Use the Reactance Calculator

1. Select capacitor or inductor mode.

2. Enter the frequency and select Hz, kHz, or MHz as required.

3. Enter capacitance or inductance and select the correct unit.

4. Calculate reactance and admittance magnitude.

5. Apply the correct sign when writing the complex impedance or admittance.

6. Compare the result with resistance, source impedance, and load impedance in the complete circuit.

7. Check the component datasheet if operating near self-resonance or outside the specified measurement frequency.

Common Reactance Calculation Mistakes

• Using capacitance in µF without converting it to farads.

• Using inductance in mH without converting it to henries.

• Omitting the factor 2π when converting frequency to angular frequency.

• Treating j as equal to -1 instead of using j² = -1.

• Forgetting that capacitive reactance is negative in complex impedance.

• Confusing reactance magnitude with complete impedance magnitude.

• Assuming resistance affects only DC.

• Applying steady-state reactance formulas directly to a switching transient.

• Ignoring ESR, winding resistance, tolerance, and self-resonance.

• Using the ideal formula beyond the component's characterized frequency range.

Frequently Asked Questions

What is the unit of reactance?

Reactance is measured in ohms, symbol Ω, just like resistance and impedance.

Why is capacitive reactance negative?

The negative sign represents the capacitor's -90° impedance phase. A calculator may show the positive magnitude, but the complex impedance is -j|X_C|.

Why is inductive reactance positive?

An ideal inductor has a +90° impedance phase, so its impedance is written as jX_L.

Does a capacitor block DC?

In ideal DC steady state, a capacitor behaves as an open circuit. During charging, discharging, or switching, transient current can still flow.

Does an inductor block DC?

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.

What is the difference between reactance and impedance?

Reactance is the imaginary component associated with energy storage. Impedance combines resistance and reactance into one complex quantity.

What is admittance?

Admittance is the reciprocal of impedance and is measured in siemens. It indicates how readily AC current flows for an applied voltage.

Can this calculator predict a real component's exact impedance?

No. It calculates the ideal reactance or admittance at one frequency. Real impedance also depends on loss, parasitic elements, tolerance, temperature, bias, and construction.

Related Online Calculation Tools

• Ohm's Law Calculator

• Capacitor Energy and Time Constant Calculator

• Series and Parallel Capacitor Calculator

• Coil Physical Properties Calculator