Inductive Reactance Calculator

Reactance, angular frequency, and current from frequency, inductance, and source voltage.

What it does

An inductor opposes changes in current. In a direct current circuit it eventually behaves like a plain wire, but in an alternating current circuit it keeps resisting, because the current never stops changing direction. That opposition is called inductive reactance and is measured in ohms, like resistance.

The formula is XL = 2 pi f L. Frequency f is in hertz and inductance L is in henries. The 2 pi factor converts ordinary frequency into angular frequency, omega, in radians per second. Because both f and L sit in the numerator, reactance grows when either one grows: a fast signal or a large coil produces more opposition.

The default example is a 60 Hz source feeding a 3 mH inductor at 120 V RMS. Angular frequency is 2 pi x 60 = 376.99 rad/s. Reactance is 376.99 x 0.003 = 1.131 ohms. Current is 120 / 1.131 = 106.103 A RMS, which is why small inductors can carry surprisingly large currents at low reactance.

Reactance is not resistance. A resistor turns electrical energy into heat, while an ideal inductor stores energy in its magnetic field and returns it later. That is why the current lags the voltage by 90 degrees and why real power dissipation in a pure inductor is zero, even though the current can be large.

The tool accepts inductance in henries, millihenries, or microhenries, converts to henries, and reports reactance with three significant decimals. It assumes an ideal inductor with no winding resistance or stray capacitance. Real components have both, and at high frequency those parasitics can dominate the behavior.

How to use

1. Enter the AC frequency in hertz.
2. Enter the inductance value.
3. Pick the inductance unit: henries, millihenries, or microhenries.
4. Enter the RMS voltage across the inductor.
5. Read the reactance in ohms and the angular frequency in rad/s.
6. Read the RMS current and compare it with the component's current rating.

Formula

f

Frequency of the AC source in hertz.

L

Inductance in henries after unit conversion.

XL

Inductive reactance in ohms.

V

RMS voltage across the inductor, in volts.

The formula assumes a sinusoidal source and an ideal inductor. Reactance is a magnitude, so the impedance is jXL, with the positive imaginary sign reflecting the 90 degree phase lead of voltage over current. At DC, frequency is zero and the ideal reactance is zero, which is why an inductor looks like a short circuit to steady current.

Worked example

Reference table

Limits

• Assumes an ideal inductor with no winding resistance, core loss, or stray capacitance.
• Assumes a sinusoidal source at a single frequency.
• Does not model saturation, which lowers effective inductance at high current.
• Ignores parasitic capacitance that can make a real inductor look capacitive at high frequency.

Common mistakes

• Leaving the inductance in millihenries while using the henry formula.
• Using peak voltage instead of RMS voltage and comparing the result with an RMS rating.
• Confusing reactance with impedance when resistance is also present.
• Expecting the current to lead the voltage; in an inductor it lags.
• Ignoring the inductor's current rating, since low reactance can mean very high current.

Try it yourself

Quick checks. Answers sit tucked under each question.

Questions

Sources

• OpenStax College Physics: Reactance, inductive and capacitive
• University of Hawaii Pressbooks: Reactance, inductive and capacitive

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