Inductive Reactance Calculator

What the inductive reactance calculator does

An inductor opposes alternating current by an amount that grows with frequency, called its inductive reactance. This calculator finds that reactance from the inductance and the frequency, and also reports its reciprocal, the susceptance.

Below is what inductive reactance is, the equation behind it, why it rises with frequency, and a worked example.

How to use it

1. Enter the inductance, choosing its unit.
2. Enter the frequency of the alternating signal.
3. Press Calculate for the inductive reactance, or Reset to clear it.

What inductive reactance is

Inductive reactance is the opposition an inductor presents to alternating current. An inductor is typically a coil of wire, and it resists changes in the current flowing through it. Because alternating current is constantly changing, the inductor constantly opposes it, and this opposition, measured in ohms, is the inductive reactance. Like capacitive reactance, it depends on frequency, but in the opposite way: an inductor lets low-frequency current pass easily and resists high-frequency current strongly.

The opposition arises from electromagnetic induction. As current changes, it creates a changing magnetic field in the coil, which in turn induces a voltage that opposes the change, a kind of electrical inertia. The faster the current alternates, the more violently it is changing, and the harder the inductor pushes back, so the opposition is greater at high frequencies. At low frequencies, and for steady direct current, the inductor offers little opposition, behaving almost like a plain wire. This calculator computes the inductive reactance from the inductance and frequency.

The equation it uses

Inductive reactance is the product of the angular frequency and the inductance:

X_L = 2πfL

Here X_L is the inductive reactance, f is the frequency, and L is the inductance, with the factor of two pi turning the frequency into an angular frequency. Both the frequency and the inductance multiply together, so increasing either one raises the reactance. This is the opposite arrangement from a capacitor, where the equivalent quantities sit in the denominator. The calculator evaluates this directly, and also reports the reciprocal of the reactance, the susceptance, which measures how easily the inductor passes alternating current.

Why it rises as frequency rises

The defining feature of inductive reactance is that it increases with frequency, growing in direct proportion. At very low frequencies, approaching direct current, the reactance is small, and for true direct current it is essentially zero, so an inductor passes steady current freely, acting like an ordinary wire. As the frequency climbs, the reactance rises steadily, choking off more and more of the current.

This is why inductors are described as passing low frequencies and blocking high ones, the exact reverse of capacitors. The effect is widely used: an inductor can let a steady or slowly varying current through while blocking rapid fluctuations, which is the basis of filters that smooth out high-frequency noise and chokes that suppress unwanted signals. The inductance matters too, with larger inductors having higher reactance at any given frequency. Recognising that reactance grows with frequency is the key to understanding how inductors shape signals, and the calculator makes it concrete by computing the reactance at any frequency you choose.

The mirror image of a capacitor

Inductors and capacitors are electrical opposites, and their reactances show it clearly. A capacitor's reactance falls as frequency rises, while an inductor's reactance climbs; a capacitor blocks direct current while passing high frequencies, while an inductor passes direct current while blocking high frequencies. Where a capacitor stores energy in an electric field between plates, an inductor stores it in a magnetic field around a coil. Almost everything about one is the reverse of the other.

This opposition is what makes the two components so powerful when used together. Combining inductors and capacitors lets designers build circuits that respond to a particular frequency, since at some frequency the two reactances become equal and interact in special ways, the basis of tuning and resonance. Like capacitive reactance, inductive reactance stores and returns energy rather than dissipating it as heat, so it is lossless, distinct from resistance. Keeping the mirror-image relationship in mind makes the behaviour of both components easier to grasp, and this calculator handles the inductive side of that pairing.

Units and precision

The calculator takes the inductance in henries or its smaller multiples, from henries down to nanohenries, and the frequency in units from hertz up to terahertz, returning the inductive reactance in ohms and its multiples, along with the susceptance in siemens. It applies the reactance relationship exactly. The result is the opposition the inductor presents at the frequency you enter, which will be higher at higher frequencies.

A worked example

Suppose a 1-millihenry inductor carries a signal at 1 kilohertz.

The inductive reactance is X_L = 2πfL = 2π × 1000 × 0.001 ≈ 6.28 ohms. Raise the frequency to 10 kilohertz and the reactance rises to about 62.8 ohms, ten times higher, since reactance is directly proportional to frequency. At very low frequencies, the same inductor would present almost no opposition, passing the current like a plain wire.

Questions people ask

How do you calculate inductive reactance?

Use X_L = 2πfL, from the frequency and the inductance. Both multiply together, so larger values give higher reactance.

Why does inductive reactance rise with frequency?

Because the inductor opposes changes in current, and higher frequency means faster changes, which it resists more strongly. For steady direct current it offers almost no opposition.

How is an inductor the opposite of a capacitor?

Its reactance rises with frequency rather than falling, and it passes direct current while blocking high frequencies, the reverse of a capacitor. It stores energy magnetically, not electrically.

What is the reactance for direct current?

Essentially zero. At zero frequency the formula gives no reactance, so an inductor passes steady direct current freely, like an ordinary wire.

References

A quick note on where the physics comes from. Inductive reactance and alternating-current behaviour are standard physics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The units follow NIST. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 2, Section 15.3, RLC Series Circuits with AC. https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac
2. HyperPhysics, Inductive Reactance. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indreact.html
3. National Institute of Standards and Technology (NIST), SP 811, Guide for the Use of the International System of Units. https://www.nist.gov/pml/special-publication-811