# Inductive Reactance Calculator

Created by Purnima Singh, PhD
Reviewed by Steven Wooding
Last updated: Feb 02, 2023

Omni's inductive reactance calculator ($X_L$ calculator) allows you to determine the effective resistance (impedance) offered by an inductor coil. Just enter the inductance of the coil and the frequency of the AC signal, and the inductor impedance calculator will give you the reactance of the inductor (inductive impedance) in no time!

Continue reading to know what inductive reactance is and the formula to calculate it. You will also find an example of how to calculate inductive reactance using the $X_L$ calculator.

## What is inductive reactance? — Inductive reactance definition

Inductive reactance or inductive impedance is the effective resistance offered by an inductor to the electric current flowing through it.

It is similar to the resistance offered by a resistor in the sense that both oppose the flow of electric charge. However, in the case of resistors, the opposition is due to the collision with electrons as they pass through it. In an inductor, it is the self-induced emf that opposes the growth and decay of current.

## Inductive reactance formula

Let us consider a simple circuit consisting of an inductor connected to an AC voltage source (figure 1). As the magnitude and direction of alternating current change continuously, the inductor will oppose any change of current through it by inducing an emf in itself.

Using the formula for Faraday's law, we can express this self-induced emf ($V$) as:

$\scriptsize V = -L \cdot \left ( \frac{dI}{dt} \right)$

where:

• $L$ — Self-inductance of the inductor; and
• $dI/dt$ — Rate of change of current through the inductor.

You can use the solenoid inductance calculator to find the self-inductance of any inductor.

To find the average current ($I$) through the inductor, we can use a version of Ohm's law:

$\scriptsize I = \frac{V}{X_L}$

where the inductive reactance ($X_L$) depends on the frequency ($\nu$) of the AC signal:

$\scriptsize X_L = 2 \pi \nu L$

We can also calculate the admittance ($B_L$), i.e., how easily the circuit allows current to flow through it, as:

$\scriptsize B_L = \frac{1}{X_L}$

## Unit of inductive reactance

To find the unit of inductive reactance, let us carry out the dimensional analysis of the formula for inductive reactance:

\scriptsize \begin{align*} X_L &= 2 \pi \nu L \\ \implies & \rm \frac{1}{sec} \cdot henry \\ & = \rm \frac{1}{sec} \cdot \frac{volt}{(amp/sec)} \\ & \rm = \frac{volt}{amp} = ohm\ (\Omega) \end{align*}

The dimensional analysis of the above formula tells us that the dimensions of inductive reactance are the same as those of resistance. Hence, the inductive reactance is measured in ohm ($\Omega$).

For measuring admittance, we use the same unit as conductance, i.e., siemens ($\rm S$).

## How to use the inductive reactance calculator?

Let us see how to use the inductive reactance calculator to calculate the reactance offered by a 14 mH coil when a 100 Hz AC flows through it.

1. Enter the inductance of the coil, i.e., 14 mH.
2. Plug in the frequency of the AC signal, i.e., 100 Hz.
3. The $X_L$ calculator will display the reactance of the inductor ($X_L$), i.e, 8.80 Ω and the admittance ($B_L$), i.e, 0.11 S.
4. You can also use this inductor impedance calculator to calculate the inductance of the coil.

We also recommend checking our capacitive reactance calculator to learn about the effective resistance offered by a capacitor to the current flowing through it.

## FAQ

### How do I calculate inductive reactance?

To calculate inductive reactance, proceed as follows:

1. Find out the frequency of the AC signal.
2. Multiply the frequency by and the inductance.
3. Congrats! You have calculated inductive reactance.

### What is the inductive reactance in DC circuit?

Zero. The inductive reactance is directly proportional to the frequency of the signal. In DC circuits, the frequency is zero. Hence the inductive reactance in DC circuits is also zero.

### What is the difference between inductive reactance and capacitive reactance?

The main differences between inductive reactance and capacitive reactance are:

• Inductive reactance is the effective resistance offered by an inductor. Capacitive reactance is the effective resistance offered by a capacitor.
• Inductive reactance is directly proportional to the frequency of the signal and the inductance. Capacitive reactance is inversely proportional to the frequency of the signal and the capacitance.

### How do I calculate inductance from reactance?

To calculate inductance from reactance, follow the given instructions:

1. Multiply the frequency of the AC signal with .
2. Divide the reactance by the value from step 1.
3. You have calculated inductance from reactance!

### What is the SI unit of inductive reactance?

Ohm. The SI unit of inductive reactance is the same as that of resistance, i.e., ohm.

Purnima Singh, PhD
Inductance (L)
mH
Frequency (f)
Hz
Reactance (Xʟ)
Ω
S
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