How to Solve Inductive Reactance Formula Calculator

This inductive reactance formula calculator can calculate inductance from reactance and can calculate the inductive reactance. Inductors have an effective resistance known as reactance that varies with frequency. When a direct current (DC) is applied to a capacitor, it acts as a short circuit. But as you apply higher frequencies to an inductor, its reactance begins to approach an open circuit. It’s important to note that while reactance is in ohms units, it is not the same as resistance. However, you can still perform calculations on it using ohms law. With a purely resistive load, the voltage over the resistor stays in phase with the current going through it, but in an inductor, the voltage leads the current by 90 degrees for any given frequency. You may also be interested in the capacitive reactance calculator.

The calculator below finds the inductive reactance (XL) for a given frequency in hertz (Hz).

Inductive Reactance Calculator

Inductive Reactance Formula

The formula used to perform this calculation is below. Remember to convert all units to Henries, Hertz, and Ohms when using the Inductive Reactance Formula.

Inductive Reactance Formula: 
\fn_jvn \small X_{L}=2\pi fL
 where:
     • XL = Inductive Reactance (ohms)
     • f = Frequency (hertz)
     • L = Inductance (henries)

Solution Examples

We will use the formula above to work out a few real world example problems. You can always check your work with the calculator.

Example #1:

For this example, we will have a 1MHz signal and a 1uH inductor. We will be solving for the inductive reactance of the inductor.

The first thing that needs to be done is to get all of the values into the correct units. The frequency of 1MHz is 1000000Hz, and 1uH is 0.000001 Henries. We will enter the values into the formula as shown.

\fn_jvn \small X_{L}=2\pi fL=2\pi 1000000\cdot 0.000001=2\pi\approx =6.3\Omega

The result is that when a signal of 1MHz is applied to this inductor, it has a reactance of 6.3 ohms.

Example #2:

For this example, we have a 1mH inductor, and we want to know what frequency we need to get an inductive reactance of 470 ohms.

As always, the first step is to convert everything to the correct units. The 1mF inductor is 0.001 Henries, and the 470 ohms is already in ohms. The formula above solves for inductive reactance (XL), so we will need to use algebra to rearrange the variables to solve for the frequency.

\fn_jvn \small X_{L}=2\pi fL\Rightarrow \frac{X_{L}}{2\pi L}=f

Now that we have solved for frequency, we can plug in the variables and solve for f.

\fn_jvn \small f=\frac{X_{L}}{2\pi L}=\frac{470}{2\pi 0.001}\approx 74802.8Hz

To use more comfortable units for our result, let’s convert the 74802.8Hz frequency into 74.8kHz.

The result is that if you want a 1mF inductor to have an inductive reactance of 470 ohms, you need to expose it to a frequency of 74.8kHz.

Example #3:

For this example, we have a signal of 1kHz, and we want to figure out what value of inductor we need to get an inductive reactance of 10 ohms.

We first need to convert everything to the appropriate units. 1kHz is 1000 Hz, and 10 ohms is already in the units of ohms. We need to use algebra to convert the formula for inductive reactance to solve for inductance.

\fn_jvn \small X_{L}=2\pi fL \Rightarrow \frac{X_{L}}{2\pi f}=L

Now that we have solved for inductance, we can plug in the variables and solve L.

\fn_jvn \small L=\frac{X_{L}}{2\pi f}=\frac{10}{2\pi 1000}=0.00159 H

This result is tiny. So we need to convert it to appropriate units. 0.00159 Henries is equal to 1.59 mH.

The result is that if you have a 1kHz signal and want an inductive reactance of 10 ohms, you need to use an inductor with a value of about 1.59 mH.

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