Inductor Reactance Calculator & Formula

This calculator works out the inductive reactance (XL) of an inductor in ohms (Ω) when you enter its inductance in henries (H) and the frequency of the AC signal in hertz (Hz). You get the reactance value instantly, which tells you how much the inductor opposes the alternating current at that frequency. The formula used is the standard one from electronics: XL = 2πfL.

Formula

The inductive reactance formula is:

XL = 2πfL

Where:

• XL = inductive reactance in ohms (Ω)
• π ≈ 3.14159
• f = frequency of the alternating current in hertz (Hz)
• L = inductance in henries (H)

This formula comes from the relationship between voltage and current in an inductor. The reactance is the imaginary part of the inductor’s impedance, representing the opposition to changes in current. It is directly proportional to both frequency and inductance.

Worked Example

Using the default values from the calculator: L = 10 mH (millihenries) and f = 1000 Hz.

1. Convert inductance to henries: 10 mH = 10 / 1000 = 0.01 H
2. Plug into the formula: XL = 2 × π × 1000 × 0.01
3. Calculate: 2 × 3.14159 × 1000 × 0.01 = 62.8318 Ω
4. Rounded to two decimal places: XL = 62.83 Ω

The calculator gives the same result: 62.83 Ω. The second output shows the same value in kilohms: 0.063 kΩ.

When to Use This Calculator

You need inductive reactance whenever you are designing or analyzing circuits that handle alternating current (AC), especially at higher frequencies. Common situations include:

• Designing filters (low-pass, high-pass, band-pass) where inductors are used with capacitors.
• Calculating the impedance of a coil in an RF circuit.
• Determining the current through an inductor in an AC circuit using Ohm’s law (I = V / XL).
• Checking the behavior of inductors in power supplies or audio crossover networks.
• Understanding how a choke blocks high-frequency noise while passing low-frequency signals.

How to Read the Result

The result is the magnitude of the inductor’s opposition to AC current at the given frequency. A higher reactance means the inductor more strongly resists changes in current. At DC (frequency = 0 Hz), the reactance is zero, so the inductor acts like a short circuit (just its wire resistance). As frequency increases, reactance rises linearly. This is why inductors are used to block high-frequency signals while allowing low-frequency or DC to pass.

Remember that reactance is not the same as resistance. Resistance dissipates power as heat; reactance stores energy temporarily in a magnetic field and returns it to the circuit. In AC analysis, reactance is combined with resistance to give impedance (Z), which is a complex quantity. For a pure inductor, impedance Z = jXL, where j is the imaginary unit.

Common Mistakes and Unit Mix-Ups

The most frequent error is forgetting to convert millihenries (mH) or microhenries (µH) to henries. The formula requires inductance in henries. For example, 100 µH = 0.0001 H. If you plug in 100 instead, your reactance will be off by a factor of 10,000.

Another common mistake is using frequency in kHz instead of Hz. Always convert to Hz: 1 kHz = 1000 Hz. The calculator handles these conversions for you if you enter the value in the specified unit (mH and Hz), but if you are doing manual calculations, double-check your units.

Rounding too early can also introduce errors, especially when multiplying by π. Keep at least three significant figures during intermediate steps.

Limitations of the Formula

The formula XL = 2πfL assumes an ideal inductor with no resistance and no capacitance between turns. Real inductors have:

• DC resistance (DCR) from the wire, which adds a resistive component to impedance.
• Parasitic capacitance between windings, which causes self-resonance at high frequencies. Above the self-resonant frequency, the inductor behaves like a capacitor.
• Core losses (hysteresis and eddy currents) if the inductor has a magnetic core, which add effective resistance.

At frequencies much lower than the self-resonant frequency, the formula is very accurate. For precise work at high frequencies, you need the full impedance model or a datasheet from the manufacturer.

Alternatives and Related Calculations

If you are working with capacitors, you will also need capacitive reactance: XC = 1 / (2πfC). This is the mirror image of inductive reactance—it decreases with frequency. Together, XL and XC determine the impedance of RLC circuits. For a series RLC circuit, total impedance magnitude is Z = √(R² + (XL – XC)²). You can also calculate the resonant frequency where XL = XC: f = 1 / (2π√(LC)).

If you know the voltage and frequency, you can find the current through the inductor using I = V / XL. For example, with 10 V RMS at 1 kHz and a 10 mH inductor (XL = 62.83 Ω), the current is about 0.159 A (159 mA).

Frequently Asked Questions

What is the difference between inductance and inductive reactance?

Inductance (L) is a physical property of the coil—it depends on the number of turns, core material, and geometry. It is measured in henries and does not change with frequency. Inductive reactance (XL) is the effect of that inductance at a particular frequency. It is a dynamic quantity that increases as frequency increases. You can think of inductance as the “capacity” to store magnetic energy, and reactance as how strongly that capacity opposes current at a given frequency.

Does inductive reactance cause power loss?

No, not in an ideal inductor. Reactance stores energy in the magnetic field during one part of the AC cycle and returns it to the circuit during the other part. Over a full cycle, the net energy is zero. Real inductors do lose some power due to the wire’s resistance and core losses, but that is separate from reactance. In a purely reactive component, the voltage and current are 90 degrees out of phase, so the average power is zero.

How do I convert mH to H?

To convert millihenries to henries, divide by 1000. For example, 5 mH = 5 / 1000 = 0.005 H. For microhenries (µH), divide by 1,000,000. The calculator automatically converts mH to H in its formula, so you can enter the value directly in mH.

What happens to inductive reactance at DC (0 Hz)?

At DC, the frequency is zero, so XL = 2π × 0 × L = 0 Ω. The inductor offers no reactance to a steady DC current. It behaves like a short circuit (only the wire resistance remains). This is why inductors are often used to pass DC while blocking high-frequency AC noise.

Why does an inductor block high frequency but pass low frequency?

Because reactance is directly proportional to frequency. At low frequencies, XL is small, so the inductor offers little opposition. At high frequencies, XL becomes large, effectively blocking the current. This property is used in low-pass filters, where an inductor in series with the load passes low frequencies and attenuates high frequencies.

Can I use this calculator for a coil with an iron core?

Yes, as long as you know the inductance value. The formula works for any inductor, regardless of core type. However, the inductance of an iron-core inductor can vary with current (saturation) and frequency (eddy currents), so the value you enter should be the effective inductance at your operating point. For most small-signal applications, the datasheet value is accurate enough.

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in L | Inductance | mH | 10 | 0
in f | Frequency | Hz | 1000 | 0
out xl | Inductive reactance | Ω | 2 * pi * (L / 1000) * f | 2
out xl_kohm | Reactance in kΩ | kΩ | (2 * pi * (L / 1000) * f) / 1000 | 3