Free Inductive Reactance Calculator
Calculate the inductive reactance Xl of a coil from its frequency and inductance using Xl = 2π·f·L, with the result shown instantly in ohms.
Enter the AC frequency and the coil's inductance to find its inductive reactance with Xl = 2π·f·L.
Xl = 2π·f·L = ω·L, with ω = 2πf. Inductance is converted from mH to henries (mH × 10⁻³). Reactance is directly proportional to frequency, so a coil opposes high-frequency AC far more than it opposes mains-frequency current.
Quick answer
Inductive reactance is found with Xl = 2π·f·L, where f is the frequency in hertz and L is the inductance in henries. For example, a 100 mH inductor (0.1 H) at 60 Hz gives Xl = 2 × π × 60 × 0.1 ≈ 37.70 Ω. Reactance rises in direct proportion to frequency, so the same coil opposes high-frequency AC far more strongly than mains-frequency current.
Formula & method
Xl = 2 · π · f · L
- Xl — Inductive reactance in ohms (Ω)
- f — Frequency of the AC signal in hertz (Hz)
- L — Inductance of the coil in henries (H); 1 mH = 0.001 H
- π — Pi, approximately 3.14159
- ω — Angular frequency in rad/s, equal to 2πf
Inductive reactance in ohms (Ω). Frequency f is in hertz and inductance L is in henries. Since this tool accepts inductance in millihenries (mH), it divides your entry by 1000 before applying the formula. The angular-frequency form is Xl = ω·L, where ω = 2πf.
Examples
- Input
- f = 60 Hz, L = 100 mH
- Result
- Xl ≈ 37.70 Ω
- Why
- Convert L to henries: 100 mH = 0.1 H. Then Xl = 2 × π × 60 × 0.1 = 2 × 3.14159 × 6 = 37.699 Ω, which rounds to 37.70 Ω.
- Input
- f = 50 Hz, L = 200 mH
- Result
- Xl ≈ 62.83 Ω
- Why
- 200 mH = 0.2 H, so Xl = 2 × π × 50 × 0.2 = 2 × 3.14159 × 10 = 62.832 Ω. Doubling the inductance versus a 100 mH coil at 50 Hz doubles the reactance.
- Input
- f = 1000 Hz, L = 10 mH
- Result
- Xl ≈ 62.83 Ω
- Why
- 10 mH = 0.01 H, so Xl = 2 × π × 1000 × 0.01 = 2 × 3.14159 × 10 = 62.832 Ω. Notice that raising frequency from 50 Hz to 1 kHz (×20) while cutting L by ×20 leaves Xl unchanged — reactance depends on the product f·L.
- Input
- f = 60 Hz, L = 500 mH
- Result
- Xl ≈ 188.50 Ω
- Why
- 500 mH = 0.5 H, so Xl = 2 × π × 60 × 0.5 = 2 × 3.14159 × 30 = 188.496 Ω, which rounds to 188.50 Ω — five times the reactance of a 100 mH coil at the same frequency.
When to use this tool
- Sizing inductors, chokes, or filter coils for AC circuits where you need the opposition (in ohms) a coil presents at a given frequency.
- Designing or analyzing RL and RLC filters, crossovers, and resonant tank circuits, where Xl must be compared against resistance or capacitive reactance.
- Estimating the AC current through an inductor with I ≈ V / Xl (ideal coil) or I = V / √(R² + Xl²) when winding resistance R is significant.
- Checking how a coil behaves across the audio or RF band, since reactance scales linearly with frequency and changes a circuit's response dramatically.
Common mistakes
- Entering inductance in henries while the field expects millihenries (mH). A 0.1 H coil must be entered as 100, not 0.1 — otherwise the reactance comes out 1000× too small.
- Forgetting the factor of 2π. Using Xl = f·L instead of Xl = 2π·f·L underestimates reactance by about 6.28×.
- Confusing inductive reactance with capacitive reactance. Xl grows with frequency (Xl = 2πfL) while capacitive reactance shrinks with frequency (Xc = 1/(2πfC)); mixing the formulas inverts the trend.
- Treating reactance as simple resistance for power. Reactance stores and returns energy and is 90° out of phase with current, so it dissipates no real power in an ideal inductor — only impedance magnitude |Z| = √(R² + Xl²) and the phase angle matter.
Frequently asked questions
What is the formula for inductive reactance?
Inductive reactance is Xl = 2π·f·L, where f is frequency in hertz and L is inductance in henries. Equivalently Xl = ω·L with angular frequency ω = 2πf. The result is in ohms (Ω).
Does inductive reactance increase or decrease with frequency?
It increases. Because Xl = 2π·f·L is directly proportional to f, doubling the frequency doubles the reactance. This is why an inductor blocks high-frequency AC more strongly than low-frequency AC, the opposite of a capacitor.
How do I convert millihenries to henries for this calculator?
Divide millihenries by 1000: 1 mH = 0.001 H, so 100 mH = 0.1 H and 500 mH = 0.5 H. This tool accepts mH directly and converts internally, so just type the millihenry value.
What is the inductive reactance of a 100 mH coil at 60 Hz?
About 37.70 Ω. Converting 100 mH to 0.1 H and applying Xl = 2 × π × 60 × 0.1 gives 37.699 Ω, which rounds to 37.70 Ω at standard North American mains frequency.
Is inductive reactance the same as impedance?
No. Reactance Xl is the imaginary part of impedance. For a real coil with series resistance R, the impedance magnitude is |Z| = √(R² + Xl²) and the current lags the voltage by the phase angle θ = arctan(Xl/R). Reactance alone ignores R.
Why does an ideal inductor dissipate no power despite having reactance?
In a pure inductor the current lags the voltage by 90°, so the average product of voltage and current over a cycle is zero. Energy is stored in the magnetic field on one half-cycle and returned on the next, giving zero real (resistive) power loss — only reactive power.
Sources & references
- Wikipedia — Electrical reactance
- HyperPhysics — Inductive Reactance
- All About Circuits — Reactance and Impedance (Inductive)
External references open in a new tab. We are independent and not affiliated with these organizations.
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