What does this calculator do?
Inductive reactance is the opposition an inductance offers to an alternating signal. It grows with frequency.
XL = 2πfL
Enter the values in the units shown. The calculator converts units automatically and displays the result in practical units.
Worked example
With f = 1 kHz and L = 10 mH, XL ≈ 62.83 Ω.
Practical tips
- Convert millihenries to henries when you calculate by hand.
- At high frequencies, also consider series resistance and parasitic capacitance.
- Reactance alone is not the total impedance of a real component.
Common mistake to avoid
Real inductance can change with current, core material and frequency; the formula describes the ideal model.
Complete inductive reactance formulas
An inductor opposes changes in current because it induces a voltage v = L · di/dt. With a sine wave, that opposition grows in direct proportion to frequency and inductance:
- Inductive reactance: XL = 2π · f · L = ω · L (Ω, with f in Hz and L in henries)
- Required inductance: L = XL / (2π · f)
- Frequency for a given reactance: f = XL / (2π · L)
- Impedance of a real coil (series R): |Z| = √(R² + XL²)
- Phase angle: φ = arctan(XL / R); in an ideal inductor the current lags the voltage by 90°
- Current: I = V / |Z| (RMS values)
Remember the conversions: 1 mH = 10⁻³ H and 1 µH = 10⁻⁶ H. The calculator takes L in millihenries and converts it for you.
Typical values
| Inductance | Frequency | XL | Typical context |
|---|---|---|---|
| 10 mH | 60 Hz | ≈ 3.77 Ω | Small coil on the mains |
| 100 mH | 60 Hz | ≈ 37.7 Ω | Low-frequency filter or choke |
| 1 H | 60 Hz | ≈ 377 Ω | Reactor or transformer winding |
| 10 mH | 1 kHz | ≈ 62.83 Ω | Audio crossover, LC filters |
| 22 µH | 500 kHz | ≈ 69.1 Ω | Switching converter inductor |
| 1 µH | 100 MHz | ≈ 628 Ω | RF choke |
Ideal values from XL = 2πfL. Note that the same 10 mH coil has about 16.7 times more reactance at 1 kHz than at 60 Hz. On 50 Hz mains, multiply the 60 Hz values by 5/6.
Worked example: a real coil on 60 Hz
A 100 mH coil with 20 Ω of winding resistance is connected to 12 V RMS at 60 Hz.
- Reactance: XL = 2π × 60 × 0.1 ≈ 37.70 Ω.
- Impedance: |Z| = √(20² + 37.70²) ≈ 42.68 Ω.
- Current: I = 12 / 42.68 ≈ 0.281 A.
- Phase angle: φ = arctan(37.70 / 20) ≈ 62.05°; the current lags the voltage by about 62°.
Using only the winding resistance (20 Ω) would have predicted 0.6 A, more than twice the real value. On DC, however, only R matters and the current really would be 0.6 A.
Common mistakes
- Not converting units: using 100 instead of 0.1 H multiplies the result by 1000.
- Adding R and XL directly: they are in quadrature (90° apart) and combine as √(R² + XL²).
- Assuming inductance is constant: with an iron or ferrite core, L drops when high currents saturate the core.
- Ignoring the self-resonant frequency: above it, the capacitance between turns dominates and the coil no longer behaves as an inductor.
- Using the wrong frequency: with non-sinusoidal signals, each harmonic sees a different reactance.
Frequently asked questions
Why does inductive reactance increase with frequency?
Because the induced voltage depends on how fast the current changes (L · di/dt). At higher frequencies the current changes faster, so the inductor opposes it more.
What is the reactance of a coil on DC?
Zero, because f = 0. In steady state the coil only presents its winding resistance. The switch-on transient is covered by the RL time constant.
Does reactance consume power?
Ideally, no: the energy is stored in the magnetic field and returned every cycle. It does create reactive power (var), which affects the power factor even though it does no useful work.
To combine inductive reactance with resistors and capacitors, use the series RLC impedance calculator, or compare it with capacitive reactance.
Educational tool. Check tolerances, datasheets, standards and real operating conditions before using the results in critical applications.