Inductive reactance tells you how much an inductor resists alternating current. It grows with frequency and with inductance, so the same coil blocks more current at high frequencies than at low ones. The good news is that the maths takes only one formula and a few careful unit conversions.
The formula
Inductive reactance is written as XL and measured in ohms. The formula is XL = 2 x pi x f x L, where f is the frequency in hertz and L is the inductance in henries. Pi is about 3.1416, so 2 x pi is about 6.2832. That shortcut is handy: XL is roughly 6.2832 x f x L.
The most common mistake is mixing up units. Inductance is often given in millihenries (mH) or microhenries (uH), not henries. Convert first: 1 mH = 0.001 H and 1 uH = 0.000001 H. Frequency must be in hertz, so 1 kHz = 1,000 Hz and 1 MHz = 1,000,000 Hz.
Worked example
Take a 100 mH inductor in a 50 Hz circuit. First convert the inductance: 100 mH = 0.1 H. Then apply the formula: XL = 6.2832 x 50 x 0.1 = 31.42 ohms. So the inductor opposes the current with about 31.4 ohms of reactance at 50 Hz.
Now raise the frequency to 5 kHz with the same inductor. XL = 6.2832 x 5,000 x 0.1 = 3,141.6 ohms. The reactance is 100 times larger because the frequency is 100 times larger. This is why inductors are used to block high frequencies while letting low frequencies pass.
From reactance to current
Once you know XL, you can find the current with a version of Ohm’s law for AC circuits: I = V / XL. If 10 volts drive our 31.42 ohm example, the current is 10 / 31.42 = 0.318 amps, or about 318 milliamps. This only holds when the inductor is the only thing limiting the current; with a resistor in series you need impedance, not just reactance.
Remember that reactance is not resistance. A perfect inductor wastes no power as heat, even though it limits current. The energy is stored in the magnetic field during one half of the cycle and returned during the next. Real inductors have some winding resistance too, which is a separate value.
Mistakes to avoid
Forgetting to convert millihenries to henries is the number one error, and it makes the answer 1,000 times too big. Using kilohertz as if it were hertz is the second one. Also check whether your frequency is the mains frequency (50 or 60 Hz) or a signal frequency, which can be thousands of times higher.
Another trap is applying the formula to DC circuits. At 0 Hz, XL = 0, which matches reality: a steady DC current sees an ideal inductor as a short circuit once the magnetic field has settled. If your circuit uses DC, inductive reactance is the wrong tool.
Inductors in series and parallel
Inductors combine like resistors, not like capacitors. In series, inductances add: a 10 mH coil in series with a 20 mH coil gives 30 mH total. In parallel, they combine by reciprocals: 10 mH in parallel with 20 mH gives 1 / (1/10 + 1/20) = 6.67 mH.
That matters for reactance because the total inductance sets XL. The 30 mH series pair at 1 kHz has XL = 6.2832 x 1,000 x 0.03 = 188.5 ohms. The 6.67 mH parallel pair at the same frequency has XL = 6.2832 x 1,000 x 0.00667 = 41.9 ohms. Same two coils, very different reactance, depending only on wiring.
Try it faster with the tool
You can follow every step above by hand, but the free Inductive Reactance Calculator – XL Formula, Free Online does the arithmetic for you. Enter your numbers and it gives the answer right away, so you can check your hand calculation or skip straight to the result.
Quick tips
- Always convert to hertz and henries before you multiply.
- Double-check the frequency: mains, audio, and radio frequencies differ by orders of magnitude.
- If the answer looks absurdly large or small, recheck the unit conversions first.