What inductive reactance actually is
Inductive reactance is the opposition a coil offers to alternating current, measured in ohms like resistance but produced by a completely different mechanism. Current through a coil builds a magnetic field, and a changing field induces a voltage that opposes the change that created it. That induced back-EMF is what limits the current, and it exists only while the current is changing.
The defining relation is v = L · di/dt. To force current through an inductor you must supply voltage in proportion to how fast you want that current to change. Raise the frequency of a sine wave of fixed amplitude and you demand a faster change, so a larger voltage is needed for the same current — the opposition rises. Reactance is therefore directly proportional to frequency, which is the mirror image of a capacitor, whose reactance falls with frequency in the capacitive reactance calculator.
This is why a coil that measures four ohms on a multimeter can still limit the current on a 120 V line to about three amps. The meter reads only the winding resistance. The reactance is invisible to a DC measurement and is usually the dominant term the moment alternating current is applied.
The formula, term by term
The working equation is XL = 2πfL, the standard result of sinusoidal steady-state AC theory. It has only three parts.
The 2πf is angular frequency ω, in radians per second. At 60 Hz, ω = 376.99 rad/s. Angular frequency, not cycles per second, is what the differentiation di/dt actually produces when you push a sine wave through it; the 2π is simply the conversion.
The inductance L is in henries, and it multiplies directly. Double the turns on a coil and, for a fixed magnetic path, inductance goes up roughly fourfold because it scales with the square of turns — so reactance goes up fourfold too.
The product is already in ohms, so you can use it in Ohm's law immediately. With a lossless coil, I = V ÷ XL, and the reactive power the coil exchanges with the supply is Q = V2 ÷ XL volt-amperes reactive, lagging.
Real coils are wound from wire, so they carry a series resistance. Once that resistance is in play the impedance is a vector sum, |Z| = √(R2 + XL2), the current is V ÷ |Z|, and the correct reactive power is I2XL. The calculator uses that form throughout; it collapses to V2 ÷ XL whenever you set the resistance to zero.
Two derived numbers follow. The phase angle θ = arctan(XL ÷ R) is exactly +90° for a lossless coil, the textbook statement that current lags voltage by a quarter cycle. The quality factor Q = XL ÷ R says how close to a pure reactance the part is at that frequency; it is the same Q that sets the sharpness of a tuned circuit.
Worked example: a 100 mH choke on 120 V, 60 Hz
Take a 100 mH filter choke whose winding measures 4 Ω on a meter, connected across 120 V at 60 Hz. Every step is reproducible by hand.
- Convert the inductance to henries. 100 mH = 0.100 H.
- Find the angular frequency. ω = 2π × 60 = 376.991 rad/s.
- Multiply for reactance. XL = 376.991 × 0.100 = 37.699 Ω.
- Combine with the winding resistance. |Z| = √(42 + 37.6992) = √(16 + 1421.22) = √1437.22 = 37.911 Ω. Note how little the 4 Ω adds: squaring buries the smaller term.
- Apply Ohm's law. I = 120 ÷ 37.911 = 3.165 A. Had you ignored the resistance entirely you would have got 120 ÷ 37.699 = 3.183 A, an error of only 0.6%.
- Find the phase angle. θ = arctan(37.699 ÷ 4) = arctan(9.425) = 83.94° lagging.
- Find the quality factor. Q = 37.699 ÷ 4 = 9.42.
- Split the power. Copper loss P = I2R = 3.1652 × 4 = 40.1 W of genuine heat; reactive power Q = I2XL = 3.1652 × 37.699 = 377.7 VAR borrowed and returned each cycle.
Now change the frequency. At 400 Hz the same coil has XL = 2π × 400 × 0.100 = 251.33 Ω, so the lossless current falls to 120 ÷ 251.33 = 0.477 A. The coil has become almost seven times more effective at blocking, in exact proportion to the frequency ratio 400 ÷ 60 = 6.667. That proportionality is why a choke placed in series with a load discriminates in favour of the fundamental: it opposes a harmonic at 400 Hz nearly seven times as hard as it opposes the 60 Hz component you want to pass.
How to read the number you get
Compare the reactance against the resistance in the same branch, because their ratio decides everything. When XL is much larger than R, the phase angle approaches 90°, the power factor of that branch approaches zero, and nearly all the volt-amperes are reactive. When they are equal, the phase angle is exactly 45° and the impedance magnitude is √2 times either one. That equality is also the corner frequency of an RL filter.
Read the quality factor as a purity score at one specific frequency. Air-cored RF inductors typically reach Q in the range of 50 to 200; ferrite power inductors are often in the tens; iron-cored mains chokes and motor windings are frequently below 10 because the copper resistance is large and core losses add more. Q is not a fixed property of a part: it climbs with frequency while reactance grows faster than resistance, then falls again once skin effect, proximity effect and core loss take over.
Treat the copper-loss figure as the thermal design number. Unlike reactive power, it is real heat inside the winding, and it grows with the square of current. A coil that is fine at 1 A dissipates four times as much at 2 A.
Finally, sanity-check against saturation. This calculator is linear: it assumes inductance stays at the value you entered. Iron and ferrite cores lose inductance sharply once the flux density passes the material limit, and the current then rises above what this page predicts, often violently. Manufacturers publish an inductance-versus-current curve for exactly this reason, and a coil chosen for a mains application must also be checked at the peak of the waveform, not the RMS value.
Inductive reactance in ohms at common frequencies
| Inductance | 60 Hz | 1 kHz | 10 kHz | 100 kHz | 1 MHz | 10 MHz |
|---|---|---|---|---|---|---|
| 1 µH | 377.0 µΩ | 6.283 mΩ | 62.83 mΩ | 0.6283 Ω | 6.283 Ω | 62.83 Ω |
| 10 µH | 3.770 mΩ | 62.83 mΩ | 0.6283 Ω | 6.283 Ω | 62.83 Ω | 628.3 Ω |
| 100 µH | 37.70 mΩ | 0.6283 Ω | 6.283 Ω | 62.83 Ω | 628.3 Ω | 6.283 kΩ |
| 1 mH | 0.3770 Ω | 6.283 Ω | 62.83 Ω | 628.3 Ω | 6.283 kΩ | 62.83 kΩ |
| 10 mH | 3.770 Ω | 62.83 Ω | 628.3 Ω | 6.283 kΩ | 62.83 kΩ | 628.3 kΩ |
| 100 mH | 37.70 Ω | 628.3 Ω | 6.283 kΩ | 62.83 kΩ | 628.3 kΩ | 6.283 MΩ |
| 1 H | 377.0 Ω | 6.283 kΩ | 62.83 kΩ | 628.3 kΩ | 6.283 MΩ | 62.83 MΩ |
Every row is ten times the row above and every column ten times the one to its left, because reactance is directly proportional to both inductance and frequency. The 377 Ω entry for 1 H at 60 Hz is worth memorising: it is simply ω itself.
Mistakes that produce a wrong reactance
- Leaving the inductance in millihenries. The formula needs henries. A 100 mH coil entered as 100 gives an answer a thousand times too large; the unit selector on this page prevents it.
- Trusting a multimeter reading. An ohmmeter measures only the winding resistance and tells you nothing about reactance. A 4 Ω reading on a mains choke is the small term, not the big one.
- Using the marked inductance at the operating current. Ferrite and powdered-iron cores lose inductance as current rises, and the datasheet curve, not the nominal value, is what applies near the rated current.
- Working past self-resonance. Every winding has turn-to-turn capacitance. Above the coil's self-resonant frequency that capacitance dominates and the impedance falls again, so the rising straight line in the table above stops being true.
- Assuming the source is a clean sine. Reactance rises with frequency, so a coil opposes harmonics more strongly than the fundamental. On a distorted supply the current waveform is not simply scaled — it is reshaped.
- Confusing reactive power with consumption. The VAR figure loads the conductors, the transformer and the supply, but an ideal inductor returns every joule it borrows. Only the copper and core losses are billable energy.
Where this fits among the other AC tools
Reactance is the input to nearly every other AC calculation rather than the end of one. Put an inductor and a capacitor in the same circuit and their reactances subtract, because they are 180° apart in phase; the frequency at which they cancel exactly is given by the RLC resonant frequency calculator, and the impedance of the full network at any frequency by the RLC impedance calculator.
In power work the same number appears in a different costume. A motor is, electrically, a large inductance in series with a resistance, so it draws lagging reactive power exactly as this page describes; that lagging VAR is what a capacitor bank cancels in the power-factor correction capacitor calculator, and it is why a motor's nameplate current exceeds what its horsepower alone would suggest in the motor full load amps calculator. Pair an inductor with a resistor instead and the corner frequency logic is the mirror of the RC case treated in the RC filter cutoff frequency calculator, with fc = R ÷ (2πL).
What this page deliberately does not model: core loss, which behaves like extra series resistance that grows with frequency and flux; skin and proximity effects, which raise the effective winding resistance well above the DC value at high frequency; mutual coupling to nearby windings; and saturation. For precision work at radio frequencies, measure the coil with an impedance analyser at the frequency you actually use.
Key terms
- Reactance (X)
- The ohms of opposition an ideal inductor or capacitor presents to sinusoidal current. Reactance stores and returns energy; resistance dissipates it.
- Back-EMF
- The voltage a changing magnetic field induces in the coil that produced it, always in the direction that opposes the change in current. It is the physical origin of inductive reactance.
- Quality factor (Q)
- XL divided by the effective series resistance at a given frequency. High Q means the coil is close to a pure reactance and gives a sharp resonance.
- Saturation
- The point at which a magnetic core can carry no more flux, so inductance collapses toward the air-cored value and current rises steeply.