Inductive Reactance Calculator
Calculate XL from inductance and frequency, then examine a practical series R–L circuit with impedance magnitude, RMS current, phase angle, power factor, real power, reactive power, apparent power, and peak magnetic energy.
Sinusoidal steady-state model. The calculation assumes a linear inductance at one frequency. Real coils can change with current, temperature, magnetic core state, winding capacitance, and frequency.
Coil response result
Complex-impedance trace
XL = 2π × 60.000 Hz × 0.100000 H = 37.699 Ω Z = 10.000 + j37.699 Ω; |Z| = 39.003 Ω I = 120.000 V ÷ 39.003 Ω = 3.077 A RMS
Reactance describes frequency-dependent opposition
Inductance
Inductance describes how voltage develops when current changes. It is measured in henries. A magnetic core, winding geometry, turns, air gap, nearby conductors, and operating point all influence the effective value. The entered value should match the relevant frequency and bias condition.
Inductive reactance
XL is the magnitude of an ideal inductor’s AC opposition in ohms. It rises in direct proportion to frequency and inductance. At zero-frequency steady-state DC, ideal XL is zero, although a real winding still has resistance and switching transients still matter.
Impedance
Impedance combines resistance and reactance as a complex quantity. For the series branch used here, Z = R + jXL and magnitude is the square root of R squared plus XL squared. Current magnitude is RMS voltage divided by that impedance magnitude.
The U.S. Department of Energy electrical fundamentals handbook describes inductive reactance as opposition to alternating current caused by inductance and gives XL = 2πfL. It also shows current lagging voltage by 90 degrees for the pure inductive case. That phase relationship is why XL cannot simply be added to resistance as ordinary scalar ohms.
Worked example: 100 mH at 60 Hz
The default inductance is 100 millihenries, or 0.100 henry. At 60 Hz, angular frequency is 2π × 60, approximately 376.991 radians per second. Multiplying by 0.100 H produces 37.699 ohms of inductive reactance.
The example adds 10 ohms of series resistance. Complex impedance is 10 + j37.699 ohms, and its magnitude is 39.003 ohms. A 120 V RMS sinusoidal source therefore produces approximately 3.077 A RMS. The impedance angle is 75.14 degrees, so current lags source voltage by the same amount.
Displacement power factor is R divided by impedance magnitude, approximately 0.2564 lagging. Winding real power I²R is about 94.66 W. Ideal inductive reactive power I²XL is about 356.86 var, while apparent power VI is about 369.20 VA. Those values close the right power triangle within rounding.
Peak magnetic energy for a linear inductor is one-half L times peak current squared. Since peak current is square root of two times RMS current for a sine wave, this becomes L times RMS current squared, or approximately 0.9466 joule. The ideal inductor returns that stored energy to the circuit rather than consuming it permanently.
A frequency sweep makes the proportionality visible
One-tenth frequency
XL is one-tenth the entered-frequency value when inductance remains constant.
Entered frequency
This is the state used by the full R–L result panel.
Ten-times frequency
Ideal XL is ten times higher, but real high-frequency parasitics may now matter more.
This exact linear sweep assumes L is constant. Core permeability can vary with frequency, flux density, DC bias, and temperature. Skin and proximity effects raise effective winding resistance. Interwinding capacitance creates a self-resonant frequency above which the component may stop behaving like a simple inductor.
A real coil is more than L
Low-frequency equivalent
A first model places winding resistance in series with ideal inductance. This calculator uses that model. It is useful when the manufacturer’s inductance and resistance are valid at the operating point and when winding capacitance, core loss, leakage, and nonlinear effects are small enough to ignore.
Expanded equivalent
Higher-fidelity models can add parallel capacitance, frequency-dependent core-loss resistance, skin-effect resistance, leakage inductance, and saturation. Transformers also require turns ratio, magnetizing branch, coupling, leakage, and load reflected across windings.
Read the datasheet test conditions beside the nominal inductance. Test frequency, test voltage, tolerance, temperature, and DC bias can explain why an LCR meter or operating circuit does not reproduce the label value. Compare like conditions before changing the model.
Interpret watts, var, VA, and power factor correctly
| Quantity | Calculation in this series model | Meaning and boundary |
|---|---|---|
| Real power, W | I²R | Average power dissipated in the entered resistance. Core loss and frequency-dependent AC resistance are not included separately. |
| Reactive power, var | I²XL | Magnitude associated with periodic magnetic energy exchange in the ideal inductive part. It is positive for an inductive load by common sign convention. |
| Apparent power, VA | VI | Product of RMS source voltage and current. For this sinusoidal linear model, VA² equals W² plus var² within rounding. |
| Displacement power factor | R/|Z| | Cosine of the phase angle between fundamental voltage and current. It is not total power factor for distorted nonsinusoidal waveforms. |
| Coil Q ratio | XL/R | A simplified ratio at the entered frequency. Datasheet Q may use measured effective series resistance and a specified test fixture. |
Reactive current still loads conductors, switches, sources, and protection even when an ideal inductor consumes no average real power. In power systems, harmonic currents, voltage distortion, magnetic loss, and other loads require a full measurement or harmonic model rather than only fundamental displacement power factor.
A defensible coil-analysis workflow
- Define waveform and frequency. A PWM edge contains many frequency components; one switching frequency does not fully describe it.
- Use operating-point data. Obtain inductance at relevant frequency, AC amplitude, DC bias, temperature, and core condition.
- Measure resistance appropriately. DC resistance understates high-frequency effective series resistance when skin, proximity, and core losses matter.
- Calculate the ideal baseline. Use XL and the series model to understand magnitude, phase, and sensitivity.
- Check self-resonance. Stay inside the component’s characterized inductive region unless a validated wideband model is available.
- Check ratings and heat. Evaluate RMS and peak current, copper and core loss, saturation, voltage stress, insulation, and cooling.
- Verify on hardware safely. Use correctly rated probes, isolation strategy, current measurement, and documented uncertainty.
Frequently asked questions
Is inductive reactance the same as resistance?
No. Both are measured in ohms, but resistance dissipates average real power while ideal inductive reactance stores and returns magnetic energy and shifts current phase. They combine as perpendicular complex components, not by ordinary scalar addition.
What happens to XL when frequency doubles?
Ideal XL doubles because XL is directly proportional to frequency. Current may not simply halve when series resistance and other circuit elements are present. Real inductance and resistance may also vary with frequency.
Why is the current angle called lagging?
An ideal inductor’s induced voltage opposes current change, producing current 90 degrees behind voltage in sinusoidal steady state. Adding series resistance moves the lag between zero and 90 degrees; this calculator reports arctangent of XL divided by R.
Can I enter zero series resistance?
Yes, for the ideal pure-inductor case. The angle becomes 90 degrees, power factor and real winding power become zero, and Q is reported as ideal infinity. Every physical winding has loss, so this is a conceptual boundary.
Does the result work for square waves or PWM?
Only one sinusoidal frequency at a time. A square or PWM waveform contains fundamental and harmonic components, each seeing a different XL. Switching converters also involve time-domain ripple, parasitic capacitance, core loss, and saturation.
Why can a coil stop looking inductive at high frequency?
Winding capacitance resonates with inductance at the self-resonant frequency. Above that region, capacitive behavior can dominate. Manufacturer impedance curves and measured equivalent circuits are more reliable than extending XL = 2πfL indefinitely.
References
- U.S. Department of Energy, Electrical Science, Volume 3: Basic AC Reactive Components
- U.S. Department of Energy, Electrical Systems and Safety Oversight Qualification Standard Reference Guide
- Naval Sea Systems Command, Applied Engineering Principles Manual: Electrical Engineering
Educational sinusoidal R–L estimate only. Verify the component’s operating-point inductance, frequency-dependent losses, self-resonance, saturation, thermal limits, insulation, circuit topology, transient conditions, and safe qualified design.