🧲 Inductor Reactance & Impedance
Calculates XL = 2πfL and Z = √(R² + XL²) for AC circuits
Inductive Reactance vs. Resistance: Why They Are Not the Same Thing
If you connect a resistor to an AC source and an inductor to the same AC source, both limit current — but they do it in fundamentally different ways, and only one of them actually opposes current using reactance. Understanding this distinction is the first step toward mastering AC circuit analysis. The comparison between pure resistance and inductive reactance reveals one of the most elegant and counterintuitive ideas in electronics.
The Basic Physics: What Actually Happens Inside an Inductor
A resistor converts electrical energy into heat. Every ohm of resistance dissipates real power, and there is no "memory" in the device — double the voltage, double the current, instant result. An inductor, by contrast, stores energy in a magnetic field. When current flows through a coil of wire, it builds a magnetic field around it. When the current tries to change, that magnetic field collapses or expands, inducing a back-EMF (electromotive force) that opposes the change. This is Faraday's law in action.
In a DC circuit, once current stabilizes, the inductor behaves almost like a short circuit (ignoring wire resistance). But in AC circuits, the current is constantly changing direction and magnitude — which means the inductor is constantly fighting those changes. The faster the current changes (higher frequency), the stronger the opposition. This opposition is called inductive reactance, symbolized as XL.
The Formula: XL = 2πfL
Inductive reactance is calculated as:
XL = 2πfL
Where f is the frequency in hertz and L is inductance in henries. The result is in ohms — the same unit as resistance — but it behaves very differently.
Let's make this concrete. A 100 μH inductor at 1 kHz has a reactance of 2π × 1000 × 0.0001 = 0.628 Ω. Push the frequency to 1 MHz and the same inductor jumps to 628 Ω. The inductor itself did not change; only the frequency did. This frequency-dependent nature is what makes inductors so powerful in filter design, RF tuning, and signal conditioning — and so irrelevant in DC power supplies where frequency is zero.
Reactance vs. Resistance: The Key Differences
The word "reactance" is chosen deliberately — it describes a reactive opposition, not a resistive one. Here is how they compare side by side:
Energy behavior: Resistance dissipates energy permanently as heat. Reactance stores energy temporarily (in a magnetic field for inductors, electric field for capacitors) and returns it to the circuit each half-cycle. An ideal inductor with zero DC resistance dissipates zero real power.
Phase relationship: In a purely resistive circuit, voltage and current are perfectly in phase. In a purely inductive circuit, the voltage leads the current by 90 degrees. This phase shift is the defining characteristic of reactive components and is why complex numbers (phasors) are used in AC circuit analysis.
Frequency dependence: Resistance does not depend on frequency (for ideal resistors). Inductive reactance scales linearly with frequency. Double the frequency, double the reactance. This is the opposite of capacitive reactance, which decreases as frequency increases — which is why inductors and capacitors are often paired in filters and resonant circuits.
Total Impedance: When R and XL Coexist
Real inductors are not ideal. Every physical coil has some wire resistance — called DC resistance (DCR) or equivalent series resistance (ESR). When both resistance and reactance are present in a series circuit, you cannot simply add them. Because they are 90 degrees out of phase, they combine as vectors:
Z = √(R² + XL²)
This is the Pythagorean theorem applied to phasors. Impedance Z is the total opposition to current in an AC circuit, expressed in ohms. It accounts for both the resistive loss and the reactive storage of the inductor together.
The phase angle φ between voltage and current across the RL combination is:
φ = arctan(XL / R)
When R is zero (ideal inductor), φ = 90°. When R dominates (low frequency or high resistance), φ approaches 0° and the circuit behaves more like a resistor. Most real inductors operate somewhere between these extremes.
Quality Factor Q: The Efficiency Metric
The Quality Factor (Q) compares inductive reactance to series resistance:
Q = XL / R
A high Q means the inductor stores much more energy than it wastes — it is an "efficient" inductor. High-Q inductors are critical in resonant circuits (like radio tuners) where sharp frequency selectivity is needed. A low-Q inductor is lossier; at high frequencies the winding resistance or core losses dominate, and the inductor behaves more like a resistor than a reactive element.
For air-core inductors at RF frequencies, Q values of 50–200 are common. Ferrite-core inductors at power frequencies might have Q of 10–50. This is why RF and power inductors are designed so differently — the operating frequency and loss mechanisms are completely different.
Practical Applications: Where This Math Actually Matters
Low-pass filters: An inductor in series with a load passes low frequencies easily (low XL) and blocks high frequencies (high XL). This is the basis of power supply chokes and EMI filters.
Resonant circuits (LC tanks): When an inductor and capacitor are combined, their reactances cancel at a specific resonant frequency f = 1 / (2π√LC). The impedance at resonance depends entirely on the series resistance — which is why Q matters so much.
Transformers: The reactance of the primary winding determines the no-load current. Insufficient inductance means high reactive current draw even with no load connected.
Inductive position sensors and metal detectors: Changes in the inductance (and therefore reactance) of a coil when metal is nearby allow precise position or proximity detection.
Wireless charging: The coupling coils in Qi wireless chargers operate at specific frequencies (typically 87–205 kHz) where their reactance and the geometry together achieve efficient power transfer.
Common Mistakes in Inductor Reactance Calculations
The most frequent error is treating XL and R as if they can be directly added: "Total opposition = R + XL." This gives wrong answers because it ignores the 90° phase difference. Always use the impedance formula Z = √(R² + XL²).
Another common mistake is forgetting unit prefixes. An inductance entered as 100 when it should be 100 μH (0.0001 H) produces a reactance one million times too large. This calculator handles nH, μH, mH, and H to eliminate that source of error.
Finally, remember that inductive reactance is frequency-specific. A 50 Ω reactance at 100 kHz drops to 5 Ω at 10 kHz. Quoting only the inductance value without specifying frequency tells you nothing about how the component will behave in a circuit.
Conclusion
Inductive reactance and impedance are not abstract theoretical concepts — they are the practical tools that determine how inductors behave in every AC circuit ever designed. Whether you are designing a power supply filter, tuning a radio frequency circuit, analyzing transformer performance, or troubleshooting an unexpected frequency response, XL = 2πfL and Z = √(R² + XL²) are the equations you reach for first. This calculator puts those equations at your fingertips, with flexible unit support and instant results, so the math never slows down the engineering.