Formula and Method for Inductive Reactance
An inductor opposes changes in current by generating a back-EMF proportional to the rate of change of that current. For a sinusoidal AC signal, this opposition works out to a frequency-dependent quantity called inductive reactance: X_L = 2πfL = ωL, where f is the frequency in hertz, L is the inductance in henries, and ω = 2πf is the angular frequency in radians per second. Reactance is measured in ohms (Ω), just like resistance, but an ideal inductor does not dissipate power — it stores energy in its magnetic field and returns it to the circuit, shifting current 90° out of phase with voltage.
How the calculation works
Enter the frequency of the AC signal and select its unit (Hz, kHz, or MHz), then enter the inductance and select its unit (H, mH, or µH). The calculator converts both to base SI units — hertz and henries — and applies X_L = 2πfL to get the reactance in ohms. It also reports the angular frequency, ω = 2πf. If you supply the RMS current flowing through the inductor, the tool applies the AC analog of Ohm's law, V_L = I × X_L, to find the RMS voltage dropped across the inductor. Finally, it reports inductive susceptance, B_L = 1 / X_L, the reciprocal of reactance measured in siemens (S), which is useful when combining parallel branches of an AC circuit.
Common mistakes
- Mixing units: forgetting to convert mH or µH to henries (or kHz/MHz to Hz) before checking the math by hand — the calculator converts automatically, but a manual check needs matching units.
- Confusing inductive and capacitive reactance: X_L = 2πfL increases with frequency, while capacitive reactance X_C = 1/(2πfC) decreases with frequency — the two behave oppositely.
- Treating reactance like resistance for power: an ideal inductor's reactance limits current but dissipates no real power, so power calculations (P = I²R) still use resistance, not X_L.
Real-world applications
- Power-supply chokes and EMI filters use inductive reactance to block high-frequency noise while passing DC or low-frequency current.
- Loudspeaker crossover networks rely on an inductor's rising reactance with frequency to route bass to woofers and treble to tweeters.
- Radio-frequency tuned circuits combine inductive and capacitive reactance so they cancel at resonance (X_L = X_C), setting a filter's or station's center frequency.
- Transformer and motor winding calculations use X_L alongside winding resistance to size cables and predict voltage drop under load.
Frequently Asked Questions
What is inductive reactance?
Inductive reactance (X_L) is the opposition an inductor presents to alternating current, caused by the back-EMF it generates as current changes direction. Unlike resistance, it does not dissipate energy as heat — it is measured in ohms (Ω) but represents temporary energy storage in the inductor's magnetic field.
What is the formula for inductive reactance?
X_L = 2πfL, where f is the frequency of the AC signal in hertz and L is the inductance in henries. This can also be written as X_L = ωL, using the angular frequency ω = 2πf in radians per second.
How does inductive reactance change with frequency?
Inductive reactance is directly proportional to frequency — doubling the frequency doubles X_L. At 0 Hz (DC), an ideal inductor has zero reactance and behaves like a plain wire; as frequency rises, it increasingly opposes current flow.
How is inductive reactance different from resistance?
Resistance dissipates electrical energy as heat and stays the same at any frequency. Inductive reactance stores energy in a magnetic field and releases it back to the circuit, and its value depends on frequency (X_L = 2πfL). Resistance and reactance combine as a phasor sum to form a circuit's total impedance, Z = √(R² + X_L²) for a simple RL circuit.
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
| Hotel housekeeping | $2–5/night | Leave daily, not just at checkout |
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General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |