AC Reactance Calculator: Inductive and Capacitive Reactance

An AC reactance calculator finds the opposition an inductor or capacitor presents to alternating current at a chosen frequency. Enter frequency and the component value, and it returns reactance in ohms; the two component types use different formulas and respond oppositely to frequency.

Formula

Inductive reactance is X_L = 2πfL. Capacitive reactance is X_C = 1 / (2πfC). In these expressions, X_L and X_C are reactance in ohms (Ω), f is frequency in hertz (Hz), L is inductance in henries (H), C is capacitance in farads (F), and π is approximately 3.14159. The calculator accepts capacitance in microfarads (µF), so its expression converts to farads by dividing by 1,000,000.

Reactance is the frequency-dependent part of opposition to AC. It is not the same as resistance: an ideal inductor or capacitor stores energy temporarily and returns it to the circuit rather than dissipating it as heat. In a real component, resistance and other losses also matter.

Worked Example

Using exactly the calculator defaults, the frequency is 60 Hz, inductance is 0.01 H, and capacitance is 100 µF.

• Inductor: X_L = 2π × 60 × 0.01 = 3.7699 Ω, which rounds to 3.77 Ω.
• Capacitor: first convert 100 µF to 0.0001 F. Then X_C = 1 / (2π × 60 × 0.0001) = 26.5258 Ω, which rounds to 26.53 Ω.

The calculator displays each result to two decimal places. These are separate component reactances, not a combined circuit impedance.

How to Use the Calculator

Enter the AC frequency, inductance, and capacitance in the labeled fields. Frequency must be in hertz and inductance in henries; capacitance is specifically entered in microfarads. The outputs give the reactance of an ideal inductor and an ideal capacitor at that frequency. If you only need one component, use its result and disregard the other.

Frequency may be the supply frequency, such as 50 or 60 Hz, or a signal frequency specified for an AC circuit. For a nonsinusoidal waveform, a single frequency may not describe the whole signal: its harmonics can encounter different reactances. Analyze each relevant frequency component separately when that level of detail is required.

What the Results Mean

Both results are expressed in ohms, but their behavior differs. Inductive reactance rises in direct proportion to frequency: double the frequency or inductance and X_L doubles. Capacitive reactance falls as frequency or capacitance rises: double either one and X_C is halved.

At the default 60 Hz, the 0.01 H inductor has 3.77 Ω of inductive reactance, while the 100 µF capacitor has 26.53 Ω of capacitive reactance. That does not, by itself, tell you the circuit current. Current also depends on the applied voltage and the circuit’s total impedance, including resistance and how components are connected.

In phasor analysis, inductive reactance is associated with positive imaginary impedance, +jX_L, and capacitive reactance with negative imaginary impedance, −jX_C. The signs matter when combining components, even though reactance magnitudes are usually reported as positive numbers.

Combining Reactance in a Circuit

For an ideal series circuit containing a resistor, inductor, and capacitor, the net reactance is X = X_L − X_C. The impedance magnitude is then |Z| = √(R² + X²), where R is resistance in ohms. At the frequency where X_L equals X_C, the ideal series circuit is at resonance and its net reactance is zero; its impedance is then determined by resistance and real-world losses.

In the example, X_L and X_C are not equal, so the example values are not at series resonance. For parallel circuits, do not simply subtract the two reactance magnitudes as though the components were in series. Use the appropriate impedance or admittance method for the circuit topology.

Common Input Mistakes and Limits

• Entering the wrong capacitance unit: the calculator expects µF, not F or nF. Convert before entering: 1 F = 1,000,000 µF, and 1 µF = 1,000 nF.
• Entering millihenries as henries: 10 mH is 0.01 H. Convert to H before entering inductance.
• Mixing frequency units: convert kilohertz to hertz by multiplying by 1,000. For instance, 2 kHz is 2,000 Hz.
• Treating reactance as total impedance: the calculator does not include resistance, wiring, component losses, or circuit connections.
• Overreading precision: two decimal places are convenient for display, but actual component tolerances and frequency accuracy may make extra calculated digits misleading.

The formulas describe ideal, linear components under sinusoidal steady-state conditions. Real inductors can have winding resistance and core losses; real capacitors have equivalent series resistance and other frequency-dependent effects. Components also have operating limits and parasitic properties. Use component data and an appropriate circuit model when accuracy near a component’s limits or at high frequencies is important.

Frequently Asked Questions

What is the formula for inductive reactance?
X_L = 2πfL, with frequency in hertz and inductance in henries. The answer is in ohms.

What is the formula for capacitive reactance?
X_C = 1/(2πfC), with capacitance expressed in farads. As frequency increases, capacitive reactance decreases.

Why do inductors and capacitors respond oppositely to frequency?
The inductor’s opposition to changing current grows with frequency, while a capacitor’s opposition to AC falls as frequency rises. The formulas express these opposite relationships.

Can reactance be negative?
Reactance magnitude is commonly shown as positive. In complex impedance, capacitive reactance has a negative sign and inductive reactance a positive sign; the sign identifies phase behavior.

Does reactance determine AC current by itself?
No. Current depends on voltage and total impedance, which can include resistance, reactance, and the circuit arrangement. Use the circuit’s complete impedance to calculate current.

What happens at zero frequency?
The formulas have different limiting behavior: ideal inductive reactance approaches zero, while capacitive reactance grows without bound as frequency approaches zero. The calculator requires a positive frequency because its capacitor formula divides by frequency.

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in f | Frequency | Hz | 60 | 0
in L | Inductance | H | 0.01 | 0
in C | Capacitance | uF | 100 | 0
out XL | Inductive reactance | ohm | 2 * pi * f * L | 2
out XC | Capacitive reactance | ohm | 1000000 / (2 * pi * f * C) | 2