Total Reactance Calculator: Combine XL and XC

A total reactance calculator finds the net reactance of an ideal series circuit from its inductive reactance and capacitive reactance. Enter frequency, inductance, and capacitance; the calculator returns signed total reactance in ohms, along with the individual reactances.

Formula

For an ideal inductor and capacitor connected in series, total reactance is the algebraic difference between their reactances:

X = X_L − X_C = 2πfL − 1/(2πfC)

• X is total reactance, in ohms (Ω). A positive result is inductive; a negative result is capacitive.
• X_L = 2πfL is inductive reactance, in ohms.
• X_C = 1/(2πfC) is capacitive reactance, expressed here as a positive magnitude in ohms.
• f is frequency in hertz (Hz), or cycles per second.
• L is inductance in henries (H).
• C is capacitance in farads (F).
• π is approximately 3.14159.

The equations assume sinusoidal alternating current and ideal components. Use frequency in hertz, inductance in henries, and capacitance in farads to get the answer in ohms. If your component values use millihenries or microfarads, convert them first: 1 mH = 0.001 H and 1 μF = 0.000001 F.

Worked Example

Using the calculator defaults, f = 60 Hz, L = 0.01 H, and C = 0.0001 F:

1. Find the inductive reactance: X_L = 2π × 60 × 0.01 = 3.7699 Ω, or 3.77 Ω.
2. Find the capacitive reactance: X_C = 1/(2π × 60 × 0.0001) = 26.5258 Ω, or 26.53 Ω.
3. Subtract the capacitive value from the inductive value: X = 3.7699 − 26.5258 = −22.7559 Ω.

Rounded to two decimal places, total reactance is −22.76 Ω. The negative sign indicates that the series circuit is net capacitive at 60 Hz.

What Total Reactance Tells You

Reactance describes how an ideal capacitor or inductor opposes alternating current. Unlike resistance, it depends on frequency and stores energy temporarily rather than dissipating it as heat. Inductive reactance increases with frequency, while capacitive reactance decreases with frequency. Their opposing effects explain why the total can be positive, negative, or zero.

A positive total means the inductive effect is larger at the frequency entered; a negative total means the capacitive effect is larger. If the result is zero, the two reactances cancel in the ideal series model. That condition is called series resonance, and its frequency is:

f₀ = 1/(2π√(LC))

At resonance, the circuit does not have zero impedance in real life: resistance and other non-ideal effects remain. The calculator reports reactance only, not total impedance or current.

When to Use This Calculator

Use it when assessing a series LC circuit at a known frequency, checking whether its net behavior is inductive or capacitive, or estimating how far it is from resonance. It can also help verify hand calculations before analyzing a larger circuit.

The result is frequency-specific. A circuit that is capacitive at one frequency may become inductive at another. To explore this, calculate the reactances again at each frequency of interest; do not treat a component pair as having one fixed total reactance for all AC signals.

Reactance is measured in ohms, just like resistance. There is no separate customary-unit conversion for the answer: the ohm is used in both metric and US customary engineering contexts. The component inputs do need consistent electrical units, though; entering 10 for a 10 mH inductor would mean 10 H unless converted.

Common Mistakes and Limits

• Adding magnitudes instead of subtracting: In a series LC circuit, inductive and capacitive reactance have opposite signs. Subtract X_C from X_L.
• Mixing prefixes: Convert mH to H and μF or nF to F before using the formula. A prefix error can change the answer by factors of 1,000 or more.
• Using angular frequency as frequency: The formulas shown use f in hertz. If you use angular frequency ω in radians per second, use X_L = ωL and X_C = 1/(ωC) instead.
• Dropping the sign: The sign identifies whether the net reactance is inductive or capacitive. Keep it when combining reactance with resistance.
• Assuming reactance equals impedance: In a real circuit with resistance, impedance combines resistance and net reactance. For a series circuit, its magnitude is |Z| = √(R² + X²), where R is resistance in ohms.

This basic calculator does not account for winding resistance, capacitor equivalent series resistance, parasitic capacitance or inductance, component tolerances, or frequency-dependent material effects. It is not suitable by itself for predicting the behavior of a complex network or a component outside its specified operating range. Real components may also heat or fail if operated beyond their ratings.

Frequently Asked Questions

How do you calculate total reactance in a series circuit?
Calculate X_L = 2πfL and X_C = 1/(2πfC), then use X = X_L − X_C. Keep the result’s sign to identify the net circuit behavior.

Can total reactance be negative?
Yes. A negative result means capacitive reactance is greater than inductive reactance at the entered frequency. It is a signed circuit quantity, not a negative physical component value.

What is total reactance at resonance?
For an ideal series LC circuit at resonance, X_L and X_C are equal, so net reactance is zero. Real circuits still have resistance and may have additional parasitic effects.

Is reactance the same as impedance?
No. Reactance is the part of impedance associated with ideal inductors and capacitors. Impedance also includes resistance; for a series circuit, its magnitude is √(R² + X²).

What units should I enter for inductance and capacitance?
Enter inductance in henries and capacitance in farads. Convert common values such as 10 mH to 0.01 H and 100 μF to 0.0001 F before calculating.

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in f | Frequency | Hz | 60 | 0
in L | Inductance | H | 0.01 | 0
in C | Capacitance | F | 0.0001 | 0
out X | Total reactance | ohm | 2*pi*f*L - 1/(2*pi*f*C) | 2
out XL | Inductive reactance | ohm | 2*pi*f*L | 2
out XC | Capacitive reactance | ohm | 1/(2*pi*f*C) | 2