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Reactance Calculator

Calculate capacitive and inductive reactance and LC resonant frequency

Frequently Asked Questions

How are capacitive and inductive reactance calculated?

Capacitive reactance Xc = 1 ÷ (2πfC); inductive reactance Xl = 2πfL. Both are in ohms, with f in hertz, C in farads, and L in henries.

How does frequency affect reactance?

Xc falls as frequency rises (a capacitor passes high frequencies); Xl rises with frequency (an inductor blocks them). This frequency dependence is the basis of filters.

What is resonance?

When Xc = Xl the reactances cancel and the LC circuit resonates at f = 1 ÷ (2π√(LC)). At resonance a series LC looks like a short and a parallel LC like an open.

Is reactance the same as resistance?

No. Reactance stores and returns energy and is frequency-dependent; resistance dissipates it. They combine as impedance Z = √(R² + X²).

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How This Calculator Works

Reactance is the opposition a capacitor or inductor presents to alternating current, measured in ohms but frequency-dependent. Capacitive reactance is X_C = 1 ÷ (2πfC): it falls as frequency or capacitance rises, so a capacitor blocks DC and passes high frequencies. Inductive reactance is X_L = 2πfL: it rises with frequency or inductance, so an inductor passes DC and chokes high frequencies. The angular frequency ω = 2πf appears in both. When an inductor and capacitor are combined, the frequency at which X_L = X_C is the resonant frequency f = 1 ÷ (2π√(LC)).

Worked Numeric Example

Take f = 1 kHz, C = 100 nF (100×10⁻⁹ F), and L = 10 mH (0.01 H). Angular frequency ω = 2π × 1000 = 6283 rad/s. X_C = 1 ÷ (6283 × 100×10⁻⁹) = 1 ÷ 6.283×10⁻⁴ ≈ 1592 Ω. X_L = 6283 × 0.01 = 62.8 Ω. Since X_C > X_L at 1 kHz the circuit is capacitive. Resonance occurs at f = 1 ÷ (2π√(0.01 × 100×10⁻⁹)) = 1 ÷ (2π√(10⁻⁹)) = 1 ÷ (2π × 3.16×10⁻⁵) ≈ 5.03 kHz, where both reactances equal ≈316 Ω and cancel.

Real-World Use

Reactance underlies every AC filter, tuned circuit, and impedance-matching network. Audio engineers compute X_C to set crossover frequencies in loudspeaker networks - a typical tweeter crossover uses a series capacitor with X_C equal to the tweeter impedance at the crossover frequency, often around 3–8 kHz. RF designers solve f = 1 ÷ (2π√(LC)) to tune oscillators and antenna matching networks. Power engineers evaluate inductive reactance of cables and reactors in distribution systems - a 200 m length of medium-voltage cable can have significant inductive reactance that must be compensated for accurate power-flow modeling. Anyone building a switch-mode power supply filter uses these formulas to pick an LC pair that attenuates output ripple at the switching frequency.

Q Factor and Bandwidth

The quality factor Q of a resonant circuit describes how sharply tuned (selective) or broadly tuned it is. For a series RLC circuit, Q = X_L ÷ R = X_C ÷ R evaluated at resonance. For a parallel RLC circuit, Q = R ÷ X_L. In both cases the 3-dB bandwidth is BW = f₀ ÷ Q, where f₀ is the resonant frequency. A high-Q circuit is sharp and selective: a crystal oscillator with Q = 100,000 at 10 MHz has a bandwidth of only 100 Hz - it will reject all but a tiny window of frequencies. An AM radio's IF filter might use Q = 50–100 to pass a 10–20 kHz channel. An antenna matching network may use Q = 5–15 for broader bandwidth to cover a frequency band. If a series LC circuit has L = 10 mH and the winding resistance is R = 10 Ω, then at the resonant frequency of 5.03 kHz the inductive reactance is X_L = 2π × 5030 × 0.01 = 315.9 Ω, giving Q = 315.9 ÷ 10 = 31.6 and bandwidth = 5030 ÷ 31.6 = 159 Hz. Increasing the inductance (while keeping the same resonant frequency by reducing C proportionally) raises Q and narrows the bandwidth. This is why air-core inductors with low winding resistance are preferred for high-Q RF applications.

Common Mistakes

Unit slips dominate: a microfarad is 10⁻⁶ F and a nanofarad is 10⁻⁹ F - mixing them throws reactance off by orders of magnitude. A capacitor labeled "100n" is 100 nF = 0.1 µF; entering 100 into a formula expecting farads gives a nonsense result. Forgetting the 2π factor (using f directly instead of ω) understates reactance by a factor of 2π ≈ 6.28. Reactance is not resistance: you cannot simply add X to R arithmetically because they are 90 degrees out of phase - total impedance is Z = √(R² + X²). Also note X_C is conventionally taken as negative in phasor analysis and X_L as positive when summing to find net reactance; this tool reports magnitudes for clarity.

Limitations & Related Tools

These ideal formulas ignore real-world parasitics: equivalent series resistance (ESR) in capacitors, winding resistance and core loss in inductors, and self-resonance from parasitic capacitance that makes a real inductor behave capacitively above its self-resonant frequency (SRF). At high frequencies, skin effect raises the effective AC resistance of wire windings significantly above the DC resistance. For full AC circuit analysis, combine this with an impedance calculator (Z = √(R² + X²)), a series vs. parallel resonance converter, and for resonant circuit selectivity see a Q-factor or RLC bandwidth tool. DC (f = 0) gives X_C → ∞ and X_L = 0, consistent with capacitors blocking DC and inductors passing it freely.

Frequently Asked Questions

What is the difference between reactance and impedance?

Reactance (X) is the purely imaginary (90-degree out-of-phase) part of impedance - it represents energy storage, not dissipation. Impedance (Z) is the complete complex opposition to current, combining both resistance R (the real, in-phase part that dissipates energy as heat) and reactance X (the imaginary, 90-degree part). The relationship is Z = R + jX for a series circuit, and the magnitude is |Z| = √(R² + X²). A pure inductor has Z = jX_L; a pure capacitor has Z = -jX_C; a real inductor with winding resistance r has Z = r + jX_L. Reactance causes voltage and current to be out of phase; resistance causes them to be in phase.

Why is capacitive reactance considered negative?

In phasor (complex number) notation, inductive reactance is assigned a positive imaginary value (+jX_L) because the voltage across an inductor leads the current by 90 degrees. Capacitive reactance is negative imaginary (-jX_C) because the voltage across a capacitor lags the current by 90 degrees. This sign convention ensures that when a capacitor and inductor are in series, their reactances subtract: X_net = X_L - X_C. At resonance they cancel exactly, leaving only the series resistance, and impedance is at its minimum. The convention is not a physical "negative opposition" - it is a bookkeeping tool for tracking phase angles in circuit analysis.

What happens at exactly the resonant frequency?

At the resonant frequency f₀ = 1 ÷ (2π√(LC)), the inductive and capacitive reactances are equal in magnitude and opposite in sign, so they cancel: X_L = X_C and X_net = 0. For a series RLC circuit, total impedance collapses to just the series resistance R - impedance is at its minimum and current is at its maximum for a given applied voltage. The voltage across the inductor and capacitor can each be Q times larger than the source voltage, which is exploited in bandpass filters and oscillators. For a parallel RLC circuit, behavior is inverted: impedance is maximum at resonance and current from the source is minimum, while large circulating currents flow between L and C internally.

How do skin effect and ESR affect real components?

Skin effect is the tendency of high-frequency AC current to flow near the conductor surface rather than through the full cross-section, effectively reducing the conducting area and raising resistance. For a copper conductor the skin depth at 10 kHz is about 0.66 mm; at 1 MHz it shrinks to 0.066 mm. This means a 1 mm diameter copper wire behaves like a much thinner, higher-resistance conductor at radio frequencies - the AC resistance can be five to ten times the DC resistance. Equivalent series resistance (ESR) in capacitors represents a similar effect plus dielectric losses, and causes capacitors to heat under high ripple-current conditions. Both effects lower the Q factor of a resonant circuit and must be measured with an impedance analyzer at the frequency of interest rather than estimated from DC resistance.

What is the self-resonant frequency of an inductor?

A real inductor has parasitic capacitance between its winding turns. This distributed capacitance forms a parallel LC circuit with the inductance itself, creating a self-resonant frequency (SRF) above which the component behaves as a capacitor rather than an inductor. For a typical 10 mH leaded RF choke the SRF might be 5–20 MHz; for a 1 µH surface-mount inductor it might be 200–800 MHz. Operating an inductor above its SRF defeats its purpose - it will have capacitive reactance instead of inductive reactance. SRF is specified on high-frequency inductor data sheets and must be checked when designing RF circuits or high-frequency power converters.