Reactance Calculator for Frequency? Formula & Use

This calculator works out the reactance of a capacitor or inductor at a given frequency. You enter the frequency and the component value (capacitance or inductance), and you get the reactance in ohms, along with the angular frequency. Reactance is the frequency-dependent opposition to alternating current (AC) that a capacitor or inductor presents, measured in ohms (Ω).

Formula

Capacitive reactance (X_C) is given by:

X_C = 1 / (2π f C)

Inductive reactance (X_L) is given by:

X_L = 2π f L

Where:

• X_C = capacitive reactance in ohms (Ω)
• X_L = inductive reactance in ohms (Ω)
• f = frequency in hertz (Hz)
• C = capacitance in farads (F)
• L = inductance in henries (H)
• π ≈ 3.14159

The angular frequency ω = 2π f, in radians per second, is also shown because it appears in many AC circuit equations.

Worked Example

Using the default values from the calculator: f = 50 Hz, C = 10 µF, L = 100 mH.

Capacitive reactance:

1. Convert capacitance to farads: 10 µF = 10 × 10^-6 F = 0.00001 F
2. Compute the denominator: 2 × π × 50 × 0.00001 = 0.00314159
3. Take the reciprocal: 1 / 0.00314159 ≈ 318.31 Ω

Inductive reactance:

1. Convert inductance to henries: 100 mH = 0.1 H
2. Compute: 2 × π × 50 × 0.1 = 31.4159 Ω

Angular frequency: ω = 2 × π × 50 ≈ 314.16 rad/s

The calculator returns X_C = 318.31 Ω, X_L = 31.42 Ω, and ω = 314.16 rad/s.

When to Use a Reactance Calculator

Reactance calculations are essential in AC circuit analysis, filter design, impedance matching, and power electronics. For example, when designing a low-pass or high-pass filter, you need to know the reactance of the capacitor or inductor at the cutoff frequency. In audio crossover networks, reactance determines how frequencies are split between tweeters and woofers. In power systems, capacitive reactance affects power factor correction, while inductive reactance limits current in motors and transformers.

You would enter the frequency of the AC signal (in hertz) and the component value. The calculator then gives the reactance, which you can compare with resistance to find impedance (Z = √(R² + X²) for series circuits).

How to Read the Results

The reactance value tells you how strongly the component opposes AC at that frequency:

• High X_C (low frequency, small capacitance) means the capacitor blocks low-frequency signals.
• Low X_C (high frequency, large capacitance) means the capacitor passes high-frequency signals easily.
• High X_L (high frequency, large inductance) means the inductor blocks high-frequency signals.
• Low X_L (low frequency, small inductance) means the inductor passes low-frequency signals easily.

Remember that reactance is not the same as resistance. Reactance does not dissipate energy; it stores and releases it. In a purely reactive component, voltage and current are 90° out of phase. The impedance magnitude combines resistance and reactance vectorially.

Common Mistakes and Unit Mix-Ups

The most frequent error is forgetting to convert microfarads (µF) to farads, or millihenries (mH) to henries. Always multiply by the appropriate power of ten:

• 1 µF = 1 × 10^-6 F
• 1 nF = 1 × 10^-9 F
• 1 pF = 1 × 10^-12 F
• 1 mH = 1 × 10^-3 H

Another common mistake is mixing up capacitive and inductive reactance signs. In complex impedance, X_C is negative (−j/ωC) and X_L is positive (jωL). This calculator returns positive magnitudes; you must apply the sign yourself when doing phasor math.

Also, the formula assumes ideal components. Real capacitors have parasitic inductance and resistance; real inductors have winding resistance and parasitic capacitance. At very high frequencies (RF), these parasitics dominate and the simple formulas become inaccurate.

Limits of the Formula

The reactance formulas are exact for ideal, linear, time-invariant components at a single sinusoidal frequency. They do not apply to:

• Non-sinusoidal waveforms (square waves, pulses) unless you decompose them into harmonics.
• Components operating near their self-resonant frequency.
• Superconducting or nonlinear components (varactors, ferrite cores under saturation).

For a capacitor, the formula breaks down when the frequency approaches the self-resonant frequency where parasitic inductance becomes significant. For an inductor, core losses and interwinding capacitance become important at high frequencies.

Frequently Asked Questions

What is the difference between reactance and impedance?

Reactance is the frequency-dependent opposition to AC from capacitors and inductors, measured in ohms. Impedance is the total opposition, combining resistance (R) and reactance (X) as a complex quantity: Z = R + jX. Resistance dissipates energy; reactance stores and releases it. Impedance is what you use in Ohm’s law for AC circuits: V = IZ.

Can reactance be negative?

Capacitive reactance is often written as a negative value in complex notation (−jX_C), while inductive reactance is positive (+jX_L). The magnitude itself is always positive. The sign indicates the phase relationship: current leads voltage in a capacitor, and lags in an inductor.

What happens when capacitive and inductive reactance are equal?

When X_C = X_L, the circuit is at resonance. In a series RLC circuit, the reactances cancel, leaving only resistance, and the current is maximum. In a parallel RLC circuit, the impedance is maximum. The resonant frequency is f₀ = 1 / (2π√(LC)).

Does reactance depend on the voltage or current?

No, for ideal linear components, reactance depends only on frequency and component value, not on voltage or current. However, real components may have voltage-dependent capacitance (varactors) or current-dependent inductance (saturable cores), which can make reactance vary with operating point.

How do I convert reactance to impedance?

For a single component, impedance is simply jX_L for an inductor or −jX_C for a capacitor. For a series combination of resistor and reactive component, Z = R + jX. For parallel combinations, use the reciprocal formula: 1/Z = 1/R + 1/(jX). The magnitude is |Z| = √(R² + X²).

What is the reactance of a capacitor at DC (0 Hz)?

At DC, frequency is zero, so X_C = 1/(2π × 0 × C) approaches infinity. An ideal capacitor blocks DC completely. An inductor at DC has X_L = 0, so it acts as a short circuit (ideal).

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in f | Frequency | Hz | 50 | 0
in c | Capacitance | µF | 10 | 0
in l | Inductance | mH | 100 | 0
out xc | Capacitive reactance | Ω | 1 / (2 * pi * f * c * 1e-6) | 2
out xl | Inductive reactance | Ω | 2 * pi * f * l * 1e-3 | 2
out w | Angular frequency | rad/s | 2 * pi * f | 2