Capacitor & Inductor Reactance Calculator

Calculate XL = 2πfL and XC = 1/(2πfC), LC resonance frequency, and unit conversions. Perfect for engineers and students.

Input Parameters

Frequency (f)

Hertz (Hz)

Capacitance (C)

Reactance (X)

Ohms (Ω)

Voltage (V)

Volts (V)

Current (I)

Amperes (A)

Results

Formulas

XC = 1 / (2π × f × C)

V = I × X, I = V / X

Key Points:

• Capacitive reactance decreases with frequency
• Inductive reactance increases with frequency
• At resonance: XL = XC, impedance is minimum
• Reactance causes 90° phase shift (V vs I)
• Capacitors lead voltage, inductors lag voltage
• Higher frequency → lower XC, higher XL

Understanding Capacitive and Inductive Reactance

Reactance is the opposition to current flow in AC circuits caused by capacitors and inductors. Unlike resistance, reactance varies with frequency and stores energy rather than dissipating it. Understanding reactance is essential for filter design, resonant circuits, impedance matching, and AC circuit analysis.

Capacitive Reactance ( $X_{C}$ )

Capacitive reactance is the opposition to AC current by a capacitor:

X_C = \ rac{1}{2 \pi f C}

$X_{C}$ : Capacitive reactance in ohms (Ω)
$f$ : Frequency in hertz (Hz)
$C$ : Capacitance in farads (F)
$\pi \approx 3.14159$
Reactance decreases as frequency increases
Capacitors block DC (infinite reactance at f=0)

Inductive Reactance ( $X_{L}$ )

Inductive reactance is the opposition to AC current by an inductor:

X_L = 2 \pi f L

$X_{L}$ : Inductive reactance in ohms (Ω)
$f$ : Frequency in hertz (Hz)
$L$ : Inductance in henries (H)
Reactance increases as frequency increases
Inductors pass DC (zero reactance at f=0)

Resonant Frequency

When

X_{L} = X_{C}

, the circuit is at resonance:

f_{resonant} = \ rac{1}{2 \pi \sqrt{L C}}

At resonance, inductive and capacitive reactances cancel
Circuit impedance is purely resistive (minimum impedance)
Used in tuning circuits, filters, and oscillators
Current is maximum in series LC circuits at resonance

Phase Relationships

Capacitors: Current leads voltage by 90° (I leads V)
Inductors: Current lags voltage by 90° (I lags V)
Resistors: Current and voltage in phase (0° difference)
Remember: "ELI the ICE man" (E leads I in L, I leads E in C)

How to Use This Calculator

Select calculation type: Capacitive reactance, Inductive reactance, or Resonant frequency
Enter frequency and capacitance for $X_{C}$
Enter frequency and inductance for $X_{L}$
Enter L and C values to find resonant frequency
Choose appropriate units (µF, nF, pF for capacitors; mH, µH for inductors)

Example Calculations

Example 1: AC Coupling Capacitor
Frequency: 60 Hz, Capacitance: 10 µF

X_C = \ rac{1}{2 \pi \ imes 60 \ imes 10 \ imes 10^{-6}} \approx 265\,\Omega

Example 2: Inductor in Power Supply Filter
Frequency: 120 Hz, Inductance: 5 H

X_L = 2 \pi \ imes 120 \ imes 5 \approx 3770\,\Omega

Example 3: LC Resonant Circuit (AM Radio Tuner)
L = 100 µH, C = 100 pF

f_{resonant} = \ rac{1}{2 \pi \sqrt{100 \ imes 10^{-6} \ imes 100 \ imes 10^{-12}}} \approx 1.59\,\ ext{MHz}

Filter Design Basics

Low-Pass Filter (RC):

$f_c = \ rac{1}{2 \pi RC}$
Passes low frequencies, attenuates high frequencies
Used for anti-aliasing, noise reduction

High-Pass Filter (RC):

$f_c = \ rac{1}{2 \pi RC}$
Passes high frequencies, attenuates low frequencies
Used for AC coupling, DC blocking

Quality Factor (Q) in Resonant Circuits

The quality factor indicates how selective or sharp the resonance is:

Q = \ rac{X_L}{R} = \ rac{X_C}{R} = \ rac{1}{R} \sqrt{\ rac{L}{C}}

Higher Q = sharper resonance peak, better selectivity
Typical Q values: 10-100 for RF circuits, 1-10 for audio
$\ ext{Bandwidth} = f_{resonant} / Q$

Common Unit Conversions

Capacitance: 1 F = 1000 mF = 1,000,000 µF = 1,000,000,000 nF = 1,000,000,000,000 pF
Inductance: 1 H = 1000 mH = 1,000,000 µH = 1,000,000,000 nH
Frequency: 1 MHz = 1000 kHz = 1,000,000 Hz

Frequently Asked Questions

Q: Why does capacitive reactance decrease with frequency?
A: At higher frequencies, the capacitor charges and discharges more rapidly, allowing more current flow and thus lower opposition (reactance).

Q: Why does inductive reactance increase with frequency?
A: Higher frequency means faster current changes, which induces larger back-EMF (voltage) opposing the current flow, increasing reactance.

Q: What's the difference between impedance and reactance?
A: Impedance (Z) is total opposition to current including resistance (R) and reactance (X):

Z = \sqrt{R^{2} + X^{2}}

. Reactance is only the AC component.

Q: How do I design a filter for a specific cutoff frequency?
A: For RC filters, choose R and C so that

f_{c} = 1/(2πRC)

. For example, R=1kΩ and C=1µF gives

f_{c} ≈ 159 Hz

Q: Can reactance be negative?
A: By convention,

X_{L}

is positive and

X_{C}

is negative when calculating total reactance. Net reactance

X = X_{L} - X_{C}

determines circuit behavior.