Calculate Reactance XL

Calculator and formulas for calculating the reactance of a coil

Reactance XL Calculator

Inductive Reactance

This function can calculate the reactance of a coil, the inductance, or the corresponding frequency. Two of the values must be known to calculate the third.

Results
Reactance XL:
Inductance L:
Frequency f:

Inductive Reactance

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Coil (Inductance)
Fundamentals

The inductive reactance XL of a coil is frequency-dependent and increases proportionally with frequency. At DC (f = 0 Hz), XL = 0 Ω, at high frequencies it becomes very large.

Basic Formula
\[X_L = 2\pi f L\]

XL in Ω, f in Hz, L in H

Example Calculations

Practical Calculation Examples

Example 1: Audio Frequency

Given: L = 10mH, f = 1kHz

\[X_L = 2\pi \cdot 1000 \cdot 0.01 = 62.8Ω\]
Medium reactance in audio range
Example 2: Determine Inductance

Given: XL = 314Ω, f = 50Hz

\[L = \frac{X_L}{2\pi f} = \frac{314}{2\pi \cdot 50} = 1.0H\]
Typical mains frequency choke
Example 3: Resonance Frequency

Given: L = 100µH, XL = 1kΩ

\[f = \frac{X_L}{2\pi L} = \frac{1000}{2\pi \cdot 100 \times 10^{-6}} = 1.59MHz\]
RF application with high impedance
Frequency Behavior
Typical Values:
f = 0 Hz (DC): XL = 0Ω
f = 50 Hz: Mains frequency
f = 1 kHz: Audio range
f = 1 MHz: RF range
Applications:
Low-f: Mains filters, motor chokes
Audio-f: Crossover, filters
RF: Antennas, resonant circuits
Switching: Current limiting

Formula for Inductance

Basic Formulas

Reactance
\[X_L = 2\pi f L\]

Basic formula for inductive reactance

Inductance
\[L = \frac{X_L}{2\pi f}\]

Calculation of inductance

Frequency
\[f = \frac{X_L}{2\pi L}\]

Calculation of frequency

Properties of Inductive Reactance

Important Properties
  • Frequency-dependent: XL increases linearly with frequency
  • Direct current: At f = 0 Hz, XL = 0 Ω (short circuit)
  • High frequency: At high frequencies, XL becomes very large
  • Phase shift: Current lags voltage by 90°
  • Lossless: Ideal coil consumes no real power
  • Energy storage: Magnetic field stores energy

Practical Applications

Mains Frequency (50/60 Hz)
  • Mains filters
  • Motor chokes
  • Transformers
  • Interference filters
Audio Range (20Hz-20kHz)
  • Frequency crossovers
  • Low-pass filters
  • Transformers
  • Crossover networks
RF Range (MHz-GHz)
  • Antennas
  • Resonant circuits
  • RF chokes
  • Impedance matching

Units and Conversions

Inductance Units
1 H = 1000 mH
1 mH = 1000 µH
1 µH = 1000 nH
1 nH = 1000 pH
Frequency Units
1 kHz = 1000 Hz
1 MHz = 1000 kHz
1 GHz = 1000 MHz
1 THz = 1000 GHz

Comparison: Inductance vs. Capacitance

Opposite Behavior
Inductance (Coil):
  • XL = 2πfL
  • Increases with frequency
  • At f = 0: XL = 0 (short circuit)
  • At f → ∞: XL → ∞ (open circuit)
Capacitance (Capacitor):
  • XC = 1/(2πfC)
  • Decreases with frequency
  • At f = 0: XC = ∞ (open circuit)
  • At f → ∞: XC → 0 (short circuit)


Other induction calculators

Inductance  •  Reactance of a coil  •  Cutoff frequency R/L  •  Differentiator R/L  •  Highpass filter R/L  •  Lowpass filter R/L  •  Series circuit R/L  •  Parallel circuit R/L  •  Transformer  •