Frequency ↔ Wavelength Converter

Overview

The Frequency-Wavelength converter provides bidirectional conversion between frequency and wavelength, accounting for the medium’s relative permittivity.

Formulas

Frequency to Wavelength

λ = c / (f × √εᵣ)

Wavelength to Frequency

f = c / (λ × √εᵣ)

Where:

  • λ = wavelength in meters

  • f = frequency in Hz

  • c = speed of light (299,792,458 m/s)

  • εᵣ = relative permittivity of the medium

Conversion Modes

The calculator supports two modes:

  1. Frequency → Wavelength: Input frequency, calculate wavelength

  2. Wavelength → Frequency: Input wavelength, calculate frequency

Output

The calculator displays:

  • Frequency (f): Operating frequency

  • λ: Wavelength

  • λ/2: Half wavelength

  • λ/4: Quarter wavelength

Example 1: Frequency to Wavelength

Input:

  • Mode: Frequency → Wavelength

  • Frequency: 1000 MHz

  • εᵣ: 4.7 (FR4)

Calculation:

f = 1×10⁹ Hz
√εᵣ = √4.7 ≈ 2.168
λ = 299,792,458 / (10⁹ × 2.168)
  = 13.8 cm

Example 2: Wavelength to Frequency

Input:

  • Mode: Wavelength → Frequency

  • Wavelength: 30 cm

  • εᵣ: 1.0 (vacuum/air)

Calculation:

λ = 0.30 m
√εᵣ = √1.0 = 1.0
f = 299,792,458 / (0.30 × 1.0)
  = 999.3 MHz

Common Material Permittivities

Material

εᵣ (Typical)

Vacuum/Air

1.0

RO4003C

3.55

FR4

4.3 - 4.7

Alumina

9.8

Notes

  • The wavelength is shorter in materials with higher permittivity

  • Permittivity must be ≥ 1