Calculator
Example Data Table
| Case | Frequency | εr | μr | λ₀ (approx) | λd (approx) |
|---|---|---|---|---|---|
| Wi‑Fi band material | 2.4 GHz | 2.25 | 1.0 | 0.125 m | 0.083 m |
| High‑ε substrate | 1.0 GHz | 9.8 | 1.0 | 0.300 m | 0.096 m |
| Low‑ε foam | 915 MHz | 1.05 | 1.0 | 0.328 m | 0.320 m |
Formula Used
In a lossless dielectric, the wave speed is lower than in free space. Using relative permittivity εr and relative permeability μr:
- n ≈ √(εr μr) (effective refractive index)
- v = c / n = c / √(εr μr) (phase velocity)
- λ₀ = c / f (free-space wavelength)
- λd = v / f = λ₀ / √(εr μr) (dielectric wavelength)
- ω = 2πf, k = ω / v, β = 2π/λd
How to Use This Calculator
- Enter either frequency or free-space wavelength (λ₀).
- Provide εr and μr for your material.
- Choose the output unit for λd.
- Optionally set a phase velocity override, if known.
- Click Calculate to view results above the form.
Use CSV or PDF export to save your calculation for design notes.
Dielectric Wavelength Guide
1) What this calculator delivers
This calculator finds wavelength inside a dielectric (λd) from frequency and material properties. It also reports free-space wavelength (λ₀), refractive index (n), phase velocity (v), angular frequency (ω), wavenumber (k), and phase constant (β). These values help estimate electrical length for RF structures.
2) Inputs and unit handling
You can enter frequency in Hz, kHz, MHz, GHz, or THz, or enter λ₀ directly in meters, centimeters, millimeters, micrometers, or nanometers. The output unit selector applies to λd so you can match drawings, PCB stackups, or lab notes without manual conversion mistakes. Precision control shows 2–12 digits.
3) Typical εr and μr values
Many plastics and foams sit near εr ≈ 1.03–1.10, common RF laminates often fall around εr ≈ 2.2–3.7, and ceramic-filled substrates can exceed εr ≈ 9. Since most dielectrics are non-magnetic, μr is usually near 1.0, so λd is mainly controlled by εr. FR‑4 is often near εr ≈ 4.0, but varies by batch and frequency.
4) How εr changes wavelength
In a lossless medium, λd scales roughly as λ₀/√(εr μr). Doubling εr does not halve λd; it reduces λd by about √2. Example: at 2.4 GHz, λ₀ is about 0.125 m. With εr = 2.25 and μr = 1, λd becomes about 0.083 m. At 1.0 GHz with εr = 9.8, λ₀ ≈ 0.300 m and λd ≈ 0.096 m. At 915 MHz with εr = 1.05, λd stays near 0.320 m.
5) Phase velocity, k, and β
Phase velocity is v = c/√(εr μr). Lower v means the same physical length represents more electrical degrees. The wave number k = ω/v and the phase constant β = 2π/λd indicate phase change per meter. For a quarter-wave section, a quick estimate is λd/4, useful for resonators and impedance transformers.
6) Practical checks and caveats
Real materials have loss and dispersion, so εr may vary with frequency and temperature. For microstrip, fields partly travel in air, so effective εr is lower than substrate εr; stripline is closer to the substrate value. If you know measured propagation speed from TDR or datasheets, use the phase-velocity override. Keep inputs positive, confirm units, and export CSV or PDF to preserve assumptions in your notes.
FAQs
1) What is dielectric wavelength?
Dielectric wavelength is the distance a sinusoidal wave travels in one cycle inside a material. It is shorter than free-space wavelength because phase velocity decreases in dielectrics.
2) Do I need to enter both frequency and λ₀?
No. Enter either frequency or free-space wavelength. The calculator derives the missing value using c = 299,792,458 m/s, then applies εr and μr to compute λd.
3) Why is μr usually set to 1?
Most insulating materials used in RF and microwave work are non-magnetic, so their relative permeability is very close to 1. Exceptions include special magnetic composites and ferrites.
4) How does εr affect antenna or trace length?
Higher εr lowers phase velocity and reduces λd, so a given electrical length requires less physical length. This is why guided structures on high-ε substrates can be more compact.
5) What does β represent here?
β is the phase constant, showing radians of phase shift per meter. For a lossless medium, β equals 2π/λd and also matches ω/v, linking wavelength, frequency, and speed.
6) When should I use the velocity override?
Use it when you have measured propagation speed or a datasheet value that already includes real effects. It can better match prototypes when εr is frequency-dependent or the structure is not ideal.