Skin Depth Calculator

Calculator Inputs

Calculation mode

Use general mode when conductivity is not overwhelmingly large relative to ωε.

Material preset

Selecting a preset fills conductivity, permeability, and permittivity values.

Frequency

Conductivity σ

Relative permeability μr

Relative permittivity εr

Initial field amplitude

This can represent electric field, magnetic field, or current density magnitude.

Evaluation depth

Target remaining amplitude %

Graph range multiplier

The chart spans from zero to multiplier × skin depth.

Graph points

Formula Used

Good conductor approximation
δ = √(2 / (ω μ σ)) = 1 / √(π f μ σ)

General lossy medium
α = ω √(μ ε / 2) × √( √(1 + (σ / (ω ε))² ) − 1 )

Skin depth from attenuation constant
δ = 1 / α

Amplitude decay with depth
A(x) = A₀ e^−αx

Power decay with depth
P(x) / P₀ = e^−2αx

Here, f is frequency, ω is angular frequency, μ is absolute permeability, ε is absolute permittivity, σ is conductivity, α is attenuation constant, and δ is the distance where amplitude drops to 1/e.

How to Use This Calculator

Choose a material preset or keep Custom Material.
Enter frequency and select its unit.
Provide conductivity, relative permeability, and relative permittivity.
Pick the good conductor model or the general lossy medium model.
Enter an initial field amplitude and an evaluation depth.
Set a target remaining amplitude percent to find required penetration depth.
Adjust graph range and points for a wider or smoother plot.
Press the calculate button to display results above the form.
Use the CSV and PDF buttons to export the result summary.

Example Data Table

Material	Frequency	Conductivity	μr	Approx. Skin Depth
Copper	1 MHz	5.96 × 10⁷ S/m	1	65.19 µm
Aluminum	1 MHz	3.50 × 10⁷ S/m	1	85.07 µm
Carbon Steel	1 MHz	6.99 × 10⁶ S/m	100	19.04 µm
Seawater	1 MHz	4 S/m	1	251.65 mm

Frequently Asked Questions

1) What is skin depth?

Skin depth is the distance inside a material where an electromagnetic field falls to about 36.8% of its surface value. Smaller skin depth means current crowds more tightly near the surface.

2) Why does skin depth decrease at higher frequency?

Higher frequency increases attenuation, so fields decay faster with depth. That makes current and field penetration shallower, especially in highly conductive metals.

3) How does permeability affect penetration?

Greater magnetic permeability lowers skin depth. Ferromagnetic materials often show much shallower penetration than nonmagnetic conductors at the same frequency and conductivity.

4) When should I use the general lossy medium mode?

Use it when the material is not an ideal good conductor, or when conductivity is not overwhelmingly larger than ωε. It is helpful for seawater, semiconductors, and mixed-loss media.

5) What does attenuation constant mean?

The attenuation constant α measures how quickly amplitude decays with distance. Larger α means faster decay, smaller penetration, and stronger surface confinement.

6) Why calculate amplitude and power at a chosen depth?

It helps evaluate shielding, heating, sensing, and conductor loss behavior. Amplitude shows field strength reduction, while power indicates how much energy remains deeper inside the material.

7) Is the good conductor equation always accurate?

No. It works best when conductivity dominates displacement effects. For low-conductivity or high-permittivity materials, the general lossy medium model is usually more appropriate.

8) Why compare different materials?

Material comparison helps with coil design, RF shielding, induction heating, busbars, plating thickness, and sensor performance. Different conductivity and permeability values change penetration dramatically.