Skin Depth Conductor Calculator

Formula used

Skin depth δ is the characteristic penetration distance of time‑varying fields in a conductor, defined by the exponential decay of field amplitude.

• δ = √(2 / (ω μ σ))
• δ = 1 / √(π f μ σ)
• ω = 2πf, μ = μ0 μr, σ = 1/ρ

This calculator also reports Rs = √(π f μ / σ) (surface resistance) and the rough attenuation estimate α ≈ 1/δ.

How to use this calculator

1. Select a material preset or choose Custom.
2. Enter frequency and pick the correct unit.
3. Enter μr, or keep the default for non‑magnetic metals.
4. Choose conductivity or resistivity, then provide the value.
5. Press Calculate to view results above the form.
6. Use CSV or PDF buttons to export your results.

Example data table

Examples are approximate and depend on alloy, temperature, and magnetic state.

1) Why skin depth matters in conductors

When an alternating electromagnetic field enters a conductor, induced currents oppose the change and force most current to flow near the surface. The distance where the field amplitude falls to about 36.8% is the skin depth, δ. Designers use δ to estimate effective cross‑section, heating, shielding, and high‑frequency loss.

2) Frequency dependence and practical ranges

Skin depth decreases with frequency because the angular frequency ω increases linearly with f. For many non‑magnetic metals, δ is several millimeters at audio frequencies, drops to tens of micrometers around radio frequencies, and becomes only a few micrometers at microwave bands. This trend drives litz wire at kHz and surface treatments at MHz–GHz.

3) Conductivity versus resistivity inputs

The calculator accepts conductivity σ or resistivity ρ, using σ = 1/ρ after unit conversion. This is useful because datasheets may list either property. High σ (low ρ) concentrates current closer to the surface, reducing δ. Temperature typically increases ρ in metals, which increases δ and raises loss at a fixed frequency.

4) The role of permeability (μr)

Permeability strongly influences δ because μ = μ0 μr appears in the denominator. Ferromagnetic materials can have μr far above 1, shrinking δ dramatically and increasing attenuation. However, μr depends on alloy, field strength, and frequency, so steel values are illustrative. For accurate work, use measured μr for your operating conditions.

5) Interpreting attenuation and field decay

In good conductors, fields decay approximately as exp(−x/δ). The calculator reports α ≈ 1/δ and converts it to dB/m to help compare materials and frequencies. For example, halving δ doubles α. Use this as a first‑order indicator for shielding thickness decisions, then validate with full‑wave or measured data for complex geometries.

6) Surface resistance and RF loss

Surface resistance Rs summarizes how strongly a conductor resists RF current confined near the surface. It grows with √f and √μ, and decreases with √σ. Rs is widely used in transmission line and cavity calculations because conductor loss often scales with Rs. Lower Rs generally means lower insertion loss and lower conductor heating.

7) Using presets and customizing materials

Material presets provide typical room‑temperature conductivity values for common metals and an illustrative steel option. If your conductor is plated, oxidized, or alloyed, switch to Custom and enter σ or ρ directly. Also update μr if the material is magnetic. This approach keeps the calculator aligned with your real manufacturing and operating conditions.

8) Engineering workflow and reporting

A practical workflow is to sweep frequency, record δ, and compare it to thickness, wire radius, or coating depth. If conductor thickness is only a few δ, current spreads deeper and loss differs from the thin‑skin assumption. Exporting CSV or PDF supports lab notebooks, design reviews, and quick traceability for compliance and electromagnetic compatibility documentation.

1) What does skin depth represent?

Skin depth is the depth where the field amplitude inside a conductor drops to 1/e of its surface value. It describes how deeply AC current and fields penetrate before becoming strongly attenuated.

2) Why does skin depth decrease at higher frequency?

Higher frequency increases angular frequency ω, which increases induced opposing currents. That strengthens attenuation, so the field and current crowd closer to the surface, reducing δ according to δ ∝ 1/√f.

3) Should I use conductivity or resistivity?

Use whichever matches your datasheet. The calculator converts resistivity to conductivity using σ = 1/ρ after unit conversion, then computes δ consistently. Either input method yields the same result.

4) How does permeability affect results?

Permeability multiplies μ0 through μ = μ0 μr. Larger μr reduces δ, often strongly for magnetic metals. Because μr varies with alloy and conditions, use measured or specified values when accuracy matters.

5) Are the steel values always correct?

No. Steel conductivity and μr vary widely by composition, heat treatment, and frequency. Treat the preset as an example. For design work, input your material’s measured σ or ρ and μr.

6) What does surface resistance mean?

Surface resistance Rs is an RF loss parameter for current confined near a conductor’s surface. Many transmission line and cavity loss formulas use Rs because conductor loss often scales with it.

7) How thick should a shield be relative to δ?

A few skin depths usually provide strong attenuation for simple cases. As thickness increases beyond several δ, additional benefit diminishes. Geometry, seams, and apertures also dominate, so validate with measurements when possible.