Skin Depth Calculator

Compute skin depth, surface resistance, and attenuation using flexible units for engineers. Choose common metals or enter custom properties, then download reports in seconds.

Calculator Inputs

Supports conductivity or resistivity entry, plus common material presets.

White theme Responsive grid

Preset values fill conductivity and permeability when blank.
Used in ω = 2πf.
μ = μ0 μr, where μ0 = 4π×10⁻⁷ H/m.
Select how you want to define the material electrically.
Leave blank to use the selected material preset.
If you enter ρ, the calculator uses σ = 1/ρ.
Reset

Formula Used

For a good conductor driven by a sinusoidal field, the skin depth δ is the characteristic penetration distance where field amplitude falls to 1/e of its surface value.

  • ω = 2πf
  • μ = μ0 μr, with μ0 = 4π×10⁻⁷ H/m
  • δ = √( 2 / (ω μ σ) ) (equivalently δ = 1 / √(π f μ σ))
  • α ≈ 1/δ (attenuation constant in Np/m, good-conductor approximation)
  • Rs = √(π f μ / σ) (surface resistance in Ω per square)

How to Use This Calculator

  1. Select a material preset or choose Custom.
  2. Enter the frequency and pick its unit (Hz, kHz, MHz, or GHz).
  3. Enter μr if you know it; magnetic alloys can change δ dramatically.
  4. Choose Conductivity or Resistivity mode, then provide one value.
  5. Press Calculate. Results appear below the header and above the form.
  6. Use Download CSV or Download PDF to export the latest results.

Example Data Table

Material f Unit μr σ (S/m) Typical δ (µm)
Copper 1 MHz 1 5.96×10⁷ ≈ 66
Aluminium 10 MHz 1 3.50×10⁷ ≈ 27
Mild Steel 60 Hz 100 6.00×10⁶ ≈ 2700
Stainless Steel 1 GHz 1 1.40×10⁶ ≈ 13

Example values are illustrative and depend on alloy, temperature, and processing.

Professional Notes on Skin Depth in Conductors

1) What skin depth means in practice

Skin depth (δ) is the distance where the field magnitude inside a conductor drops to about 37% of the surface value. It is a diffusion effect driven by alternating fields and induced currents. Smaller δ means current crowds closer to the surface.

2) Frequency dependence you can quantify

δ scales roughly with 1/√f, so a 100× frequency increase reduces δ by about 10×. For copper near room temperature, δ is about 2.1 mm at 60 Hz, about 66 µm at 1 MHz, and about 2 µm at 1 GHz. These magnitudes guide conductor sizing at RF.

3) Material properties that move the result

Conductivity (σ) and relative permeability (μr) appear inside the square root, so modest changes matter. A lower σ increases δ, while higher μr decreases δ. Magnetic steels can have μr from a few tens to several hundreds, which can shrink δ and raise losses.

4) Temperature and alloy effects

Many metals show higher resistivity at higher temperature, effectively lowering σ. If σ falls by 20%, δ increases by about 12%. This is why warm power busbars and heated RF parts can show noticeably different loss than their cold designs.

5) Surface resistance and heating

The surface resistance Rs grows with √f and √μ, and falls with √σ. Rs is often used in transmission line and cavity loss estimates. When δ is much smaller than thickness, extra thickness adds little benefit; improving surface quality and plating can help more.

6) Thickness checks and design rules

A practical rule is that a thickness of about 3δ carries most of the current, while 5δ is effectively “thick” for many designs. If your conductor thickness is below a few δ, current spreads through more of the cross‑section and DC-style sizing becomes relevant.

7) Shielding and enclosure insight

In shielding, higher frequency generally reduces δ and increases absorption within the metal. However, seams and apertures can dominate the total leakage. Use δ to pick wall material and thickness, then confirm mechanical joints and openings for system-level performance.

8) How to interpret calculator outputs

Use δ in meters, millimeters, or micrometers depending on scale. Pair δ with Rs to compare loss sensitivity across materials. If μr is uncertain, run a sensitivity sweep (for example 1, 10, 100) to bracket outcomes and document assumptions for reviews.

FAQs

1) Why does current crowd near the surface?

Alternating current creates magnetic fields that induce opposing eddy currents. The net effect pushes current density toward the surface as frequency increases, producing an exponential decay of fields inside the conductor.

2) Can I use resistivity instead of conductivity?

Yes. Resistivity ρ is the reciprocal of conductivity σ. The calculator converts using σ = 1/ρ, then applies the same skin depth formula, so you can enter whichever value you have available.

3) What if my metal is magnetic?

Enter an estimated μr. Higher μr reduces skin depth and can increase losses. For steels and iron alloys, μr may vary strongly with composition, field level, and frequency, so treat results as a range.

4) Does thicker conductor always reduce loss?

Not always. When thickness is several skin depths, most current already flows near the surface. Additional thickness brings diminishing returns; surface finish, plating, and geometry often matter more at high frequency.

5) Are the presets exact?

They are typical room‑temperature values used for quick estimates. Real conductivity and permeability depend on alloy, heat treatment, and temperature. For critical work, use measured material data from your supplier or lab.

6) What does α ≈ 1/δ mean?

For good conductors, the field inside decays approximately as e^(−x/δ). The attenuation constant α is roughly 1/δ in nepers per meter, indicating how rapidly amplitude decreases with depth.

7) When should I worry about this in projects?

Skin effect becomes important when δ is smaller than conductor dimensions, which often happens at audio, RF, and microwave ranges. It affects losses, impedance, shielding, and heating in power electronics and antennas.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.