Skin Depth Calculator

About the Skin Depth Calculator

Skin depth is the distance into a conductor at which an electromagnetic wave's amplitude decays to 1/e (37%) of its surface value. At DC, current flows uniformly through a conductor's cross-section. At higher frequencies, current concentrates near the surface — the skin effect — increasing effective resistance and reducing the useful cross-sectional area.

The skin depth δ = √(2ρ/ωµ) depends on resistivity ρ, angular frequency ω, and magnetic permeability µ. For copper at 60 Hz, δ ≈ 8.5 mm — large enough that household wiring is nearly unaffected. But at 1 MHz, δ shrinks to 66 µm, and at 2.4 GHz (WiFi), it is just 1.3 µm. This is why RF conductors are often hollow tubes or thin plated surfaces.

Ferromagnetic materials have much smaller skin depths because their high permeability (µᵣ = 100–1000) concentrates the magnetic field. This calculator computes skin depth, AC/DC resistance ratio, effective cross-sectional area, and shielding effectiveness for any conductor material and frequency.

When This Page Helps

Understanding skin depth is essential for designing power cables, PCB traces, RF antennas, EMI shielding, and induction heating coils. This calculator helps electrical engineers optimize conductor sizing and shielding thickness for any frequency.

How to Use the Inputs

1. Select a material preset or enter custom resistivity and permeability.
2. Choose input mode: resistivity (Ω·m) or conductivity (S/m).
3. Enter the operating frequency in Hz.
4. Optionally enter wire radius to see AC/DC resistance ratio.
5. Review skin depth, attenuation, and conductor utilization.
6. Consult the material table for common conductor properties.

Example Calculation

Tips & Best Practices

• At 5δ into the material, the field is attenuated by 99.3% — useful for shielding calculations.
• Skin depth decreases with √frequency — doubling frequency reduces δ by 29%.
• Litz wire (many thin insulated strands) mitigates skin effect at frequencies up to ~1 MHz.
• For PCB traces at GHz, only a few µm of copper carries current — surface finish matters.
• Steel has 10-20× smaller skin depth than copper due to high permeability.

When To Use This Calculator

Calculate electromagnetic skin depth for conductors at any frequency. Includes AC resistance ratio, shielding depth, and material comparison table. Use it when you need a repeatable calculation in the physics / general category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Frequently Asked Questions

• What is the skin effect?

  At AC frequencies, eddy currents within a conductor oppose the interior field, pushing current to flow near the surface. This increases effective resistance and is called the skin effect.

• Why does skin depth matter for power cables?

  For large conductors at 50/60 Hz, the center carries little current. Utilities use hollow conductors or bundled conductors (ACSR) to maximize effective cross-section.

• How does temperature affect skin depth?

  Higher temperature increases resistivity, which increases skin depth. Copper at 100°C has about 8% larger δ than at 20°C.

• Why is skin depth smaller in steel?

  Steel has high relative permeability (µᵣ = 100-600), which appears in the denominator under the square root, dramatically reducing δ.

• How do I calculate shielding effectiveness?

  Attenuation through a shield of thickness t is approximately e^(−t/δ) or 8.686×t/δ dB. For 40 dB shielding, you need about 4.6δ thickness.

• What about skin effect at DC?

  At DC (f = 0), skin depth is infinite — current distributes uniformly. Skin effect only occurs with time-varying fields.