Calculate electromagnetic skin depth for conductors at any frequency. Includes AC resistance ratio, shielding depth, and material comparison table.
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.
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. The note above highlights common interpretation risks for this workflow. Use this guidance when comparing outputs across similar calculators. Keep this check aligned with your reporting standard.
Skin depth: δ = √(2ρ/(ωµ)), where ρ = resistivity (Ω·m), ω = 2πf (rad/s), µ = µ₀µᵣ (H/m). Attenuation constant: α = 1/δ. AC/DC resistance ratio ≈ a/(2δ) for a >> δ, where a = conductor radius.
Result: 8.53 mm
For copper at 60 Hz: δ = √(2×1.68×10⁻⁸/(2π×60×4π×10⁻⁷)) ≈ 8.53 mm. A 2 mm diameter wire has δ >> radius, so current distribution is nearly uniform.
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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.
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.
Higher temperature increases resistivity, which increases skin depth. Copper at 100°C has about 8% larger δ than at 20°C.
Steel has high relative permeability (µᵣ = 100-600), which appears in the denominator under the square root, dramatically reducing δ. Use the examples and notes as a quick consistency check before trusting any value.
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.
At DC (f = 0), skin depth is infinite — current distributes uniformly. Skin effect only occurs with time-varying fields.