Skin Effect Depth Calculator
Find the skin depth of a conductor at a given frequency from its resistivity and relative permeability, with an estimated AC/DC resistance ratio.
🔌 What is Skin Effect Depth?
Skin effect depth (skin depth) is the characteristic distance below a conductor's surface at which AC current density has fallen to about 37% (1/e) of its surface value. As frequency rises, alternating current increasingly concentrates near the conductor's outer surface rather than spreading through its full cross-section, given by delta = sqrt(rho / (pi f mu)), where rho is resistivity and mu is the material's absolute permeability.
Electrical engineers use skin depth to predict added AC resistance in conductors at radio and switching frequencies, size Litz wire strand diameter for high-frequency windings, and understand why power-line-frequency conductors (where skin depth is typically much larger than the conductor) rarely need special skin-effect mitigation, while RF and switch-mode power conductors often do.
A common point of confusion is applying the simple Rac/Rdc = r/(2*delta) approximation everywhere. That formula is only valid when the conductor's radius is much larger than the skin depth, current genuinely confined to a thin surface shell. When skin depth is comparable to or larger than the radius, current still flows through most of the cross-section, and this calculator flags that case rather than reporting a misleading ratio.
This calculator computes skin depth in both millimeters and micrometers from your frequency, resistivity, and relative permeability, and, when you provide a conductor radius, estimates the AC/DC resistance ratio while checking whether that approximation is actually valid for your inputs.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Copper Wire at 1 MHz
f = 1,000,000 Hz, ρ = 16.8 nΩ·m (copper), μr = 1, r = 0.5 mm
Example 2 — Copper Busbar at Power-Line Frequency (Ratio Not Applicable)
f = 60 Hz, ρ = 16.8 nΩ·m (copper), μr = 1, r = 5 mm
Example 3 — Steel Conductor at Power-Line Frequency
f = 50 Hz, ρ = 100 nΩ·m (steel), μr = 300, r = 10 mm
❓ Frequently Asked Questions
🔗 Related Calculators
What is skin effect?
Skin effect is the tendency of alternating current to concentrate near the outer surface (skin) of a conductor rather than flow uniformly through its entire cross-section, becoming more pronounced at higher frequencies. This effectively reduces the conductor's usable cross-sectional area, increasing its AC resistance above its DC resistance.
What is the formula for skin depth?
Skin depth delta = sqrt(rho / (pi f mu)), where rho is the conductor's resistivity, f is frequency, and mu is the absolute permeability (mu = mu0 x mur, where mu0 is the permeability of free space and mur is the material's relative permeability).
Why does skin depth decrease with frequency?
Higher-frequency currents change direction faster, inducing stronger opposing eddy currents in the conductor's interior that push current flow toward the surface more strongly. Since skin depth is proportional to 1/sqrt(f), quadrupling frequency halves skin depth, a gradual, not sudden, effect.
Why does relative permeability matter for skin depth?
Higher permeability materials concentrate magnetic flux more strongly, which intensifies the induced eddy currents that push conduction toward the surface, so skin depth is inversely proportional to sqrt(mur). Magnetic materials like steel (mur in the hundreds) have a much smaller skin depth than non-magnetic copper or aluminum at the same frequency.
What is the AC to DC resistance ratio approximation?
For a round conductor with radius much larger than its skin depth, AC resistance is approximately Rac/Rdc = r / (2 x delta), since current effectively flows only within a thin annular shell near the surface, this ratio shows how much the conductor's effective resistance increases at that frequency.
Why does this calculator sometimes show the AC/DC ratio as not applicable?
The r/(2*delta) approximation is only valid when the conductor radius is much larger than the skin depth, if skin depth is comparable to or larger than the radius, current still flows through most of the conductor's cross-section, and this simplified ratio would give a misleading result, so the calculator flags it as not applicable instead.
What is a typical skin depth for copper at power-line frequency?
Copper at 50 or 60 Hz has a skin depth of roughly 9 to 10 millimeters, larger than nearly all common power conductor radii, which is why skin effect is usually negligible for standard wire and cable sizes at ordinary power-line frequencies.
How is skin effect addressed in practical designs?
Litz wire, bundles of thin, individually insulated strands woven together, is the standard technique for high-frequency windings (transformers, inductors) since it forces current to share more evenly across many small conductors, each thin enough to stay within a skin depth or two of its own surface.
Does skin effect affect DC circuits?
No, skin effect is purely an AC phenomenon caused by time-varying magnetic fields inducing opposing currents. A true DC circuit has no time-varying current, so there is no skin effect at all, current flows uniformly through the conductor's entire cross-section.
What units does this calculator use?
Frequency is entered in Hertz, resistivity in nano-ohm-meters, relative permeability is dimensionless, and conductor radius (optional) in millimeters. Skin depth results are shown in both millimeters and micrometers.