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Skin Depth Calculator

Calculate the skin depth of a conductor in meters and micrometers from frequency, resistivity, and relative permeability

Frequently Asked Questions

Why does AC resistance increase with frequency?

At DC, current distributes itself uniformly across the full cross-section of a conductor, minimizing resistance. As frequency rises, the changing magnetic field inside the conductor induces eddy currents that oppose the current in the interior and reinforce it near the surface. The result is that current crowds into a thin surface layer of thickness equal to the skin depth. The effective conducting area decreases as 1/√f, and since resistance is inversely proportional to conducting area, the AC resistance increases as √f. For a 1 mm diameter copper wire, the AC resistance at 10 MHz is about 10 times its DC resistance. This is why RF engineers use the skin-depth calculation to estimate conductor losses rather than simply using the DC resistance value.

Is skin depth the same in steel as in copper?

No - the skin depth depends on both the electrical conductivity and the magnetic permeability of the material. Copper has very high conductivity and μr = 1 (non-magnetic), giving a relatively large skin depth (8.5 mm at 60 Hz). Steel has much lower conductivity than copper (roughly 1/7th for mild steel) but a much higher relative permeability (μr = 100-1000 depending on grade and flux density). The permeability effect dominates: the skin depth in steel at 60 Hz is only about 0.6-1.0 mm, roughly ten times smaller than copper. At higher frequencies, the comparison shifts further in copper's favor. Aluminum falls between the two: roughly half the conductivity of copper and non-magnetic (μr = 1), giving a skin depth about 30% larger than copper at the same frequency.

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How This Calculator Works

The skin effect causes alternating current to concentrate near the surface of a conductor rather than flowing uniformly through it. The skin depth is the distance below the surface at which the current density has fallen to about thirty-seven percent of its surface value. It shrinks as frequency rises, which is why high-frequency circuits behave so differently from direct-current ones.

Why It Matters

Because current crowds toward the surface, the effective resistance of a wire increases at high frequencies and the interior carries little current. This is why radio engineers use hollow tubing, plated conductors, and litz wire, and why printed circuit board traces need careful width and plating choices at gigahertz frequencies.

How To Use It

Enter the frequency in hertz, the resistivity of the conductor in ohm-meters, and the relative permeability. Copper resistivity is about 1.68 times ten to the minus eight ohm-meters, and most non-magnetic metals have a relative permeability of one. The calculator returns the skin depth in meters and micrometers.

Tips

Skin depth falls as the square root of frequency.
Magnetic materials with high permeability have very shallow skin depths.
Silver and copper have similar, very low resistivity.

Skin Effect in Power Systems and RF

The skin effect manifests very differently depending on the frequency range. At power line frequencies (50-60 Hz), the skin depth in copper is approximately 8.5 mm. Since most copper wire used in power distribution has a radius smaller than 8.5 mm, the current distribution is nearly uniform throughout the conductor cross-section, and the skin effect adds little to the DC resistance. Only large conductors - thick bus bars, high-current cables - experience significant skin effect at power frequencies, which is why multi-strand cables and hollow conductors are used in utility-scale power transmission.

As frequency rises, the skin depth shrinks rapidly: at 1 MHz (common in AM radio and switching power supplies), δ ≈ 66 μm in copper. A wire thicker than about 130 μm (0.13 mm) wastes interior copper because it carries no current at this frequency. At 1 GHz, δ shrinks to about 2 μm - thinner than a human hair - and at 100 GHz, it is only 0.2 μm. The practical implication is that above audio frequencies, the conductor's cross-sectional area is not what matters; only the surface area (circumference times length) determines resistance.

Litz Wire

Litz wire addresses the skin effect in the frequency range of 20 kHz to about 1 MHz - the range relevant to switching power supplies, audio power amplifiers, induction heaters, and high-frequency transformers. The concept is straightforward: instead of one solid conductor whose interior carries no current, use many fine individually insulated strands, each thin enough that the skin depth is comparable to or larger than the strand radius. The strands are twisted or braided so that each strand occupies all radial positions equally over a given length, preventing any individual strand from always being on the outside. The result is a conductor with a cross-sectional area close to the sum of all strand areas, rather than just a thin shell. Litz wire with strand diameter 0.1 mm is effective to about 1 MHz; finer strands (0.05 mm) extend the benefit to higher frequencies, at greater cost and fragility.

Skin Effect in PCB and RF Design

At microwave frequencies, the skin depth in copper is only a few micrometers, which means that virtually all the signal current flows in a very thin layer at the surface of the conductor. This has several important practical consequences for PCB and RF design. First, the conductor loss of a microstrip trace increases with the square root of frequency due to the skin effect - a trace that has acceptable loss at 1 GHz will have about 3.2 times higher loss at 10 GHz. Second, the surface roughness of the copper foil becomes critical: if the surface roughness is comparable to the skin depth (as it is for standard electrodeposited foil above a few GHz), the current must follow the rough surface contour, which increases the effective path length and therefore the resistance. Low-profile copper foils with surface roughness below 0.5 μm are specified for 5G and mmWave PCB designs.

Silver and gold plating on RF connectors and contact surfaces is valuable because silver has the lowest resistivity of any metal (1.59×10^-8 Ωm, slightly lower than copper at 1.68×10^-8 Ωm), and since all the current is at the surface, the bulk metal properties are irrelevant - only the thin plated layer matters. Gold plating (higher resistivity than copper but excellent corrosion resistance) is used on connector mating surfaces to prevent oxide formation that would add contact resistance. Standard PCB surface finishes for RF applications include electroless nickel immersion gold (ENIG) for solderability and corrosion resistance, and silver for the lowest conductor loss in high-performance microwave circuits.

Coaxial Cable Design

The skin effect explains a key design choice in coaxial cable: the current on the center conductor flows on its outer surface, while the current on the outer conductor (braid or foil) flows on its inner surface. The outer conductor's outer surface carries essentially no signal current. This is why RF coaxial cables use a silver-plated copper braid - the silver plating reduces the resistance of the inner surface where the signal current flows, and the braid construction provides flexibility. The outer jacket and armor are purely mechanical and have no effect on electrical performance at RF frequencies. For the same reason, hollow center conductors (copper tube instead of solid wire) perform identically to solid conductors at microwave frequencies while reducing weight - a consideration in aerospace cabling.

Skin Depth in Magnetic Materials

Ferromagnetic materials like steel and ferrites behave very differently from copper in the skin effect calculation. The formula shows that skin depth is inversely proportional to the square root of both conductivity and relative permeability (μr). Steel has high μr (typically 100-1000) but much lower conductivity than copper (about 10 S/m vs. 5.8×10⁷ S/m). The net result is a much smaller skin depth than copper at the same frequency. At 60 Hz, the skin depth in steel is about 0.6-1.0 mm, compared to 8.5 mm in copper. This small skin depth in steel causes high eddy current losses, which is why transformer and motor lamination thickness is chosen to be several skin depths at the operating frequency.

Power transformer cores use thin laminations (typically 0.35 mm for 50-60 Hz, or thinner for higher frequencies) to keep the eddy current loop area small. The lamination surface is coated with a thin insulating layer to prevent current from flowing between laminations. Above about 100 kHz, even the thinnest practical steel laminations have losses too high for efficient operation, and ferrite cores take over. Ferrite is a ceramic semiconductor with very low conductivity (essentially an insulator), so eddy currents are negligible regardless of skin depth. Ferrites are used in switch-mode power supply transformers from 100 kHz to several MHz, in RF chokes, and in broadband transformers through hundreds of megahertz.

Shielding

The skin effect is also the physical basis for electromagnetic shielding. When an electromagnetic wave hits a conductor, eddy currents induced in the surface layer oppose the penetrating field, and the field decays exponentially with the skin depth δ. A shield that is several skin depths thick provides excellent attenuation: one skin depth provides 8.7 dB of attenuation, two skin depths give 17 dB, and five skin depths give 43 dB. A 1 mm thick copper sheet has over 15 skin depths at 1 MHz, making it effectively opaque to RF at that frequency. Thin copper foil (0.035 mm, or 1 oz PCB copper) is still about 0.5 skin depths thick at 1 GHz, providing useful but not complete shielding. This is why RF shielding cans on PCBs use multiple-ounce copper or plated steel rather than thin foil.