PCB Skin Effect Depth Calculator

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Calculation Reference

This calculator uses the standard depth-of-penetration formula for good conductors. Resistivity (ρ) and relative permeability (μ_r) are material properties — select a common conductor to auto-fill typical values, or choose "Custom" to enter your own.

ρ = resistivity of the conductor
f = signal frequency
μ = μ_r × μ₀ (absolute permeability)
μ₀ = 4π × 10^-7 H/m

Skin Depth (δ) = √( ρ / ( π × f × μ ) )

Source: Johnson, "Transmission Lines and Networks," McGraw-Hill 1963.

Resistivity rises with temperature, so the reference values above (specified at 20°C) are corrected using each material's temperature coefficient of resistivity (α) before computing skin depth. This keeps the estimate consistent with your board's actual operating temperature rather than a cold-bench datasheet value.

ρ(T) = ρ_20°C × [ 1 + α × ( T − 20 ) ]

Reference values used for the material dropdown (resistivity and temperature coefficient α at 20°C, non-magnetic materials use μ_r = 1):

Material	Resistivity (×10^-8 Ω·m)	Relative Permeability (μ_r)	α (per °C)
Copper	1.68	1	0.00393
Silver	1.59	1	0.0038
Gold	2.44	1	0.0034
Aluminum	2.65	1	0.0039
Nickel	6.99	~100 (varies by alloy)	0.006

At very high frequencies, once skin depth shrinks to only a few micrometers, copper foil surface roughness becomes an additional loss mechanism not captured by this formula — see the FAQ below.

Frequently Asked Questions

What is skin effect depth and why does it matter for PCB design?

Skin depth is the distance below a conductor's surface at which current density has fallen to about 37 percent (1/e) of its value at the surface. As signal frequency rises, current increasingly concentrates in a thin outer shell of the conductor rather than using its full cross-section, which raises AC resistance above the simple DC value. For PCB traces and vias carrying high-frequency or fast-edge signals, this can meaningfully increase conductor loss even though the copper thickness itself hasn't changed.

How is skin depth calculated?

This calculator uses the standard depth-of-penetration formula for good conductors: skin depth equals the square root of resistivity divided by the product of pi, frequency, and the material's absolute magnetic permeability (relative permeability times the permeability of free space). Resistivity and relative permeability are material properties; frequency is the only variable you control in the design.

Why is nickel's skin depth so much smaller than copper's, even though it's a worse conductor?

Skin depth depends on both resistivity and relative magnetic permeability, and nickel is ferromagnetic with a relative permeability far above 1, unlike copper, silver, gold, and aluminum which are essentially non-magnetic (relative permeability of about 1). That high permeability pulls current toward the surface far more aggressively than resistivity alone would suggest, which is why nickel and other ferromagnetic finishes show a much thinner skin depth at the same frequency.

The relative permeability value shown for nickel looks approximate. Why?

Unlike resistivity, the relative permeability of ferromagnetic materials such as nickel, iron, and many steels is not a fixed constant. It varies with alloy composition, purity, mechanical treatment, and even the signal frequency itself, so published values for nickel commonly range from roughly 100 to several hundred depending on the source. This calculator uses a representative reference value; if you're working with a specific plating or alloy, check its datasheet and enter the correct value using the custom material option for a more accurate result.

How do I know if skin effect matters for my PCB trace?

A common rule of thumb is that skin effect becomes significant once the skin depth drops below about half your copper thickness, since at that point the current can no longer spread through the full cross-section even at DC-adjacent frequencies. This calculator compares your calculated skin depth against standard copper weights so you can quickly see whether a given signal frequency pushes your design into that regime.

How can I reduce the impact of skin effect in a design?

Since skin effect concentrates current at the surface regardless of total conductor thickness, adding more copper thickness beyond roughly twice the skin depth provides little benefit; instead, designers typically widen traces to increase surface area, use multiple parallel conductors or vias, or switch to Litz wire in wound components, all of which increase the perimeter available for current to flow through at high frequency.

Why does this calculator ask for an operating temperature?

Resistivity is not a fixed constant; it rises with temperature at a rate described by each material's temperature coefficient of resistivity. The resistivity values pre-filled by the material dropdown are standard 20°C reference figures, so if your board actually runs hotter, entering that temperature corrects the resistivity (and therefore the skin depth) to better reflect real operating conditions rather than a cold-bench datasheet number.

Why does the tool warn me about surface roughness at very high frequencies?

This calculator models an idealized, perfectly smooth conductor. In reality, copper foil has microscopic surface roughness left over from manufacturing, and once skin depth shrinks down to roughly that same scale (typically a few micrometers or less, common above the low gigahertz range), current has to travel a longer, bumpier effective path along the rough surface. That adds loss beyond what the idealized skin depth formula predicts, an effect usually modeled separately with roughness correction factors such as the Hammerstad-Jensen or Huray models, which this calculator does not include.