Skin Depth Calculator
As alternating current rises in frequency, it stops using the full cross-section of a conductor and crowds into a thin surface layer. The skin depth is the characteristic distance over which current density falls to about 37 percent of the surface value. It governs the effective AC resistance of wires, PCB traces, and RF transmission lines. This calculator uses the standard formula for skin depth in a good conductor, taking frequency, resistivity, and relative permeability, and returns skin depth in micrometres along with the angular frequency.
Skin depth formula
mu = mu_r * mu0, with mu0 = 4 * pi * 1e-7 H/m
omega = 2 * pi * frequency
delta = sqrt( resistivity / (pi * frequency * mu) )
Equivalently delta = sqrt( 2 * resistivity / (omega * mu) )
The formula is the standard good-conductor approximation, valid when resistivity is small and displacement current is negligible. The result is shown in metres and in micrometres for convenience.
Skin effect facts
- Skin depth scales as 1 over the square root of frequency: four times the frequency halves the depth.
- Copper skin depth is about 66 micrometres at 1 MHz and about 2.1 micrometres at 1 GHz.
- Magnetic materials with high relative permeability have much smaller skin depths.
- RF plating is usually several skin depths thick so that most current flows in the plated layer.
- Surface roughness on the order of a skin depth raises AC loss above the smooth-conductor value.
Skin depth: frequently asked questions
What is skin depth?
Skin depth is the distance below a conductor's surface at which the alternating current density falls to 1/e (about 37 percent) of its surface value. As frequency rises, current crowds into a thinner surface layer, so the effective resistance of the conductor increases. The skin depth depends on frequency, resistivity, and magnetic permeability.
What is the skin depth formula?
Skin depth delta equals the square root of (resistivity divided by (pi times frequency times permeability)). Permeability is the relative permeability times the permeability of free space, 4*pi*1e-7 henries per metre. For non-magnetic conductors such as copper and aluminium, relative permeability is 1.
What resistivity should I use for copper?
Annealed copper has a resistivity of about 1.68e-8 ohm-metres at room temperature. This is a standard material property, exposed here as an editable input so you can substitute aluminium (about 2.65e-8), silver (about 1.59e-8), or a value from your own datasheet.
Why is skin depth important in RF design?
At high frequency, only a thin surface layer carries current, so plating thickness, surface roughness, and conductor diameter all affect loss. Knowing skin depth helps size traces, choose plating thickness (typically several skin depths), and estimate AC resistance for transmission lines and inductors.
Does skin depth depend on conductor diameter?
No. Skin depth is a property of the material and frequency only. The conductor's diameter determines how much of its cross-section is used: when the radius is much larger than the skin depth, most of the interior carries little current and the AC resistance is much higher than the DC resistance.
Official sources
- NIST: Permeability of free space (mu0).
- NIST: Physical Measurement Laboratory: electromagnetic properties.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.