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RF Skin Depth Calculator

Enter frequency and material properties to find the RF skin depth.

Result

66.085 µm
0.066085 mm
6.6085 × 10⁻⁵ m

How it is calculated

The tool applies the classical skin-depth formula δ = 1 / √(π × f × μ × σ). Here f is the frequency in hertz (Hz), σ is the conductivity in siemens per metre (S/m), and μ = μ0 × μr where μ0 = 4π × 10-7 H/m and μr is the relative permeability (dimensionless; left blank it is treated as 1, which suits copper, aluminium and other non-magnetic metals). The depth is calculated in metres and then shown in micrometres, millimetres and scientific notation in metres. Frequency and conductivity must both be above zero, otherwise there is no result. The formula assumes a good conductor, a flat surface and a single frequency.

Worked example

Copper at 1 MHz: f = 1000000 Hz, σ = 5.8e7 S/m, μr = 1. Then μ = 4π × 10-7 ≈ 1.2566 × 10-6 H/m. The product π × f × μ × σ ≈ 2.29 × 108, its square root is about 15 132, and the reciprocal gives δ ≈ 6.6085 × 10⁻⁵ m. The tool shows this as 66.085 µm (0.066085 mm), so at 1 MHz the current in copper flows in roughly the outer 66 µm.

Try this example →

Common mistakes

  • Entering frequency in kHz or MHz. The field is in hertz, so 1 MHz must be typed as 1000000; typing 1 gives a depth about 1000 times too large.
  • Using resistivity or conductivity in the wrong unit, for instance MS/m. The field expects S/m, and copper is about 5.8e7 (58 MS/m).
  • Leaving μr at 1 for iron, steel or nickel. Their relative permeability is far above 1, which makes the skin depth much smaller; the field is there for them.
  • Reading the result as the conductor thickness needed. It is the depth at which current density has fallen to about 37% (1/e), so trace or wall thickness is usually chosen as a few skin depths.

About this calculator

At high frequencies, alternating current in a conductor doesn't flow evenly through the whole cross-section — it crowds toward the surface, a phenomenon called the skin effect. Skin depth (δ) is the distance below the surface where current density has dropped to about 37% (1/e) of its surface value, calculated as δ = √(1/(π·f·μ·σ)), where f is frequency, μ is the material's permeability, and σ is its conductivity.

Higher frequency, higher conductivity, or higher permeability all shrink the skin depth, meaning the current effectively uses only a thin outer shell of the conductor. RF and microwave engineers rely on this figure when designing antennas, PCB traces, and waveguides — since a conductor thicker than a few skin depths wastes material, and PCB trace resistance at RF frequencies must be calculated from the skin depth, not the full trace thickness.

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Comments (1)

  • Editorial team

    The depth shrinks with the square root of frequency, so a hundred times the frequency gives a depth ten times smaller. The default shows copper at 60 Hz, about 8.4 mm, which matters for thick mains busbars; at radio frequencies the same metal drops to micrometres. Which metal and frequency band are you working with? Post the conductivity you used.

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