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Skin Depth Calculator

Find how deep AC current penetrates a conductor.

How it is calculated

The skin depth is δ = √(ρ ÷ (π × f × μ)), where ρ is the resistivity in ohm-metres (Ω·m), f is the frequency in hertz and μ = 4π × 10−7 × μr is the absolute permeability in henries per metre. The permeability field is the relative permeability μr (1 for non-magnetic metals such as copper or aluminium); if you leave it empty or enter zero or less, the tool uses 1. Resistivity and frequency must both be above zero. The result is given in micrometres and in millimetres. It is the depth at which current density falls to 1/e of its surface value, and it assumes a good conductor with a constant, linear permeability.

Worked example

Take copper with resistivity 0.0000000168 Ω·m at 1,000,000 Hz (1 MHz) and μr = 1. Then μ = 4π × 10−7 ≈ 1.2566 × 10−6 H/m. The denominator is π × 1,000,000 × 1.2566 × 10−6 ≈ 3.948, so δ = √(0.0000000168 ÷ 3.948) ≈ 6.523 × 10−5 m. That is 65.23 µm, or 0.0652 mm. Raising μr to 100 shrinks it to 6.52 µm.

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Common mistakes

  • Entering resistivity in Ω·mm²/m or µΩ·cm. The field takes ohm-metres, so copper is about 0.0000000168, not 0.0168 or 1.68.
  • Entering frequency in kHz or MHz. It is in hertz, so 1 MHz must be typed as 1000000.
  • Typing the absolute permeability (about 0.00000126) into the permeability box. It wants the relative value; non-magnetic metals are 1, and iron or steel are far higher.
  • Reading the result as the only current path. Current does not stop at δ; it decays gradually, so about 63% of the amplitude is gone at one skin depth and conductors are usually sized at several times δ.
  • Using the value for a thin foil or a nonlinear magnetic material, where permeability changes with field strength and the simple formula no longer holds.

Sources

About this calculator

The skin depth describes how deeply an alternating current penetrates into a conductor before its density falls to 1/e (about 37%) of its surface value, given by δ = √(2ρ / (ωμ)), where ρ is the resistivity, ω = 2πf is the angular frequency, and μ is the permeability of the material. Because δ shrinks as frequency rises, high-frequency AC current tends to flow mostly near the conductor's surface — the "skin effect" — leaving the core of the wire largely unused.

RF and power electronics engineers use skin depth to size conductors for radio-frequency circuits, transformers, and induction heaters, to explain why high-voltage transmission lines and RF cables sometimes use hollow or stranded (Litz) wire instead of solid conductors, and to estimate the effective AC resistance of a wire, which rises with frequency as usable cross-section shrinks.

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  • Editorial team

    Skin depth shows why thick conductors stop helping at high frequency. For copper (1.68 × 10⁻⁸ Ω·m) the tool gives 8.4217 mm at 60 Hz but only 65.23 µm at 1 MHz, so at radio frequencies nearly all the current rides in a thin outer layer, and a hollow or plated conductor can do as well as a solid one. For a magnetic metal, remember to enter its relative permeability. Which conductor and frequency are you working with?

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