Skin Depth Calculator (Skin Effect in Conductors)
Alternating current crowds towards the surface of a conductor, so at high frequency only a thin outer layer carries it and the AC resistance rises. This skin depth calculator finds that layer's depth for copper, aluminium and other metals at any frequency — see skin effect in conductors for why it matters in busbars, cables and RF circuits.
How to use the skin depth calculator
Choose the conductor material, enter its relative permeability (1 for non-magnetic metals) and the frequency. The calculator returns the skin depth δ. At depth δ the current density is 37% of its surface value; about 86% of the current flows within the outer δ of a thick conductor.
Skin depth formula
δ = √(ρ ÷ (π f μ0 μr))
μ0 = 1.25663706212 × 10⁻⁶ H/m; resistivities are at 20 °C.
Example
Copper (ρ = 1.678 × 10⁻⁸ Ω·m, μr = 1) at 50 Hz:
- π × 50 × 1.2566 × 10⁻⁶ = 1.974 × 10⁻⁴
- δ = √(1.678 × 10⁻⁸ ÷ 1.974 × 10⁻⁴) = 9.22 mm
Skin depth vs frequency
| Frequency | Copper | Aluminium | Stainless steel 304 |
|---|---|---|---|
| 50 Hz | 9.22 mm | 11.6 mm | 60.4 mm |
| 60 Hz | 8.42 mm | 10.6 mm | 55.1 mm |
| 400 Hz | 3.26 mm | 4.1 mm | 21.4 mm |
| 1 kHz | 2.06 mm | 2.59 mm | 13.5 mm |
| 10 kHz | 652 µm | 819 µm | 4.27 mm |
| 100 kHz | 206 µm | 259 µm | 1.35 mm |
| 1 MHz | 65.2 µm | 81.9 µm | 427 µm |
| 10 MHz | 20.6 µm | 25.9 µm | 135 µm |
| 100 MHz | 6.52 µm | 8.19 µm | 42.7 µm |
| 1 GHz | 2.06 µm | 2.59 µm | 13.5 µm |
Practical consequences
- Busbars and large cables: at 50/60 Hz, bars thicker than about 10 mm (copper) gain little capacity; large cables use segmented (Milliken) conductors — see the busbar size calculator.
- Switch-mode power supplies: at 100 kHz copper’s δ is about 0.2 mm, so windings use Litz wire or copper foil.
- RF and PCB traces: above about 100 MHz current flows in a few micrometres, so surface roughness and plating matter.
- Resistivity rises with temperature, so hot conductors have a slightly larger skin depth.
Frequently asked questions
What is the skin depth formula?
δ = √(ρ ÷ (π f μ₀ μr)), where ρ is the resistivity, f the frequency and μ₀μr the permeability. It is the depth at which current density falls to 1/e (about 37%) of its surface value.
What is the skin depth of copper at 50 Hz?
About 9.2 mm (8.4 mm at 60 Hz). Copper conductors thicker than about 2δ — roughly 18 mm — gain little from extra thickness at power frequency.
How does skin depth change with frequency?
It falls with the square root of frequency. Copper's skin depth is about 2.1 mm at 1 kHz, 65 µm at 1 MHz and 2.1 µm at 1 GHz.
How do I reduce skin effect losses?
Use flat or hollow conductors, several smaller conductors in parallel, or Litz wire (many insulated, twisted strands) for kHz-range transformers and inductors.
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