Introduction
When AC (alternating current) flows through a wire, it does not spread out evenly. Most of the current moves near the outside surface of the wire. This is called the skin effect. The skin depth is how deep the current goes before it drops to about 37% of its strength at the surface.
This skin depth calculator finds that depth. Enter the frequency, pick a material like copper, aluminum, brass, or steel, and press Calculate. You can also type your own resistivity and relative permeability values if your material is not on the list.
The calculator shows the skin depth, the conductivity, and the resistivity in the units you choose. It also gives you a step-by-step solution, a cross-section diagram of the wire, and a chart of skin depth versus frequency.
Skin depth matters because it changes how much of a wire really carries current. Higher frequency means a thinner skin, more resistance, and more heat. Engineers use this to pick wire sizes, design coils and transformers, plan PCB traces, and choose shielding and plating thickness.
How to use our Skin Depth Calculator
Enter the frequency, pick your metal, and set a conductor radius. The calculator shows the skin depth, the conductivity, the resistivity, and a picture of how deep the current flows in the wire.
Frequency (f): Type the AC frequency of your signal, then pick the unit: Hz, kHz, MHz, or GHz. Higher frequency means a smaller skin depth.
Material Preset: Pick the metal you are using, like copper, aluminum, brass, or steel. The preset fills in the resistivity and permeability for you. Pick "Custom" if you want to type your own numbers.
Resistivity (ρ): This is how much the material fights current flow. It fills in on its own from the preset. With "Custom" picked, type your value and choose the unit, such as μΩ·m or Ω·cm.
Relative Permeability (μᵣ): This tells how magnetic the material is. Use 1 for copper, aluminum, gold, and silver. Use a bigger number, like 100, for steel or nickel. It also fills in on its own unless you pick "Custom".
Output Format: Choose how the numbers look. Pick Scientific, Engineering, or Fixed. This changes every result on the page.
Display Units: Under each result you can change the unit. Show conductivity in S/m or S/cm, resistivity in Ω·m or μΩ·cm, and skin depth in mm, μm, mils, and more.
Reference Conductor Radius: Type the radius of your wire and pick mm, cm, or in. You can also drag the slider. This draws the cross-section diagram and gives you the skin depth count across the wire and the shell area percent.
Click Calculate to see your results and the step-by-step math. Click Reset to Defaults to start over with copper at 100 kHz.
What Is Skin Depth?
When alternating current (AC) flows through a wire, it does not spread out evenly. Instead, it crowds near the outside surface of the wire. This is called the skin effect. Skin depth (the Greek letter δ, "delta") is the distance from the surface where the current drops to about 37% of its surface value. Most of the current flows inside this thin outer layer.
The Skin Depth Formula
Skin depth is found with this equation:
δ = √( ρ / (π · f · μ₀ · μᵣ) )
- δ is skin depth, in meters
- ρ is resistivity of the metal, in ohm-meters (Ω·m)
- f is frequency of the current, in hertz (Hz)
- μ₀ is permeability of free space, 4π × 10⁻⁷ H/m
- μᵣ is relative permeability of the metal (1 for copper, aluminum, gold, and silver)
Conductivity (σ) is just the flip side of resistivity: σ = 1 / ρ.
What Changes Skin Depth
- Higher frequency = smaller skin depth. If you raise the frequency 100 times, the skin depth drops 10 times.
- Higher resistivity = larger skin depth. Current soaks deeper into poor conductors like steel or graphite.
- Magnetic metals have tiny skin depths. Steel and nickel have a high μᵣ, so current stays in a very thin shell.
Why Skin Depth Matters
Because the middle of a thick wire carries almost no current at high frequency, the wire acts smaller than it looks. That means more resistance, more heat, and more power lost. Engineers use skin depth to:
- Pick wire sizes for AC power lines and transformers
- Choose Litz wire or hollow tubes instead of solid wire at radio frequencies
- Set copper thickness on printed circuit boards
- Plan silver or gold plating thickness on RF connectors and waveguides
- Design induction heating, shielding, and eddy current testing
Copper Skin Depth Examples
| Frequency | Skin depth in copper |
|---|---|
| 60 Hz | about 8.5 mm |
| 1 kHz | about 2.1 mm |
| 100 kHz | about 0.21 mm (209 μm) |
| 1 MHz | about 66 μm |
| 1 GHz | about 2.1 μm |
Quick Rule of Thumb
Compare the skin depth to the radius of your conductor. If the skin depth is bigger than the radius, current fills the whole wire and skin effect barely matters. If the skin depth is much smaller than the radius, the inside metal is mostly wasted, and a thinner or stranded conductor may work just as well, though its DC resistance will be higher.