# Skin Depth Calculator

URL: https://speedycalculator.com/calculators/physics/skin-depth/
Last updated: 2026-10-30

> The skin depth calculator finds how deep alternating current penetrates into a conductor at a given frequency, from its resistivity and relative permeability, with common metals as presets.

## Inputs

- Conductor
- Resistivity ρ (Ω·m, µΩ·cm)
- Relative permeability μ_r
- Frequency f (MHz, kHz, GHz, Hz)

## Results

- Skin depth δ

## Formula

```
δ = √(ρ / (π·f·μ₀·μ_r))
```

## Explanation

At high frequencies, current crowds near the surface of a conductor – the skin effect. In copper the current is mostly within 8.5 mm of the surface at 60 Hz, but only 2 µm at 1 GHz. That is why RF cables are often silver-plated and Litz wire is made of many thin strands.

### How to use the Skin Depth Calculator

- **Conductor**
- **Resistivity ρ**
- **Relative permeability μ_r**
- **Frequency f**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the conductor or enter its resistivity and relative permeability, then the frequency.

### Inputs explained

FieldWhat to enterConductorChoose one: Copper, Aluminium, Gold, Silver …Resistivity ρUnits: Ω·m, µΩ·cmRelative permeability μ_rA numberFrequency fUnits: MHz, kHz, GHz, Hz

### Example values

How the main result changes when **Resistivity ρ** changes and everything else stays at the example values above:

Resistivity ρ (Ω·m)Skin depth δ (µm)8.4000e-965.23431.2600e-865.23431.6800e-865.23432.1000e-865.23432.5200e-865.23433.3600e-865.2343

## Worked example

Inputs — Conductor: Copper; Frequency f: 1 MHz.

Results — **Skin depth δ = 65.23431 µm**.

## Key terms

- **Skin effect**: Concentration of AC current near a conductor's surface.

## FAQ

**What is the skin depth of copper at 50 Hz?**
About 9.2 mm.

**Why does current avoid the centre?**
Eddy currents oppose changes of current deep inside.

**Why are magnetic metals worse?**
High permeability shrinks the skin depth dramatically.

**How is the skin effect reduced?**
With Litz wire or hollow and plated conductors.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)