# Skin Depth Calculator

Understanding the skin effect and calculating the skin depth is essential for designing **efficient and effective electrical circuits**. With this tool, you can calculate the skin depth of copper and many other conductors; **you only need to know the frequency and the material used**.

## The skin effect

When an alternating current flows through a conductor, the electric field associated with the current will cause the **flow of electrons to concentrate near the conductor's surface**. This phenomenon is known as the **skin effect**, and its cause is the eddy currents. Eddy currents refer to currents in the conductor that, as a consequence of Faraday's Law, are induced by a changing magnetic field.

The **skin depth** is the distance from the conductor's surface at which the current density reduces to 1/e (approximately 37%) of its original value.

The skin effect reduces the effective cross-section of the conductor and, as you can observe in our wire resistance calculator, increases the effective resistance.

## Skin depth formula

To calculate the skin depth, we use the following formula:

, where:

- $\delta$ — Skin depth, calculated in meters ($\text m$);
- $\rho$ — Conductor resistivity, in ohms meters ($\Omega \cdot \text m$);
- $f$ — Frequency of the AC signal, in hertz ($\text{Hz}$);
- $\mu_0 = 4\pi \times 10^{-7} \text{ H/m}$ — The permeability of free space, in henries per meter; and
- $\mu_\text r$ — Relative magnetic permeability of the conductor, a
**unitless**quantity (learn more about it in our magnetic permeability calculator).

We can use the units we want in the **calculator**, and it will provide the correct result. Still, to properly use the skin depth **formula**, we must **use the units mentioned above** to warranty dimensional homogeneity. We must consider that:

**Resistivity**is usually given in $\text μ \Omega \cdot \text{cm}$. To use it in the skin depth equation, we must convert it to $\text μ \Omega \cdot \text{cm}$, remembering that $1\ \text μ \Omega \cdot \text{cm} = 10^{-8}\ \Omega \cdot \text m$.**Skin depth**is usually required in $\text{mm}$ (or even $\text{μm}$ for high frequencies). To convert it to $\text{mm}$ or $\text{μm}$, remember that $1\ \text m = 10^3 \text{ mm} = 10^6 \text{ μm}$, or use our length converter.- For radio frequency applications, frequencies are high and usually expressed in gigahertz ($\text{GHz}$). To convert them to $\text{Hz}$, remember that $1 \text{ GHz} = 10^9\text{ Hz}$.

For example, let's use the skin depth equation to calculate the **skin depth of copper** at $\text{Hz}$.

So, the **skin depth of copper** at **60 Hz** is **8.417 mm.**

🙋 Remember that, for copper, $\rho = 1.678 \text{ μ}\Omega \cdot \text {cm} = 1.678 \times 10^{-8}\ \Omega \cdot \text m$ and $\mu_\text r = 0.999991$.