Skin Depth Calculator

Skin Depth

Calculate the skin depth (δ) of an electromagnetic wave in a conducting material at a given frequency.

Last updated: March 2026 | By ForgeCalc Engineering

Skin Depth (δ)
66.09
Micrometers (μm)
In Millimeters
0.0661 mm

What is Skin Depth?

Skin depth (δ) is a measure of how far an alternating current (AC) or electromagnetic wave penetrates into a conductor. As the frequency of the current increases, the current density becomes higher near the surface (the "skin") of the conductor and decreases exponentially as you move deeper into the material.

The skin depth is defined as the distance at which the current density has decreased to 1/e (about 37%) of its value at the surface. This phenomenon is known as the "Skin Effect."

The Formula

δ = √(2 / (ω × μ × σ))

Where:
δ (delta) is the skin depth (m)
ω (omega) is the angular frequency (2πf)
μ (mu) is the permeability of the material (μ₀ × μ_r)
σ (sigma) is the electrical conductivity (S/m)

Frequently Asked Questions

Why does skin depth decrease with frequency?

Higher frequencies induce stronger eddy currents within the conductor that oppose the main current flow in the center, forcing the current to the outer edges.

How does this affect wire design?

At high frequencies, the center of a solid wire carries very little current. To reduce weight and cost, engineers often use hollow tubes or 'Litz wire' (many small insulated strands) to maximize the available surface area.

What is the skin depth of copper at 60Hz?

At 60Hz, the skin depth of copper is about 8.5mm. This means for typical household wiring, the skin effect is negligible, but for large industrial busbars, it is a significant design factor.

How does permeability affect skin depth?

Materials with high magnetic permeability (like iron or steel) have much smaller skin depths than non-magnetic materials like copper, even if their conductivity is lower.

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