Skin Depth Calculator

Skin Depth Calculator. At high frequencies, alternating current doesn't flow evenly through a conductor — it concentrates near the surface, a phenomenon called the skin effect. The Skin Depth Calculator quantifies this by calculating exactly how deep current penetrates into a conductor. Select your Conductor Material (copper, aluminum, silver, and more), enter the signal Frequency, and adjust Resistivity and Relative Permeability if needed, to get the Skin Depth (δ) in µm, mm, and nm, plus the current density at that depth as a percentage of the surface value. Also try the use the Coulomb's Law Calculator.

Conductor Material *

Select a preset material to auto-fill resistivity and permeability, or choose Custom to enter your own values.

Frequency *

Signal frequency in Hertz (e.g. 1000000 for 1 MHz).

Resistivity (ρ) *

Ω·m

Electrical resistivity of the conductor in Ohm-meters. Auto-filled when a material is selected.

Relative Permeability (μr) *

Relative magnetic permeability of the conductor. Most non-magnetic metals have μr ≈ 1.

Results

Skin Depth (δ)

Skin Depth (mm)

Skin Depth (nm)

Current Density at Depth (% of surface)

What is skin effect?

Skin effect is the tendency of an alternating current (AC) to concentrate near the outer surface of a conductor rather than flowing uniformly through its entire cross-section. As frequency increases, the current density becomes higher at the surface and decreases exponentially toward the center. This effectively reduces the usable cross-section of the conductor, increasing its AC resistance. See also our calculate Total Electric Potential (V), Potential due to Charge 1 & Potential due to Charge 2 — Electric Potential.

What is skin depth?

Skin depth (δ) is the distance from the surface of a conductor at which the current density has fallen to approximately 37% (1/e) of its value at the surface. It quantifies how deeply an AC signal penetrates into a conducting material and is the key measure of skin effect severity.

What is the formula for skin depth?

The skin depth formula is δ = √(ρ / (π × f × μ₀ × μr)), where ρ is the electrical resistivity of the conductor (Ω·m), f is the signal frequency (Hz), μ₀ is the permeability of free space (4π × 10⁻⁷ H/m), and μr is the relative permeability of the material. Higher frequency or higher permeability results in a smaller skin depth.

Why is there no skin effect with DC signals?

Skin effect only occurs with alternating current. DC signals do not alternate in direction, so there are no opposing electromagnetic fields generated inside the conductor to push current toward the surface. With DC, current distributes uniformly across the entire cross-section of the conductor. You might also find our Magnetic Declination Calculator useful.

How is skin depth related to frequency?

Skin depth is inversely proportional to the square root of frequency. This means that as frequency increases, the skin depth decreases — the current is confined to an ever-thinner surface layer. At very high frequencies (RF and microwave), the skin depth can be just a few micrometers or less, which is why hollow conductors are used in RF applications.

How do I reduce skin effect?

Common techniques to mitigate skin effect include using Litz wire (many thin insulated strands woven together), silver-plating conductors (since silver has low resistivity at the surface where current flows), using hollow tubes instead of solid rods for RF conductors, and choosing materials with lower resistivity. Operating at lower frequencies also reduces skin effect.

What is the skin depth of copper at 1 MHz?

At 1 MHz, copper (resistivity ≈ 1.68 × 10⁻⁸ Ω·m, μr = 1) has a skin depth of approximately 66 µm (0.066 mm). This means that at 1 MHz, most of the current flows within the outermost 66 micrometers of the copper conductor's surface.

Why are RF antennas made from hollow tubes?

At high radio frequencies, the skin depth is so small that current only flows in a thin layer near the conductor surface. The core material contributes almost no electrical conduction. Using hollow tubes instead of solid rods saves material and weight while providing essentially the same electrical performance, since the interior of a solid rod would carry negligible current anyway. Check out our calculate Electromagnetic Induction as well.