Skin Depth Calculator
Compute skin depth in electrical conductors at any frequency using δ = √(ρ/πfμ₀μᵣ). Free RF skin effect calculator with material presets, interactive charts, and formula breakdown.
About This Calculator
The Skin Depth Calculator computes the skin depth δ in electrical conductors using the formula δ = √(ρ / πfμ₀μᵣ), where ρ is the electrical resistivity of the conductor material, f is the frequency of the alternating current signal, μ₀ = 4π × 10⁻⁷ H/m is the vacuum permeability, and μᵣ is the relative magnetic permeability of the conductor.
When an AC signal flows through a conductor, the current distribution is not uniform — current density is highest at the surface and decreases exponentially toward the center. This phenomenon, called the skin effect, becomes more pronounced at higher frequencies. At radio frequencies (MHz to GHz), current flows only through an extremely thin surface layer (a few microns), which is why RF antennas and conductors use hollow tubes instead of solid metal rods to save weight and cost.
The calculator supports five common conductor materials with auto-populated properties: copper (ρ = 1.678 × 10⁻⁸ Ω·m, μᵣ = 0.999), aluminum (ρ = 2.65 × 10⁻⁸ Ω·m, μᵣ = 1.000022), gold (ρ = 2.44 × 10⁻⁸ Ω·m, μᵣ = 1), silver (ρ = 1.59 × 10⁻⁸ Ω·m, μᵣ = 0.99998), and nickel (ρ = 6.99 × 10⁻⁸ Ω·m, μᵣ = 150). A custom option allows entering any resistivity and relative permeability for specialized materials or alloys.
Skin depth is a critical parameter in RF engineering, PCB design, power electronics, antenna design, and electrical engineering. Understanding skin depth helps engineers choose appropriate wire gauges, design efficient high-frequency transformers, minimize resistive losses, and determine whether skin effect is negligible for a given application.
Regional Notes: Mains AC frequency is 50 Hz in most countries (Europe, Asia, Africa, Australia) and 60 Hz in North America and parts of South America and Asia. The skin depth difference between 50 Hz and 60 Hz is small — approximately 9.2 mm vs 8.5 mm for copper. This calculator works correctly for any frequency worldwide, from Hz to GHz.
Frequently Asked Questions
What is skin depth?
Skin depth is the distance from the surface of a conductor where the current density drops to about 37% (1/e) of its value at the surface. It occurs because alternating current tends to flow near the surface of a conductor due to the skin effect — a phenomenon caused by eddy currents induced by the changing magnetic field inside the conductor.
How do you calculate skin depth?
Skin depth is calculated using the formula δ = √(ρ / πfμ₀μᵣ) where ρ is the resistivity of the conductor, f is the frequency of the AC signal, μ₀ is the permeability of free space (4π × 10⁻⁷ H/m), and μᵣ is the relative magnetic permeability of the conductor.
What is the skin depth of copper at 60 Hz?
The skin depth of copper at 60 Hz is approximately 8.5 mm. This means that at standard household AC frequencies, current flows through most of a typical wire cross-section, making skin effect negligible for most household wiring applications.
Why is there no skin effect in DC?
Skin effect depends on the frequency of the signal. Since the frequency of a DC signal is zero, the skin depth becomes infinite, meaning current distributes uniformly across the entire cross-section. There is no changing magnetic field to induce opposing eddy currents in DC.
How does frequency affect skin depth?
Skin depth is inversely proportional to the square root of frequency. Higher frequencies produce smaller skin depths. For example, copper at 50 Hz has a skin depth of about 9.2 mm, while at 2.4 GHz (Wi-Fi frequency) it shrinks to approximately 1.3 μm — barely a few microns.
Why are RF antennas made from hollow tubes?
At radio frequencies, the skin depth is extremely small (a few microns), so current flows only through a thin outer layer of the conductor. Hollow tubes provide the same conducting surface area as solid rods but use much less material, reducing weight and cost without sacrificing performance.
How can I reduce the skin effect in conductors?
To reduce the skin effect: (1) use conductors with lower magnetic permeability, (2) reduce the conductor size, (3) use hollow tubes instead of solid rods for high-frequency signals, or (4) use Litz wire — specially designed woven strands of several insulated thin wires instead of a single thick wire.
What is the difference between skin depth in copper vs aluminum?
Copper has lower resistivity (1.678 × 10⁻⁸ Ω·m) than aluminum (2.65 × 10⁻⁸ Ω·m), so copper has a smaller skin depth at the same frequency. For example at 60 Hz, copper skin depth is about 8.5 mm while aluminum is about 10.6 mm. Both materials have relative permeability near 1 (non-magnetic).