Skin Depth Calculator
Calculate electromagnetic skin depth in conductors for AC signals and radio frequencies
Calculate Skin Depth
Select conductor material or choose custom to enter your own values
AC signal frequency
Skin Depth Results
Skin Depth Values
Skin Effect Analysis
Current flows in very thin surface layer
Formula: δ = √(ρ/(π·f·μ₀·μᵣ))
Where: δ = skin depth, ρ = resistivity, f = frequency, μ₀ = 4π×10⁻⁷ H/m, μᵣ = relative permeability
Practical Implications
Example Calculation
Copper Wire at 2.4 GHz (WiFi)
Material: Copper (ρ = 1.678×10⁻⁸ Ω·m, μᵣ = 0.999991)
Frequency: 2.4 GHz (WiFi frequency)
Application: RF antenna design
Calculation
δ = √(ρ/(π·f·μ₀·μᵣ))
δ = √(1.678×10⁻⁸/(π × 2.4×10⁹ × 4π×10⁻⁷ × 0.999991))
δ = √(1.678×10⁻⁸/3.017×10⁻³)
δ ≈ 1.33 μm
This explains why WiFi antennas use thin copper traces or hollow tubes!
Frequency Ranges
Audio Frequency
20 Hz - 20 kHz
Minimal skin effect
Radio Frequency
3 kHz - 300 MHz
Moderate skin effect
Microwave
300 MHz - 300 GHz
Significant skin effect
Common Materials
Applications
RF antenna design
Power transmission lines
High-frequency circuits
Electromagnetic shielding
Induction heating
Understanding Skin Effect and Skin Depth
What is Skin Effect?
The skin effect is the tendency of alternating current (AC) to distribute unevenly through a conductor's cross-section, with current density being highest near the surface and decreasing exponentially toward the center. This phenomenon occurs because changing magnetic fields induce eddy currents that oppose the main current flow.
Physical Mechanism
- •AC current creates time-varying magnetic fields
- •Faraday's law induces opposing eddy currents
- •Current is "pushed" toward the surface
- •Effect increases with frequency
Skin Depth Formula
δ = √(ρ/(π·f·μ₀·μᵣ))
- δ: Skin depth (distance where current drops to 1/e ≈ 37%)
- ρ: Resistivity of the conductor (Ω·m)
- f: Frequency of AC signal (Hz)
- μ₀: Permeability of free space (4π×10⁻⁷ H/m)
- μᵣ: Relative magnetic permeability (dimensionless)
Key Insight: Skin depth is inversely proportional to √frequency. Doubling frequency reduces skin depth by factor of √2 ≈ 1.41.
Practical Consequences
- •Increased Resistance: Effective resistance increases with frequency
- •Power Loss: Higher I²R losses due to reduced effective area
- •Design Impact: Hollow conductors as effective as solid ones
- •Material Waste: Core material unused at high frequencies
Mitigation Strategies
- Litz Wire: Multiple insulated strands reduce skin effect
- Hollow Conductors: Tubes for RF applications save material
- Surface Plating: Thin layer of high-conductivity material
- Parallel Conductors: Multiple smaller wires instead of one large
- Material Selection: Low resistivity and permeability materials