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Skin Depth & AC Conductor Resistance Calculator

In alternating current (AC) conductors, changing magnetic flux induces eddy currents that oppose current flow in the center, crowding charges toward the outer surface.

Operating frequency in Hertz (e.g. 60 Hz mains, 1 MHz RF, 2.4 GHz WiFi).

Electrical resistivity (Copper = 1.68×10⁻⁸, Aluminum = 2.65×10⁻⁸, Silver = 1.59×10⁻⁸ Ω·m).

Magnetic permeability (Copper/Aluminum ≈ 1.0, Iron ≈ 100 to 5000).

Optional wire diameter to evaluate high-frequency AC resistance multiplication.

Calculated Result
65.23 µm

Skin Depth (δ)

Skin Depth (δ)

65.23 µm (0.0652 mm)

Frequency

1.00 MHz

Resistivity (ρ)

1.68e-8 Ω·m

Conductor Relative Permeability (μ_r)

1

AC-to-DC Resistance Ratio (R_ac / R_dc)

4.092x higher resistance at RF

Effective Conduction Area

0.1916 mm²

Calculation Breakdown

  1. 1. Permeability Calculationμ = μ_r · μ₀ = 1 · (4π × 10⁻⁷) = 1.257e-6 H/m
  2. 2. Skin Depth Formulaδ = √(ρ / (π · f · μ)) = √(1.68e-8 / [π · 1000000 · 1.26e-6]) = 65.23 µm
  3. 3. Current Crowding AnalysisApproximately 63.2% of the current flows within 1 skin depth (65.23 µm) from the surface; 98.2% flows within 4 skin depths.

Skin Depth in Copper vs Frequency

Interactive visualization based on your current inputs

Skin Depth (µm)
0.02.1k4.3k6.4k8.5k60 Hz (Mains)1 kHz (Audio)100 kHz (SMPS)1 MHz (RF)10 MHzFrequencySkin Depth (µm)

What Is the Skin Depth & AC Conductor Resistance Calculator?

Skin depth is the measure of the non-uniform distribution of electric current near the surface of a conductor carrying alternating current.

How Does the Skin Depth & AC Conductor Resistance Calculator Work?

Faraday’s induction law generates opposing back-EMF near the center axis of conductors, forcing current into a thin outer annular ring.

Skin Depth & AC Conductor Resistance Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

\delta = \sqrt{\frac{\rho}{\pi \cdot f \cdot \mu_r \cdot \mu_0}}, \quad \frac{R_{ac}}{R_{dc}} \approx \frac{r}{2\delta} + 0.26

Skin depth delta is square root of resistivity over pi times frequency times absolute permeability. AC resistance increases as wire radius exceeds skin depth.

How to Use the Skin Depth & AC Conductor Resistance Calculator

  1. Input the operating frequency in Hertz.
  2. Specify material resistivity and relative magnetic permeability.
  3. Optionally supply wire diameter in millimeters.

Step-by-Step Example Calculation

Copper Wire (1 mm) at 1 MHz

Input Values:

frequencyHz:1000000
resistivityOhmMeter:1.68e-8
relativePermeability:1.0
wireDiameterMm:1.0
Worked Steps: At 1 MHz in copper, skin depth is only 65.25 µm. High-frequency AC resistance is 4.09x greater than DC resistance.

Understanding Your Result

Skin Depth (µm): Thickness where current density drops to 36.8%.

AC/DC Resistance Ratio: Factor increase in conductor dissipation at RF.

Effective Conduction Area: True annular carrying cross-section.

Factors That Affect the Result

  • Decreases with higher frequency and higher magnetic permeability; increases with higher resistivity.

When Should You Use This Calculator?

  • RF antenna cabling, switch-mode power transformer design, induction heating coils, and coaxial cable engineering.

Assumptions & Limitations

  • Valid for homogeneous conductors with diameters larger than skin depth.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard Maxwell electromagnetic boundary value solution with exact permeability constant μ₀.

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