⚡ Skin Depth Calculator
Calculate AC current penetration depth in conductors
Default: 4π×10⁻⁷ H/m (free space) for non-magnetic materials
How to Use This Calculator
Select Material (Optional)
Choose a material from the dropdown to auto-fill permeability and conductivity values, or select "Custom" to enter your own values.
Enter Frequency
Input the AC frequency in Hertz (Hz). Higher frequencies result in smaller skin depths (less current penetration).
Enter Permeability and Conductivity (if custom)
For custom materials, input permeability in H/m and conductivity in S/m. For non-magnetic materials, use 4π×10⁻⁷ H/m.
Calculate
Click the "Calculate Skin Depth" button to get the skin depth in meters. This represents the depth at which current density drops to 1/e (37%) of surface value.
Formula
δ = √(2 / (ω × μ × σ))
where ω = 2πf
Where:
- δ = Skin Depth (meters, m)
- ω = Angular Frequency = 2πf (radians per second)
- f = Frequency (Hertz, Hz)
- μ = Permeability (Henries per meter, H/m)
- σ = Conductivity (Siemens per meter, S/m)
Example Calculation:
For copper at f = 1 MHz (σ = 5.96×10⁷ S/m, μ = 4π×10⁻⁷ H/m):
ω = 2π × 1×10⁶ = 6.283×10⁶ rad/s
δ = √(2 / (6.283×10⁶ × 4π×10⁻⁷ × 5.96×10⁷))
δ = 6.61×10⁻⁵ m = 66.1 μm
Note: Skin depth is the depth where current density decreases to 1/e (≈37%) of the surface value. At higher frequencies, current concentrates near the surface, increasing effective resistance.
About Skin Depth Calculator
The Skin Depth Calculator determines the depth at which AC current penetrates into a conductor. At high frequencies, AC current tends to flow near the surface due to the skin effect, reducing the effective cross-sectional area and increasing resistance. Skin depth is the depth where current density drops to 1/e (approximately 37%) of the surface value.
When to Use This Calculator
- RF Engineering: Calculate skin depth for high-frequency circuits
- Cable Design: Design conductors for AC power transmission
- Power Systems: Analyze AC resistance in power lines
- Antenna Design: Understand current distribution in antenna elements
- Electromagnetic Analysis: Study AC current distribution in conductors
Why Use Our Calculator?
- ✅ Material Database: Pre-loaded values for common conductor materials
- ✅ Quick Calculation: Instantly determine skin depth
- ✅ Frequency Analysis: Understand how frequency affects current penetration
- ✅ Free Tool: No registration or payment required
- ✅ Educational: Learn about skin effect and AC resistance
Common Applications
High-Frequency Circuit Design: Calculate skin depth to design conductors for RF and microwave circuits. At high frequencies, current concentrates near the surface, so hollow or plated conductors can be used to save material and weight while maintaining performance.
Power Transmission: Analyze AC resistance in power lines. At power frequencies (50-60 Hz), skin depth is large (several mm to cm), so solid conductors work well. At higher frequencies, stranded or Litz wire (multiple insulated strands) is used to increase effective surface area.
Wire Gauge Selection: Determine appropriate wire gauge considering skin effect. If wire diameter is much larger than skin depth, the center of the wire carries little current, wasting material. Optimal wire size balances material cost and resistance.
Tips for Best Results
- Skin depth decreases with increasing frequency (δ ∝ 1/√f)
- Higher conductivity materials have smaller skin depths
- If wire radius is much greater than the skin depth, the center carries little current
- Use Litz wire (multiple insulated strands) to reduce skin effect losses
- At 60 Hz, skin depth in copper is ~8.5 mm
Frequently Asked Questions
What is skin depth?
Skin depth (δ) is the depth at which AC current density decreases to 1/e (≈37%) of the surface value. It represents how deep AC current penetrates into a conductor. Due to the skin effect, AC current tends to flow near the surface, especially at high frequencies.
Why does skin depth decrease with frequency?
Skin depth is inversely proportional to the square root of frequency: δ ∝ 1/√f. At higher frequencies, induced eddy currents create opposing magnetic fields that push current toward the surface. This concentrates current in a thinner layer, reducing effective penetration depth.
How does skin effect affect resistance?
Skin effect reduces the effective cross-sectional area carrying current, increasing AC resistance above DC resistance. If wire diameter is much greater than the skin depth, much of the conductor carries little current, effectively wasting material. AC resistance can be significantly higher than DC resistance at high frequencies.
What is Litz wire and why is it used?
Litz wire consists of multiple insulated strands twisted together. Each strand is smaller than skin depth, allowing current to flow throughout each strand rather than just at the surface. This reduces AC resistance and skin effect losses, making Litz wire ideal for high-frequency applications like inductors and transformers.
Is skin effect significant at power frequencies (50-60 Hz)?
At 60 Hz, skin depth in copper is approximately 8.5 mm. For typical power cables (10-20 mm diameter), skin effect is moderate but noticeable. AC resistance is typically 5-20% higher than DC resistance. For larger conductors, stranded or hollow designs reduce skin effect impact.
How do I reduce skin effect losses?
Use smaller diameter conductors (diameter ≤ skin depth), Litz wire (multiple insulated strands), or hollow conductors for high-frequency applications. For power frequencies, stranded cables help. Surface plating with high-conductivity materials (silver) can also help, though cost-effective only for specific applications.