Skin Depth Calculator: AC Circuits and Electroma...
Calculate the skin depth of conductors in AC circuits. Understand why high-frequency currents flow only near the conductor surface and how it affects resistance a...
What is Skin Depth?
The skin effect is the tendency of AC current to concentrate near the surface of a conductor, not through its entire cross-section. The skin depth (δ) is the depth at which current density falls to 1/e (≈37%) of its surface value. It decreases with increasing frequency, making high-frequency conductors effectively hollow.
⚡ Skin Depth Calculator
Free calculator for instant results.
📐 Formula
δ = √(2ρ / ωμ)
ρ = resistivity (Ω·m), ω = 2πf (angular frequency), μ = magnetic permeability = μ₀μᵣ (H/m). δ in meters.
📝 Worked Example
Copper (ρ=1.72×10⁻⁸ Ω·m) at f=1 MHz:
ω = 2π×10⁶ = 6.28×10⁶
δ = √(2×1.72×10⁻⁸ / (6.28×10⁶ × 4π×10⁻⁷)) = 66 μm
At 10 GHz: δ ≈ 0.66 μm
📝 How to Use
❓ FAQ
Why does skin effect increase wire resistance at high frequencies?
Only the outer shell of conductor carries current. The effective cross-section decreases, increasing resistance. This is why large conductors and Litz wire are used in RF applications.
What is the practical implication for coaxial cables?
The inner conductor's skin depth determines the effective current-carrying area. Outer conductors shield EM fields — effective shielding requires thickness >> δ.
Veer Kumavat
Founder & AuthorVeer is a 14-year-old student from Nashik, Maharashtra, who built SciFi Calculators to help students worldwide master STEM subjects. He is passionate about making complex science and math problems accessible through intuitive digital tools.