Skin Effect Calculator
Compute skin depth, surface resistance, and AC resistance increase vs DC for conductors across frequency. Fast, unit-aware, and exportable results.
Skin Effect Calculator:
Skin depth in a conductor at angular frequency \( \delta = \sqrt{\frac{2}{\omega \mu \sigma}} \) is conductivity. This calculator takes frequency, material (σ, μr), and geometry, and returns δ (m), surface resistance \( R_{s}=\sqrt{\frac{\pi f \mu}{\sigma}}(\Omega), \) , and an estimated AC/DC resistance ratio — instantly showing whether skin effect significantly raises loss for your frequency and conductor size.
simple skin effect Tools formula
Formula reference: δ = sqrt(2 / (ω μ
σ)), ω = 2πf, μ = μ₀·μᵣ (μ₀ = 4π×10⁻⁷ H/m).
DC resistance per length: R_dc = 1 / (σ π a²).
Approximations: for a/δ > 3 → R_ac ≈ R_dc · (a / (2δ)). Otherwise R_ac ≈ R_dc · [1 + (a²)/(8
δ²)].
This Skin Effect Calculator computes the electromagnetic skin depth δ, surface resistance Rs, and approximate AC resistance increase for conductors given frequency and material properties. Enter frequency, conductivity (or choose a material like copper, aluminum), relative permeability, and conductor geometry (solid round wire radius, flat strip thickness, or sheet). The tool uses the standard skin-depth formula \( \delta =\sqrt{\frac{2}{\omega \mu \sigma}} (or \delta=\sqrt{\frac{1}{\pi f \mu \sigma}}) \) derives surface resistance \( R_{s}=\sqrt{\frac{\pi f \mu}{\sigma}} \) and provides practical outputs: skin depth (m/mm/µm), surface resistance (Ω), AC resistance per length estimate, fractional current penetration, and guidance when the simple approximations break down. Export results to CSV or copy to clipboard for documentation.
Work & Installation — Input to Output Summary
Work: Computes skin depth, surface resistance, and approximate AC resistance change for typical conductor geometries; warns When approximations are invalid, and suggests FEM for complex cases.
Installation:
- Insert HTML container + CSS.
- Add single JS module with formulas, units handling, and material presets (Cu, Al, Ag, Fe).
Input: Frequency (Hz), Material / Conductivity σ (S/m), Relative permeability μr, Conductor geometry (solid round radius or diameter, sheet thickness, or flat strip dims), Units.
Output: Skin depth δ (m, mm, µm), Surface resistance R_s (Ω), Approx. AC resistance per unit length (Ω/m), AC/DC resistance ratio, Fraction of current within δ, Notes & approximation warnings, Copy / Export CSV.
Testing and Final Adjustments
Test frequencies (10 Hz -GHz), material settings (copper, aluminum, steel), and geometries: very thin sheets (thickness 1/2 1000 times 1/2 1000 times 1/2 1000 times 1/2 1000 times 1/2 1000 times 1/2 1000 times 1/2 1000 times 1/2 1000 times 1/2 1000 times 1/2 Check δ with hand for known cases (i.e. copper at 50 Hz and 1 MHz). Check unit conversions and extreme value processing (do not divide by zero). Add UX: display a fast indicator with Is skin effect significant that goes through the conductor radius 3 delta, displays a display steps option that displays intermediate values and formulas, and display warnings when the simplified geometrical approximations go beyond 10 per cent error (recommend FEM/EM solver).
Frequently Asked Questions - Skin Effect Calculator:
What is skin depth?
Skin depth δ is the distance into a conductor where AC current density falls to 1/e of its surface value, δ=√(2/(ωμσ)).
Which inputs does the calculator need?
Frequency, material conductivity (or preset), relative permeability μr, and conductor geometry (radius/ thickness).
How do I get skin depth for copper at 50 Hz?
Enter f=50 Hz, choose copper (σ≈5.8e7 S/m, μr≈1); the tool computes δ automatically.
What is surface resistance Rs?
Surface resistance Rs = √(π f μ / σ). It represents the effective sheet resistance due to skin effect (Ω).
When is skin effect important?
When conductor dimensions (thickness or radius) are comparable to or larger than a few skin depths (e.g., radius > 3δ), AC resistance rises significantly vs DC.
Does the calculator include skin effect in stranded conductors or Litz wire?
No — stranded or Litz-wire behavior depends on strand geometry and transposition; the tool reports homogeneous conductor results and suggests specialized models for Litz/stranded cables.
Can I input custom materials?
Yes — you can enter conductivity (S/m) and relative permeability μr for any material.
How accurate are AC resistance estimates?
Good for quick engineering estimates; exact resistance for intermediate geometries or complex cross-sections may need numerical EM simulation (FEM).
Does frequency range include RF and microwave?
Yes — the formulas are valid across wide frequency ranges, but check units and note that at very high frequencies additional effects (surface roughness, proximity effect) may matter.
Can I export results?
Yes — results can be copied to clipboard or exported as CSV for documentation and further analysis.
