Calculator Inputs
The page stays single column overall, while the calculator uses three columns on large screens, two on smaller screens, and one on mobile.
Example Data Table
This worked example uses copper at 1 MHz with a 1 mm radius and 10 m length.
| Example Item | Example Value | Notes |
|---|---|---|
| Material | Copper | Preset conductivity near 5.8 × 10⁷ S/m |
| Frequency | 1 MHz | Higher frequency makes skin effect stronger |
| Radius | 1 mm | Solid round conductor assumption |
| Length | 10 m | Used for resistance estimation |
| Skin Depth | ≈ 0.0661 mm | Very shallow current penetration |
| Estimated DC Resistance | ≈ 0.0549 Ω | Full cross-section conducts under DC |
| Estimated AC Resistance | ≈ 0.4294 Ω | Current crowds near the surface |
| AC/DC Ratio | ≈ 7.82 | Resistance rises sharply at RF |
Formula Used
Skin depth: δ = √(2ρ / ωμ) = 1 / √(πfμσ)
Angular frequency: ω = 2πf
Absolute permeability: μ = μ₀μᵣ
Surface resistance: Rs = √(πfμ / σ)
DC resistance: Rdc = ρL / A
Estimated AC resistance: Rac = ρL / Aeff
Effective area estimate for a round solid conductor: Aeff ≈ π[r² - (r - δ)²], capped at the full area when δ ≥ r.
Current density decay: J(x) = J0e-x/δ
The AC resistance model is an engineering approximation for solid round conductors. It is practical for design screening and loss comparison.
How to Use This Calculator
- Select a material preset or choose custom.
- Enter frequency, conductor radius, and conductor length.
- Review conductivity, permeability, and temperature settings.
- Set the surface current density used for the decay plot.
- Press Calculate Skin Effect.
- Read the result summary above the form.
- Study the detailed table and the Plotly graph.
- Use the CSV or PDF buttons to export the result block.
8 FAQs
1. What does skin effect mean?
Skin effect is the tendency of alternating current to concentrate near a conductor’s surface. As frequency rises, current penetrates less deeply, so the effective conducting area shrinks and AC resistance increases.
2. Why does frequency matter so much?
Skin depth is inversely related to the square root of frequency. Doubling frequency does not halve skin depth, but increasing frequency greatly reduces penetration and can significantly increase loss.
3. Why is permeability included?
Magnetic permeability changes how strongly fields interact with the conductor. Higher permeability reduces skin depth, so ferromagnetic materials often show much stronger skin effect than nonmagnetic conductors.
4. Why does temperature change the answer?
Conductivity usually drops as temperature rises. Lower conductivity raises resistivity, which changes skin depth and resistance. This matters in power electronics, RF hardware, and hot operating environments.
5. Is the AC resistance result exact?
It is an engineering estimate based on effective conducting area for a solid round conductor. It is very useful for screening and comparison, but full-field solutions are better for strict high-accuracy analysis.
6. When is skin effect usually negligible?
Skin effect is small when the conductor radius is much less than the skin depth. In that case, current remains distributed through most of the cross-section and AC resistance stays near DC resistance.
7. How can designers reduce skin-effect loss?
Common methods include using litz wire, plated surfaces, wider conductors, hollow tubing, shorter paths, lower frequencies, or materials with better conductivity when the design allows them.
8. What does the graph show?
The graph plots current density decay from the conductor surface inward. A sharp drop indicates strong skin effect, while a flatter curve means current can penetrate more deeply into the conductor.