Choose a material preset or enter custom values. For non-magnetic metals, set relative permeability near 1.
Example Data Table
| Case | Material | Frequency | μr | σ (S/m) | Typical δ (approx.) |
|---|---|---|---|---|---|
| Power | Copper | 60 Hz | 1 | 5.8×107 | ~8.5 mm |
| Audio | Aluminum | 10 kHz | 1 | 3.5×107 | ~0.85 mm |
| RF | Copper | 1 MHz | 1 | 5.8×107 | ~66 µm |
| Microwave | Silver | 2.4 GHz | 1 | 6.3×107 | ~1.3 µm |
Values are illustrative and depend on alloy, temperature, and magnetic state.
Formula Used
Skin depth δ describes how deeply alternating current penetrates a conductor before it decays significantly. For a good conductor with sinusoidal excitation:
- ω = 2πf (angular frequency)
- μ = μ0 μr (absolute permeability)
- δ = √(2 / (ω μ σ))
- Equivalent form: δ = √(1 / (π f μ σ))
Units: f in Hz, μ in H/m, σ in S/m, producing δ in meters.
How to Use This Calculator
- Select a frequency value and unit.
- Pick a material preset or keep custom.
- Choose conductivity or resistivity mode.
- Enter μr for magnetic behavior if needed.
- Click Calculate to see results above.
- Use CSV or PDF buttons to export outputs.
Practical Notes
- At higher frequencies, current crowds near the surface, raising AC resistance.
- Higher permeability often reduces skin depth, especially in steels.
- Conductivity varies with temperature and alloy composition.
- For thick conductors, skin depth helps estimate effective cross-section.
In-Depth Guide
1) What skin depth represents
Skin depth (δ) is a practical thickness measure for alternating current flow in conductors. At a depth of one δ, the current density drops to about 37% of its surface value. This calculator outputs δ in meters, millimeters, micrometers, and mils to match common electrical and manufacturing contexts.
2) Why engineers care about skin effect
When frequency rises, effective current-carrying area shrinks, so AC resistance increases. That change impacts copper losses, heating, efficiency, and impedance in cables, busbars, transformers, inductors, and RF components. Skin effect is also a driver behind plating choices and conductor geometry decisions.
3) Inputs that control the result
The model depends on frequency f, conductivity σ, and permeability μ = μ0 μr. Higher f, higher μr, or higher σ all reduce δ. If you provide resistivity ρ, the calculator converts it using σ = 1/ρ.
4) Typical conductivity data you may use
Room-temperature copper is often near 5.8×107 S/m, aluminum about 3.5×107 S/m, and silver about 6.3×107 S/m. Stainless steels vary widely and can be closer to 106 S/m, while carbon steels may also have large μr values that strongly reduce δ.
5) Frequency benchmarks with real scale
At 50–60 Hz, copper skin depth is on the order of several millimeters, so thick bars still carry current through much of their cross-section. Around 1 MHz, δ is typically tens of micrometers, making surface finish and plating more relevant. In the GHz range, δ can be near one micrometer, so surface treatments can dominate loss.
6) Design implications for conductors and coils
Compare conductor thickness to δ when estimating AC resistance. If thickness is many times δ, most current flows near the surface and additional thickness adds little benefit. For windings, using multiple strands (litz wire) can reduce AC loss when strand diameter is comparable to δ.
7) Measurement and modeling considerations
Conductivity changes with temperature, purity, and alloying, and permeability can be nonlinear for ferromagnetic materials. For precision work, use material datasheets at the operating temperature, and consider that μr may vary with field strength and frequency. This tool is ideal for fast, conservative estimates and comparisons.
8) Common pitfalls and quick checks
Always confirm units: frequency must be in Hz after scaling, and resistivity must be in Ω·m. If results look too large at high frequency, check that σ was not entered in MS/m instead of S/m. For non-magnetic metals, μr should be near 1; using 100 by mistake can shrink δ by ten times.
FAQs
1) Is skin depth the same as wire radius?
No. Skin depth is a penetration distance in the material. Wire radius is geometry. When radius is much larger than δ, current concentrates near the surface and AC resistance rises.
2) What happens to skin depth when frequency doubles?
Skin depth decreases by a factor of √2 because δ ∝ 1/√f. Higher frequency pushes current closer to the surface.
3) Should I use conductivity or resistivity inputs?
Use whichever data you have. The calculator converts resistivity using σ = 1/ρ. Ensure resistivity is in Ω·m, not Ω·cm.
4) Why does permeability matter so much?
Skin depth scales as 1/√μ. Ferromagnetic materials can have μr far above 1, which reduces δ and increases AC loss significantly.
5) Can I apply this to plated conductors?
Yes for first-order insight. If plating thickness is several δ of the plating material, most current stays in the plating. Otherwise, current shares with the base metal.
6) Does temperature change the result?
Yes. Metals typically lose conductivity as temperature rises, which increases δ. Use conductivity values appropriate for your operating temperature when accuracy matters.
7) Is this valid for all frequencies and materials?
It is best for good conductors with sinusoidal steady-state excitation. Extremely high frequencies, strong magnetic nonlinearities, or complex composites may need more detailed electromagnetic modeling.