Calculators
Skin Depth Calculator
Estimate conductor skin depth from frequency and material properties.
Skin Depth Calculator tool
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About This Tool
Alternating current does not always spread uniformly through a conductor. As frequency rises, electromagnetic fields cause current density to concentrate nearer the surface, a phenomenon called the skin effect. Skin depth is a convenient characteristic distance for describing that decay. This calculator applies the standard good-conductor approximation in either direction: calculate depth from frequency or frequency from a target depth, using electrical conductivity and magnetic permeability with editable approximate presets for common nonmagnetic conductors.
How To Use It
- Choose whether to solve for skin depth or frequency, then select a common conductor preset or custom material properties.
- Enter the signal frequency or target depth and choose its engineering unit.
- For a custom material, enter conductivity in siemens per meter and relative permeability as a dimensionless positive value.
- Read the estimated skin depth in a convenient unit and use the assumptions below before applying it to a real conductor design.
Examples
Copper at 60 Hz
Using σ ≈ 5.8×10^7 S/m and μr ≈ 1, the good-conductor formula gives a skin depth of roughly 8.5 mm. Low-frequency current therefore penetrates much farther into copper than radio-frequency current.
Copper at 1 MHz
At 1 MHz with the same approximate material properties, copper skin depth is about 66 µm. Increasing frequency strongly reduces the characteristic penetration distance.
Frequency scaling
Skin depth is proportional to 1/√f when material properties stay constant. Multiplying frequency by four therefore divides the calculated skin depth by two.
Frequency for a 1 mm copper skin depth
With σ ≈ 5.8×10^7 S/m and μr ≈ 1, a target skin depth of 1 mm corresponds to approximately 4.37 kHz under the good-conductor model.
Useful Notes
Skin depth formula
For a good conductor, δ = √(2/(ωμσ)), where δ is skin depth in meters, ω = 2πf is angular frequency in radians per second, μ is absolute permeability in henries per meter, and σ is conductivity in siemens per meter. Using ω = 2πf gives the equivalent form δ = 1/√(πfμσ).
What one skin depth means
In the ideal exponential model, current density and field amplitude fall with depth approximately as e^(-x/δ). At x = δ, the amplitude is 1/e, about 36.8% of the surface value. Skin depth is therefore a decay scale, not a hard boundary beyond which no current flows.
Why frequency matters
The formula shows that skin depth decreases with the square root of frequency. Higher-frequency current becomes more concentrated near the surface, which can increase effective AC resistance compared with DC resistance. Geometry, proximity effect, and surrounding conductors can further change real current distribution.
Conductivity and temperature
Higher conductivity produces a smaller calculated skin depth when other inputs are fixed. Conductivity itself changes with material composition and temperature, so the presets are approximate reference values. Use an appropriate datasheet or measured conductivity when precision matters.
Magnetic materials need caution
Relative permeability near 1 is a useful approximation for copper, aluminum, and silver. Ferromagnetic materials can have much larger, nonlinear, and frequency-dependent permeability. Entering a single μr can illustrate the formula, but it may not accurately represent a real magnetic conductor over frequency.
Model limitations
This calculator uses the good-conductor approximation and assumes homogeneous linear material properties. It does not calculate wire AC resistance, proximity effect, surface roughness, plating behavior, finite-thickness field solutions, dielectric loss, heating, or safe current capacity. Those tasks require geometry and application-specific analysis.
FAQ
Does current stop after one skin depth?
No. Skin depth describes exponential decay. At one skin depth the ideal amplitude is about 36.8% of the surface value; it continues decreasing rather than abruptly becoming zero.
Why does copper skin depth get smaller at high frequency?
For fixed material properties, δ is proportional to 1/√f. Increasing frequency strengthens the skin-effect concentration and reduces the characteristic penetration distance.
Can I calculate frequency from a target skin depth?
Yes. Choose Frequency for target depth, enter the desired depth and material properties, and the calculator rearranges the same good-conductor equation to solve for frequency.
Are the copper, aluminum, and silver presets exact?
No. They are approximate conductivity values with μr near 1 for convenient estimates. Actual conductivity varies with alloy, purity, temperature, and source data.
Can this calculator determine AC wire resistance?
Not by itself. AC resistance also depends on conductor geometry, size relative to skin depth, proximity to other conductors, surface condition, and other effects.
Can I use a large relative permeability for steel?
You can explore the equation, but a single constant μr may be a poor model for ferromagnetic material because permeability can depend on frequency, field level, composition, and magnetic history.