Skin Depth Calculator
Calculate AC or RF skin depth from conductor material, frequency, resistivity, and relative permeability.
Calculator is for informational purposes only. Terms and Conditions
Uses the standard good-conductor approximation; material properties are treated as frequency-independent input values.
Enter conductor and frequency values
Choose a preset conductor or use Manual Properties to enter your own resistivity and permeability.
Frequency must be greater than zero. Preset resistivity values are reference values at 20 °C.
Skin Depth Result
Skin depth is shown first, followed by penetration multiples and surface resistance.
Result details
- 1 skin depth—
Show calculation steps Review conversions, equation, substitution, and checks
- Enter valid values to see the complete calculation.
Current Density with Depth
Normalized current-density amplitude follows J/J₀ = e^(−x/δ) in the good-conductor model.
- Calculating the example state…
Method, Sources, and Assumptions
Calculation basis, reference material values, limitations, and verification guidance.
The calculator uses the NIST classical good-conductor relationship δ = √(2ρ/ωμ), written equivalently as δ = √[ρ/(πfμ₀μr)], with reference conductor resistivities from NIST wire tables.
- Copper preset: standard annealed copper, 1.7241 µΩ·cm at 20 °C (100% IACS).
- Aluminum preset: EC-H19 conductor, 61% IACS at 20 °C; resistivity is derived from the IACS reference as 1.7241/0.61 µΩ·cm.
- Preset relative permeability is approximated as μr = 1 for these nonferromagnetic conductors.
- For ferromagnetic materials, layered plating, strong proximity effect, or frequency-dependent material properties, use project-specific data or a more complete electromagnetic model.
Calculator guide
How to Read a Skin Depth Result
The skin depth calculator above determines how far an alternating electromagnetic field penetrates into a conductor before its local field or current-density amplitude falls to \(1/e\), about 36.8% of the surface value. For the fastest calculation, choose a conductor preset and enter frequency. If you select Manual Properties, enter electrical resistivity and relative permeability directly.
The primary output is skin depth \(\delta\). The calculator also reports 3\(\delta\), 5\(\delta\), and surface resistance so you can compare the electromagnetic penetration depth with a real conductor. Skin depth is not a hard current boundary: current density decays exponentially with depth rather than stopping abruptly at \(\delta\).
- Fastest input path
- Conductor preset + frequency
- Primary output
- Skin depth, \(\delta\)
- Key assumption
- Classical good-conductor model using the active material properties
How to Use the Skin Depth Calculator
Use a preset for a quick copper or aluminum calculation, or switch to Manual Properties when you have project-specific resistivity and permeability data.
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Choose the conductor material
The calculator provides Copper, Aluminum EC-H19, and Manual Properties. The copper and aluminum presets populate the reference electrical properties used by the calculation; Manual Properties unlocks resistivity and relative permeability for editing.
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Enter the operating frequency
Enter frequency in Hz, kHz, MHz, or GHz. The tool requires a value greater than 0 Hz because the finite skin-depth expression is an AC relationship. At steady DC, the frequency-dependent skin effect does not confine current to a finite surface layer.
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Enter project-specific properties when needed
In Manual Properties mode, enter resistivity in Ω·m, µΩ·cm, or nΩ·m and relative permeability as a dimensionless ratio. For magnetic materials, use permeability data appropriate to the alloy, frequency, field level, and operating condition rather than assuming one generic value.
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Interpret the result against the conductor geometry
Read \(\delta\) first, then compare 3\(\delta\) and 5\(\delta\) with the conductor thickness, radius, or plating thickness. Surface resistance is useful for high-frequency conductor-loss analysis, but it is not the total AC resistance of an arbitrary conductor by itself.
Skin Depth Formula and Calculation Method
The calculator uses the classical good-conductor skin-depth relationship. Holding the other properties constant, skin depth decreases as frequency, conductivity, or magnetic permeability increases and increases as resistivity increases.
Skin depth from resistivity
Plain-language form: skin depth equals the square root of resistivity divided by \(\pi\), frequency, vacuum permeability, and relative permeability.
This is equivalent to \(\delta=\sqrt{2\rho/(\omega\mu)}\), with \(\omega=2\pi f\) and \(\mu=\mu_0\mu_r\).
Equivalent conductivity and surface-resistance forms
Because conductivity is the reciprocal of resistivity, the same skin-depth relationship can be written with \(\sigma\). The calculator also uses the corresponding good-conductor surface-resistance relationship.
- \(\delta\)
- Skin depth Characteristic depth over which local field or current-density amplitude decays by a factor of \(e\).
- \(\rho\)
- Electrical resistivity Bulk opposition of the conductor material to electric current.
- \(f\)
- Frequency Frequency of the alternating electromagnetic field or current.
- \(\mu_0\)
- Vacuum permeability Magnetic constant used with relative permeability to obtain the material permeability.
- \(\mu_r\)
- Relative permeability Ratio of material permeability to vacuum permeability.
- \(\sigma\)
- Electrical conductivity Reciprocal of resistivity, \(\sigma=1/\rho\).
- \(R_s\)
- Surface resistance Resistive part of the good-conductor surface impedance used in high-frequency conductor-loss calculations.
Worked Example: Copper at 1 MHz
Consider the same illustrative state loaded by the calculator: standard annealed copper at 20 °C, a frequency of 1 MHz, and \(\mu_r=1\). NIST gives the standard annealed copper resistivity as 1.7241 µΩ·cm at 20 °C.
Convert the units
Substitute the values
Result
\(\delta\approx66.1\ \mu\text{m}\)
The calculator also returns approximately 198 µm for 3\(\delta\), 330 µm for 5\(\delta\), and about 261 µΩ/□ for surface resistance at this example state.
What Skin Depth, 3δ, 5δ, and Surface Resistance Mean
The primary result \(\delta\) is a decay length, not a conductor-thickness recommendation. For the ideal exponential model, normalized local current-density amplitude follows \(J/J_0=e^{-x/\delta}\).
One skin depth
At \(x=\delta\), local amplitude is \(e^{-1}\), about 36.8% of the surface value. This is the defining skin-depth point.
Three and five skin depths
At 3\(\delta\), local amplitude is about 5.0% of the surface value; at 5\(\delta\), it is about 0.67%. These multiples show how rapidly the exponential tail decays.
Surface resistance
\(R_s\) characterizes the resistive surface behavior of a good conductor at high frequency. It is useful in RF conductor-loss models but is not the total AC resistance of an arbitrary wire, trace, busbar, or winding.
Skin depth and surface resistance move in opposite directions with frequency
Holding resistivity and permeability constant, skin depth varies as \(f^{-1/2}\) while surface resistance varies as \(f^{1/2}\). A 100× increase in frequency therefore reduces \(\delta\) to one tenth while increasing \(R_s\) by 10×.
Compare skin depth with geometry
The classical value of \(\delta\) does not include wire diameter or PCB trace width. Geometry matters when you decide whether skin effect is important. A 1 mm wire and a 100 mm busbar made from the same homogeneous material at the same frequency have the same classical skin depth, but their current distributions and AC/DC resistance ratios can be very different because their dimensions relative to \(\delta\) are very different.
Copper and Aluminum Skin Depth Reference Values
The copper values below use the same 1.7241 µΩ·cm at 20 °C reference and \(\mu_r=1\) as the calculator. The aluminum comparison uses the calculator’s EC-H19 61% IACS preset. These are derived values from the active model, not universal values for every alloy or temperature.
| Frequency | Skin depth | 3δ depth | 5δ depth |
|---|---|---|---|
| 50 Hz | 9.35 mm | 28.0 mm | 46.7 mm |
| 60 Hz | 8.53 mm | 25.6 mm | 42.7 mm |
| 400 Hz | 3.30 mm | 9.91 mm | 16.5 mm |
| 1 kHz | 2.09 mm | 6.27 mm | 10.4 mm |
| 10 kHz | 661 µm | 1.98 mm | 3.30 mm |
| 100 kHz | 209 µm | 627 µm | 1.04 mm |
| 1 MHz | 66.1 µm | 198 µm | 330 µm |
| 10 MHz | 20.9 µm | 62.7 µm | 104 µm |
| 100 MHz | 6.61 µm | 19.8 µm | 33.0 µm |
| 1 GHz | 2.09 µm | 6.27 µm | 10.4 µm |
| 2.4 GHz | 1.35 µm | 4.05 µm | 6.74 µm |
| 5 GHz | 0.935 µm | 2.80 µm | 4.67 µm |
| 10 GHz | 0.661 µm | 1.98 µm | 3.30 µm |
| Conductor preset | Skin depth at 1 MHz |
|---|---|
| Copper | 66.1 µm |
| Aluminum EC-H19 | 84.6 µm |
Reference material property: NIST Circular 470 states the internationally agreed resistivity of standard annealed copper as 1.7241 µΩ·cm at 20 °C.
Applying Skin Depth to Real Conductors
Skin depth becomes most useful when you compare it with a real conductor dimension. The comparison helps indicate whether current is distributed through much of the cross section or is strongly concentrated near a surface, but it does not replace a geometry-specific loss calculation.
PCB traces and copper thickness
At 1 MHz, the copper preset gives \(\delta\approx66.1\) µm; at 100 MHz it falls to about 6.61 µm; at 1 GHz it is about 2.09 µm. As frequency rises, a fixed copper thickness represents more skin depths, so current becomes increasingly concentrated near the conducting surfaces. PCB loss still depends on trace geometry, return-current path, dielectric properties, and surface roughness.
Round wire and Litz wire
Skin depth itself does not depend on wire diameter, but skin-effect severity does depend on conductor size relative to \(\delta\). High-frequency windings often use many individually insulated strands to reduce AC loss, but strand selection cannot be based on skin depth alone because proximity effect and winding geometry also matter.
RF plating and multilayer conductors
Several skin depths can be a useful first comparison for a conductive plating layer, but 3\(\delta\) or 5\(\delta\) is not a universal plating requirement. If the layer is thin enough that fields penetrate into the substrate, the conductivities and thicknesses of both materials can affect the surface impedance.
EMI shielding
Skin depth helps describe absorption within a conductive shield, but shielding effectiveness is not determined by skin depth alone. Reflection, openings, seams, material permeability, field type, frequency, and shield geometry can all materially affect the result.
What Changes Skin Effect in Real Conductors
The calculated \(\delta\) isolates the material-and-frequency relationship. Actual conductor loss can depart from that simplified result when operating temperature, magnetic behavior, neighboring conductors, surface condition, or layering changes the physical system.
Temperature changes resistivity
NIST lists a temperature coefficient of electrical resistivity near 0.00394/°C for 100% IACS copper at 20 °C. Because \(\delta\propto\sqrt{\rho}\), a 10% increase in resistivity increases skin depth by only \(\sqrt{1.10}-1\approx4.9\%\) when frequency and permeability remain unchanged.
Magnetic materials need frequency-specific permeability
The equation scales as \(1/\sqrt{\mu_r}\), so permeability strongly affects the answer. For ferromagnetic materials, \(\mu_r\) is not a single universal constant; use data appropriate to alloy, frequency, field strength, magnetic state, and temperature.
Proximity effect can dominate winding and busbar loss
Skin depth describes self-field penetration into a conductor. Nearby conductors can redistribute current further through proximity effect, so transformer windings, inductors, tightly spaced busbars, and dense conductor arrangements often need a geometry-aware AC-resistance model.
Surface roughness and plating matter at RF
When skin depth becomes comparable with surface features or conductive-layer thickness, the simple bulk-resistivity model may not predict actual RF loss accurately. Use the actual conductor finish, plating stack, roughness information, and frequency-dependent material data when those effects matter.
Assumptions, Limits, and When to Use a More Detailed Model
The calculator is an exact numerical evaluation of the classical good-conductor approximation for the properties you enter; it is not a complete electromagnetic solution for every conductor geometry or material.
Good-conductor condition
The standard derivation assumes conduction current dominates displacement current, commonly expressed as \(\sigma\gg\omega\epsilon\). If that condition is not satisfied, use the general lossy-medium propagation constant rather than this simplified skin-depth equation.
Homogeneous bulk properties
The calculation treats resistivity and permeability as uniform bulk inputs. Layered plating, composite conductors, coatings, anisotropic materials, and strongly frequency-dependent properties need a model that represents those layers or property changes explicitly.
No proximity-effect solution
The tool does not know conductor spacing, return-current path, winding arrangement, or neighboring magnetic fields. It therefore cannot determine total AC resistance when proximity effect materially redistributes current.
No abrupt thickness rule
Neither 3\(\delta\) nor 5\(\delta\) is a universal code or design requirement. Required plating, conductor thickness, shielding effectiveness, or loss performance depends on the specific electromagnetic and mechanical objective.
Sources and Calculation Verification
The calculation method, copper material property, temperature sensitivity, and example values were checked against NIST and university electromagnetic references. The worked example was also independently verified with the \(1/\sqrt f\) frequency relationship.
- NIST Technical Note 1374 — Coaxial Reference Standards — Good-conductor skin-depth and surface-resistance relationships and treatment of layered plated conductors.
- NIST Circular 470 — Precision Resistors and Their Measurement — Standard annealed copper resistivity reference of 1.7241 µΩ·cm at 20 °C.
- NIST Monograph 40 — Thermocouple Materials — Copper property table including resistivity at 20 °C and temperature coefficient of electrical resistivity.
- MIT OpenCourseWare — Electromagnetic Fields and Energy, Chapter 10 — Electromagnetic field penetration, skin effect, and good-conductor theory.
The frequency table is derived from \(\delta=\sqrt{\rho/(\pi f\mu_0\mu_r)}\) using the calculator’s copper preset. Values are rounded for engineering readability rather than displayed with unsupported precision.
Skin Depth Calculator FAQ
These questions address common interpretation and verification issues that arise after calculating skin depth.
What is skin depth compared with skin effect?
Skin effect is the physical redistribution of alternating current toward conductor surfaces. Skin depth is the characteristic penetration distance used to quantify that redistribution in the classical good-conductor model.
What is the skin depth of copper at 60 Hz?
Using 1.7241 µΩ·cm at 20 °C and \(\mu_r=1\), the calculator gives approximately 8.53 mm. Different copper resistivity or operating temperature will shift the result.
What is the skin depth of copper at 1 MHz?
Using the calculator’s standard annealed copper reference at 20 °C, the result is approximately 66.1 µm. The corresponding 3\(\delta\) and 5\(\delta\) depths are approximately 198 µm and 330 µm.
What is the skin depth of copper at 1 GHz?
The same copper reference gives approximately 2.09 µm at 1 GHz. At this scale, surface finish, plating, and actual RF geometry can become important to conductor loss.
Does skin depth depend on wire diameter?
Not in the classical skin-depth formula itself. Skin depth depends on frequency, resistivity or conductivity, and permeability. Wire diameter matters when deciding how strongly skin effect changes current distribution and total AC resistance.
Why does skin depth decrease when frequency increases?
Holding material properties constant, \(\delta\propto1/\sqrt f\). A fourfold increase in frequency reduces skin depth by half, and a 100-fold increase reduces it to one tenth.
Is there a finite skin depth at DC?
No. In the classical expression, \(f=0\) sends \(\delta\) toward infinity. Steady DC current is therefore not confined by this frequency-dependent skin-effect mechanism.
What is the difference between skin effect and proximity effect?
Skin effect is redistribution caused by a conductor’s own time-varying electromagnetic field. Proximity effect is additional redistribution caused by fields from nearby conductors. The skin-depth calculator models the first relationship, not the complete proximity-effect geometry.
How many skin depths are enough?
There is no universal required number. At 3\(\delta\), local current-density amplitude is about 5.0% of the surface value, and at 5\(\delta\) it is abou