Skin Depth Calculator
Calculate the AC skin depth of a conductor at any frequency, with temperature-corrected resistivity for 20+ materials including copper, aluminum, steel, and seawater. See the current density fade into the conductor cross-section, get the AC/DC resistance ratio for round wire, surface resistance in ohms per square, EMI shielding absorption loss, and a log-log skin depth vs frequency chart with a full step-by-step formula breakdown.
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About Skin Depth Calculator
The Skin Depth Calculator works out how far an alternating current actually penetrates into a conductor. At DC, current fills the whole cross-section. Raise the frequency and the current is squeezed into a thin shell at the surface — the skin effect. Skin depth (δ) is the standard measure of that shell: the depth at which the current density has dropped to 1/e ≈ 36.8% of its surface value. This tool computes δ for 20+ materials, corrects the resistivity for temperature, draws the current density fading into the conductor, and turns the number into the things engineers actually need: AC/DC resistance ratio, surface resistance in Ω/□, and shield absorption loss in dB.
What Is Skin Depth?
When alternating current flows in a conductor it produces a changing magnetic field inside the metal. That changing field induces eddy currents which oppose the original current in the centre of the conductor and reinforce it near the surface. The net result is that current density decays exponentially with depth:
where \( J_0 \) is the current density at the surface, \( d \) is the depth below the surface, and \( \delta \) is the skin depth. Skin depth is therefore not a hard boundary — current does flow deeper than δ, just exponentially less of it. One skin depth in, the current density is 36.8% of the surface value; three skin depths in, 5.0%; five skin depths in, 0.67%.
Skin Depth Formula
For a good conductor — one where conduction current dominates displacement current — the skin depth is:
- δ — skin depth, in metres
- ρ — resistivity of the conductor, in Ω·m (copper: 1.68 × 10⁻⁸ Ω·m at 20 °C)
- σ — conductivity, in S/m (copper: 5.96 × 10⁷ S/m)
- f — frequency, in Hz; ω = 2πf is the angular frequency in rad/s
- μr — relative permeability (1 for copper, aluminum, silver; ~1000 for carbon steel)
The two things worth internalising: skin depth falls as 1/√f, so a 100× rise in frequency shrinks it only 10×; and it falls as 1/√μr, which is why a ferromagnetic material behaves completely differently from copper at the same frequency.
Skin Depth of Copper, Aluminum, and Steel by Frequency
| Frequency | Copper | Aluminum | Carbon Steel 1010 |
|---|---|---|---|
| 50 Hz | 9.23 mm | 11.6 mm | 851 µm |
| 60 Hz | 8.42 mm | 10.6 mm | 777 µm |
| 400 Hz | 3.26 mm | 4.10 mm | 301 µm |
| 1 kHz | 2.06 mm | 2.59 mm | 190 µm |
| 10 kHz | 652 µm | 819 µm | 60.2 µm |
| 100 kHz | 206 µm | 259 µm | 19.0 µm |
| 1 MHz | 65.2 µm | 81.9 µm | 6.02 µm |
| 10 MHz | 20.6 µm | 25.9 µm | 1.90 µm |
| 100 MHz | 6.52 µm | 8.19 µm | 602 nm |
| 1 GHz | 2.06 µm | 2.59 µm | 190 nm |
| 2.4 GHz | 1.33 µm | 1.67 µm | 123 nm |
| 10 GHz | 652 nm | 819 nm | 60.2 nm |
Values at 20 °C using ρ = 1.68 × 10⁻⁸ Ω·m for copper, 2.65 × 10⁻⁸ Ω·m for aluminum, and 1.43 × 10⁻⁷ Ω·m with μr = 1000 for carbon steel.
How Much Current Flows Within N Skin Depths?
Because the decay is exponential, the fraction of current carried above a depth t in a flat conductor is \( 1 - e^{-t/\delta} \). That produces the rule of thumb that makes conductors thicker than five skin depths pointless:
| Depth | Current density remaining | Cumulative current carried |
|---|---|---|
| 1 δ | 36.79% | 63.21% |
| 2 δ | 13.53% | 86.47% |
| 3 δ | 4.98% | 95.02% |
| 4 δ | 1.83% | 98.17% |
| 5 δ | 0.67% | 99.33% |
Skin Effect and AC Resistance
If current only uses a shell one skin depth thick, the effective cross-section shrinks and resistance rises. For an isolated round wire of radius a, once a is comfortably larger than δ the AC resistance is well approximated by treating the conduction path as an annulus:
Below a = 2δ the annulus model breaks down and the low-frequency expansion of the exact Bessel-function solution, \( 1 + (a/\delta)^4/48 \), is used instead. The two expressions meet exactly at a = 2δ, where both give 4/3, so the calculator switches between them without a visible step.
Practical consequences engineers meet every day:
At 60 Hz a copper conductor thicker than about 17 mm gains almost nothing in the middle — utilities use stranded or hollow conductors instead of a solid rod.
Switch-mode and induction-heating windings use many individually insulated strands thinner than a skin depth, so every strand conducts across its full cross-section.
Because RF current lives in the surface, silver or gold plating three to five skin depths thick performs like a solid silver or gold conductor at a fraction of the cost.
Above roughly 3.5 MHz a 1 oz copper trace (35 µm) is thicker than one skin depth, so trace loss starts climbing with √f instead of staying flat.
A shield wall works by absorption; each skin depth of thickness costs the field about 8.7 dB, so shield design is really a skin-depth calculation.
Induction heat is deposited within roughly one skin depth, so the working frequency is chosen to place δ where the heat is wanted in the workpiece.
Skin Depth and EMI Shield Thickness
The absorption loss of a solid shield wall of thickness t is set entirely by how many skin depths thick it is:
One skin depth of wall gives about 8.7 dB, three gives about 26 dB, and five gives about 43 dB. Absorption is only part of the story — reflection loss at the two air/metal boundaries usually adds far more at low frequencies, so a real shield generally performs better than the absorption figure alone. Absorption is nevertheless the term that dominates at high frequency and for magnetic materials.
Does Temperature Change Skin Depth?
Yes, and most calculators ignore it. Resistivity rises with temperature according to \( \rho(T) = \rho_{20}\left[1 + \alpha (T - 20)\right] \), and since \( \delta \propto \sqrt{\rho} \), a hot conductor has a larger skin depth. Copper at 100 °C has ρ about 31% higher than at 20 °C, which stretches the skin depth by about 15% — from 65.2 µm to 74.8 µm at 1 MHz. For motor windings, busbars, and power inductors running well above ambient, using the 20 °C figure quietly understates both the skin depth and the AC resistance you will measure in service.
When the Simple Formula Stops Working
The formula above assumes a good conductor, meaning conduction current dominates displacement current: \( \sigma \gg \omega \varepsilon \). Every metal satisfies this by an enormous margin all the way through the microwave bands, so for copper, aluminum, or steel the formula is effectively exact at any frequency you are likely to type in. It starts to drift for poor conductors — seawater, doped semiconductors, bulk graphite, conductive plastics — once the frequency reaches the point where the loss tangent \( \sigma/(\omega\varepsilon) \) falls below about 10. The calculator computes that ratio for you and warns when the good-conductor approximation is no longer safe.
How to Use This Calculator
- Choose the material: Pick copper, aluminum, steel, mu-metal, seawater or any of the 20+ presets, or select Custom material and type your own resistivity and relative permeability.
- Enter the frequency: Type the value and pick Hz, kHz, MHz, or GHz. Set the Conductor temperature if the part runs hotter than 20 °C.
- Add the conductor size (optional): Choose Round wire (diameter) or Sheet / shield (thickness) and enter the size in mm, µm, mil, inches, or an AWG gauge.
- Click Calculate Skin Depth: The tool returns δ in four units at once, plus surface resistance and conductivity.
- Read the visual: The shaded cross-section shows the current density fading inward, with a dashed ring marking one skin depth. The log-log chart shows how δ moves with frequency and how your material compares with copper and steel.
Frequently Asked Questions
What is skin depth?
Skin depth is the distance below the surface of a conductor at which an alternating current density has fallen to 1/e, about 36.8 percent, of its value at the surface. It describes how far high-frequency current penetrates into a conductor instead of flowing uniformly through it.
What is the skin depth formula?
For a good conductor the skin depth is the square root of rho divided by pi times frequency times mu, where rho is resistivity in ohm-metres, frequency is in hertz, and mu is the absolute permeability, equal to 4 pi times 10 to the minus 7 multiplied by the relative permeability.
What is the skin depth of copper?
Copper has a skin depth of about 8.4 mm at 60 Hz, 2.1 mm at 1 kHz, 65 micrometres at 1 MHz, 2.1 micrometres at 1 GHz, and 1.3 micrometres at 2.4 GHz, all at 20 degrees Celsius.
Why does skin depth decrease with frequency?
An alternating current creates a changing magnetic field inside the conductor, which induces eddy currents that oppose the current in the centre and reinforce it near the surface. The effect grows with frequency, so the current is pushed into an ever thinner surface layer. Skin depth falls as one over the square root of frequency, so a hundredfold rise in frequency shrinks it tenfold.
Does temperature change skin depth?
Yes. Resistivity rises with temperature for most metals, and skin depth is proportional to the square root of resistivity, so a hot conductor has a larger skin depth. Copper at 100 degrees Celsius has a skin depth roughly 15 percent larger than the same copper at 20 degrees Celsius.
Why does steel have a much smaller skin depth than copper?
Skin depth is inversely proportional to the square root of permeability. Carbon steel is ferromagnetic with a relative permeability of roughly 1000, which on its own would shrink the skin depth by a factor of about 32. Its higher resistivity pushes back the other way, leaving a skin depth roughly 11 times smaller than copper at the same frequency. That is why steel is an effective magnetic shield and why steel conductors carry high-frequency current poorly.
How thick should a conductor or plating be?
Making a conductor much thicker than about five skin depths adds almost no extra conductivity, because 99.3 percent of the current already flows within five skin depths of the surface. For plating, three to five skin depths of silver or gold is a common rule of thumb at the operating frequency.
Additional Resources
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"Skin Depth Calculator" at https://MiniWebtool.com// from MiniWebtool, https://MiniWebtool.com/
by miniwebtool team. Updated: August 20, 2026