Skin Depth Calculator finds how deep AC current flows in copper, iron and 11 other metals at your frequency. It also checks plating thickness and the AC resistance of a round wire.
Pick the metal and the frequency. Wire size and layer thickness sit in the second section below.
Material Properties
Filled in by the material you picked. Change either one to enter your own metal or alloy.
Wire and Layer Check
Enter a round wire to get its AC resistance, and a plating or copper thickness to check it against skin depth.
Skin Depth vs Frequency
| Frequency | Skin Depth | Five Skin Depths |
|---|---|---|
| 60 Hz | 8.447 mm | 42.23 mm |
| 400 Hz | 3.271 mm | 16.36 mm |
| 1 kHz | 2.069 mm | 10.35 mm |
| 10 kHz | 654.3 µm | 3.271 mm |
| 100 kHz | 206.9 µm | 1.035 mm |
| 1 MHz | 65.43 µm | 327.1 µm |
| 10 MHz | 20.69 µm | 103.5 µm |
| 100 MHz | 6.543 µm | 32.71 µm |
| 1 GHz | 2.069 µm | 10.35 µm |
| 10 GHz | 654.3 nm | 3.271 µm |
| 100 GHz | 206.9 nm | 1.035 µm |
Other Metals Compared
| Metal | Skin Depth | Surface Resistance |
|---|---|---|
| Copper | 65.43 µm | 258.3 µΩ/sq |
| Silver | 64.26 µm | 253.7 µΩ/sq |
| Gold | 74.65 µm | 294.7 µΩ/sq |
| Aluminum | 81.93 µm | 323.4 µΩ/sq |
| Brass (70/30) | 133.2 µm | 525.7 µΩ/sq |
| Tin | 178.7 µm | 705.3 µΩ/sq |
| Lead | 228.4 µm | 901.8 µΩ/sq |
| Tungsten | 117.0 µm | 461.7 µΩ/sq |
| Titanium | 369.8 µm | 1.460 mΩ/sq |
| Nickel | 9.348 µm | 7.381 mΩ/sq |
| Iron | 7.153 µm | 14.12 mΩ/sq |
| Mu-Metal | 1.992 µm | 235.9 mΩ/sq |
| Stainless Steel 304 | 422.8 µm | 1.703 mΩ/sq |
Skin Depth Calculator for Copper and Other Metals
The Skin Depth Calculator needs only two choices to start, a conductor and a frequency. Thirteen metals are listed, and each one loads its own resistivity and relative permeability. With copper at 1 MHz the result is 65.43 µm, which is 2.576 mil.
Two closed sections in the Skin Depth Calculator add the detail. Material Properties lets you type your own resistivity and permeability for an alloy that is not listed. Wire and Layer Check takes a round wire and a plating or copper thickness, and compares both with the skin depth.
The cards then answer the questions that follow from the depth itself. They show how thick the conductor should be, whether your layer is thick enough, how much the resistance of your wire rises, and how much shielding the metal absorbs.
Skin Depth Formula and Units
Alternating current crowds toward the surface of a conductor. Skin depth is the distance below the surface where the current density has dropped to 37% of its surface value. It depends on three things only.
Here ρ is the resistivity in ohm-meters, f is the frequency in hertz and μr is the relative permeability. μ0 is the permeability of free space, 4π × 10⁻⁷ H/m. The result is in meters, and the Skin Depth Calculator shows it in µm, mm or nm with the same depth in mil or µin beside it.
Published results for copper at 1 MHz range from 65.2 µm to 66.1 µm, and the cause is the resistivity each source picks. The RF Cafe resistivity table uses 16.9 nΩ·m, which gives 65.43 µm. A value of 16.8 gives 65.23 µm, and the annealed copper standard of 17.24 gives 66.08 µm.
Skin Depth vs Frequency in Copper
Skin depth falls with the square root of frequency. Ten times the frequency makes the depth 3.16 times thinner, and a hundred times makes it ten times thinner. The chart below is copper at 16.9 nΩ·m.
| Frequency | Skin Depth | Five Skin Depths |
|---|---|---|
| 60 Hz | 8.447 mm | 42.23 mm |
| 400 Hz | 3.271 mm | 16.36 mm |
| 100 kHz | 206.9 µm | 1.035 mm |
| 1 MHz | 65.43 µm | 327.1 µm |
| 13.56 MHz | 17.77 µm | 88.84 µm |
| 100 MHz | 6.543 µm | 32.71 µm |
| 1 GHz | 2.069 µm | 10.35 µm |
| 2.4 GHz | 1.336 µm | 6.678 µm |
| 10 GHz | 654.3 nm | 3.271 µm |
| 77 GHz | 235.8 nm | 1.179 µm |
The Skin Depth Calculator builds the same chart for the metal you picked, under Skin Depth vs Frequency. A second table, Other Metals Compared, lists all thirteen metals at your frequency with the surface resistance of each.
Skin Depth in Steel and Iron
Magnetic metals have a much thinner skin. Permeability sits under the square root, so iron at a relative permeability of 500 comes out far shallower than copper, even though it conducts worse. At 60 Hz the Skin Depth Calculator gives 0.92 mm for iron against 8.45 mm for copper.
Stainless steel 304 behaves the other way. It is nearly non-magnetic and has high resistivity, so its skin depth at 60 Hz is 54.6 mm. To use the tool as a skin depth calculator for steel, choose Custom and enter the resistivity from the mill sheet. Pick the 100 Steel preset for permeability as a starting point.
Treat every magnetic result as a rough figure. Permeability changes with the alloy, the field strength and the frequency. RF Cafe notes that a relative permeability as low as 1 has been measured for nickel at 10 GHz, where the low-frequency value is 200.
Five Skin Depths for Plating and PCB Copper
One skin depth is not enough metal. Microwaves101 gives the working rule, which is to plan on at least five skin depths of low-loss conductor. The first card shows that thickness, and it is 327.1 µm for copper at 1 MHz.
The second card in the Skin Depth Calculator checks a layer you already have. Standard 1 oz copper is 35.56 µm thick, which is only 0.543 skin depths at 1 MHz. It reaches five skin depths from 84.6 MHz up. Half-ounce copper gets there from 338 MHz, close to the 330 MHz that Microwaves101 quotes, and 2 oz copper from 21.2 MHz.
Plating works the same way. At 2.4 GHz the skin depth of gold is 1.524 µm. A 100 µin gold layer is 1.67 skin depths there, so part of the current still runs in the metal underneath. Five skin depths of gold at that frequency is 300 µin. For the DC side of a trace, the PCB Trace Resistance Calculator gives the resistance from length, width and copper weight.
AC Resistance of a Round Wire
Skin effect raises the resistance of a wire once its radius is larger than the skin depth. The third card in the Skin Depth Calculator gives the ratio of AC to DC resistance for one straight round wire. AWG 24 copper at 1 MHz has a radius of 3.90 skin depths and 2.23 times its DC resistance, 55.98 Ω per 1,000 ft against 25.16 Ω.
The Largest Full-Use Wire row is the biggest gauge whose diameter is still within two skin depths. In copper that is AWG 19 at 20 kHz, AWG 26 at 100 kHz and AWG 36 at 1 MHz. A thicker wire at those frequencies carries little current in its core.
Windings and bundled cables lose more than this figure. Neighboring turns push the current to one side of each wire, and that proximity loss adds to the skin effect. Strand size for litz wire is usually chosen well below the full-use gauge for that reason.
Surface Resistance and Shield Absorption
Surface resistance is the resistance of a square of conductor that is one skin depth thick. It sets the conductor loss in traces, coax and waveguide. It is the resistivity divided by the skin depth.
Copper comes to 258.3 µΩ per square at 1 MHz and 8.17 mΩ per square at 1 GHz. Because skin depth shrinks with the square root of frequency, surface resistance grows at the same rate. For the line itself, the Microstrip Impedance Calculator covers trace width and impedance.
The same card gives the shielding a metal layer absorbs. In Compliance Magazine states the rule from Henry Ott's EMC text, which is about 8.69 dB for every skin depth of thickness.
A 1 oz copper layer at 1 MHz absorbs 4.72 dB. Reaching 40 dB takes 4.6 skin depths, or 301.3 µm of copper at that frequency. Absorption is only one part of shielding, since reflection at the surface adds to it. The Decibel Calculator turns a dB figure into a power or voltage ratio.
Skin Depth FAQ
Does skin depth depend on the size of the wire?
No. Skin depth is a property of the metal and the frequency. Wire size decides whether that depth matters. When the wire radius is smaller than the skin depth, current still uses the whole cross-section and the resistance stays near its DC value.
The Skin Depth Calculator reports the frequency where that changes for your wire. For AWG 24 copper it is about 65.7 kHz, the point where the skin depth equals the wire radius of 0.255 mm.
Does temperature change skin depth?
Yes, through resistivity. The listed values are for room temperature, and the resistivity of copper rises by about 0.39% per degree Celsius. At 100°C it is near 22.2 nΩ·m, up from 16.9.
Enter that figure under Material Properties and the skin depth at 1 MHz grows from 65.43 µm to 75.0 µm. Surface resistance rises by the same 15%, so a hot conductor has more loss even though the current spreads deeper.