Case 1
- Frequency f (Hz)
- 1000000Hz
- Resistivity ρ (Ω·m)
- 1.68e-8Ω·m
- Relative permeability µr
- 1
65.234µm
Open with these valuesSkin Depth Calculator
Change any value to update the result.
65.234µm
Skin depth: 65.234 µmExamples
How the result moves
Relative permeability µr → Skin depth (µm)Your current valid inputs, with one value varied across the range.
How the result moves
Held fixed: Frequency f (Hz) 1,000,000.000 Hz, Resistivity ρ (Ω·m) 0.000000016800 Ω·m.
| Relative permeability µr | Skin depth (µm) |
|---|---|
| 1.000Your value | 65.234 |
| 1.250 | 58.347 |
| 1.500 | 53.263 |
| 1.750 | 49.312 |
| 2.000 | 46.127 |
In copper at 1 MHz the skin depth is 65.2 µm — below that the current density has already fallen to about 37 % of the surface value. Depth shrinks with the square root of frequency: the same copper carries current 9.2 mm deep at 50 Hz but only 2 µm deep at 1 GHz.
Worked examples
Case 2
- Frequency f (Hz)
- 50Hz
- Resistivity ρ (Ω·m)
- 1.68e-8Ω·m
- Relative permeability µr
- 1
9,225.497µm
Open with these valuesCase 3
- Frequency f (Hz)
- 1000000000Hz
- Resistivity ρ (Ω·m)
- 1.68e-8Ω·m
- Relative permeability µr
- 1
2.063µm
Open with these valuesHow it's calculated
δ = √(ρ / (π × f × µ₀ × µr))
- StepEnter the frequency of the alternating current, in hertz.Frequency f (Hz)=1,000,000Hz
- StepEnter the resistivity in ohm-metres — copper is 0.0000000168 at 20 °C.Resistivity ρ (Ω·m)=0.0000000168Ω·m
- StepEnter the relative permeability: 1 for copper, aluminium or gold.Relative permeability µr=1
- ResultRead the depth in micrometres; 1000 µm is one millimetre.65.234µm
Reference table
| Frequency, ρ, µr | The same depth in mm | Skin depth (µm) |
|---|---|---|
| 1000000000, 0.0000000168, 1 | 0.002063 mm | 2.063 |
| 1000000, 0.0000000168, 100 | 0.006523 mm | 6.523 |
| 1000000, 0.0000000168, 1 | 0.065234 mm | 65.234 |
| 1000000, 0.0000000282, 1 | 0.084517 mm | 84.517 |
| 50, 0.0000000168, 1 | 9.225497 mm | 9225.497 |
Questions
How do I calculate the skin depth of a conductor?
Divide the resistivity by π times the frequency, the permeability of free space and the relative permeability, then take the square root: δ = √(ρ / (π × f × µ₀ × µr)). For copper at 1 MHz with µr of 1 that is about 65.2 µm. The magnetic constant µ₀ is 4π × 10⁻⁷ H/m.
What is the skin effect?
The skin effect is the tendency of an alternating current to flow near the surface of a conductor rather than evenly through it. The higher the frequency, the more the current crowds towards the surface. The skin depth is the distance below the surface at which the current density has dropped to about 37 % of its surface value.
Why does skin depth shrink as frequency rises?
The frequency sits under a square root in the denominator, so the depth is proportional to one over the square root of f. Raise the frequency a hundredfold and the depth drops tenfold. In copper it is about 9 mm at 50 Hz but only 2 µm at 1 GHz.
What resistivity should I enter for common metals?
About 0.0000000168 Ω·m for copper, 0.0000000282 for aluminium and 0.0000000244 for gold, each with a relative permeability of 1. Magnetic metals such as iron or steel have a far higher µr, which makes their skin depth much smaller at the same frequency.
What units does the result use?
Enter hertz, ohm-metres and a plain number for the permeability; the depth comes back in micrometres. Divide by 1000 for millimetres, so 9225 µm is 9.225 mm. The reference table below shows both for every row.