liminfoSkin Effect Calculator
Free web tool: Skin Effect Calculator
Skin Depth (δ)
66.083 µm
DC Resistance
21.951 m\u2126/m
AC Resistance
88.918 m\u2126/m
Rac/Rdc Ratio
4.051x
Skin Depth vs Frequency (Copper)
| Frequency | Skin Depth |
|---|---|
| 50 Hz | 9.346 mm |
| 60 Hz | 8.531 mm |
| 1 kHz | 2.090 mm |
| 10 kHz | 660.831 µm |
| 100 kHz | 208.973 µm |
| 1 MHz | 66.083 µm |
| 10 MHz | 20.897 µm |
| 100 MHz | 6.608 µm |
| 1 GHz | 2.090 µm |
| 10 GHz | 660.8 nm |
About Skin Effect Calculator
The Skin Effect Calculator computes the electromagnetic skin depth (δ) and the resulting AC resistance increase for round conductors at any frequency. Select a material (copper, aluminum, gold, silver, mild steel, or nickel), enter the frequency and wire diameter, and the tool instantly calculates skin depth in mm or µm, DC resistance per metre, AC resistance per metre, and the Rac/Rdc ratio that quantifies how much higher the AC resistance is compared to DC.
Skin effect is the tendency of alternating current to concentrate near the outer surface of a conductor as frequency increases. The skin depth formula is δ = √(2ρ / ωμ), where ρ is the material resistivity, ω = 2πf is the angular frequency, and μ = μ₀μᵣ is the absolute permeability. For wires thinner than one skin depth, current distributes uniformly and Rac ≈ Rdc. As frequency rises, current is confined to a ring of thickness δ near the conductor surface, and the effective cross-sectional area shrinks, raising resistance. Ferromagnetic materials like steel and nickel show extreme skin effect due to their high relative permeability (μᵣ ≈ 100–600).
A reference table shows skin depth for the selected material across ten decades from 50 Hz to 10 GHz, giving designers an instant cross-frequency overview. All computations run client-side using standard electromagnetic formulas. The tool is useful for RF engineers designing coils and PCB traces, power engineers selecting cable cross-sections, and students studying electromagnetic field theory.
Key Features
- Skin depth calculation using δ = √(2ρ/ωμ) for six common conductor materials
- Frequency input from 50 Hz to GHz range with Hz / kHz / MHz / GHz unit selector
- DC and AC resistance per metre (mΩ/m) with wire diameter input in mm
- Rac/Rdc ratio with visual warning when ratio exceeds 2× (significant skin effect)
- Material database includes copper, aluminum, gold, silver, mild steel, and nickel with actual resistivity and relative permeability values
- Reference table of skin depths at 10 standard frequencies (50 Hz – 10 GHz) for the selected material
- Automatic unit formatting: skin depth displayed in mm, µm, or nm as appropriate
- 100% client-side computation — no server required, works offline
Frequently Asked Questions
What is the skin effect?
The skin effect is the phenomenon where alternating current (AC) tends to flow near the surface of a conductor rather than uniformly through its cross-section. At higher frequencies, the current density decays exponentially from the surface inward, concentrating within a thin layer called the skin depth. This reduces the effective conducting area and increases AC resistance.
What is skin depth (δ)?
Skin depth δ is the depth below the conductor surface at which the current density falls to 1/e (about 37%) of its value at the surface. It is calculated as δ = √(2ρ / ωμ), where ρ is resistivity (Ω·m), ω = 2πf is angular frequency (rad/s), and μ is absolute permeability (H/m). Smaller δ means stronger skin effect.
Why does steel show much stronger skin effect than copper?
Mild steel has a relative permeability μᵣ ≈ 100, and nickel has μᵣ ≈ 600, whereas copper and aluminum have μᵣ ≈ 1. Since skin depth is inversely proportional to √μ, ferromagnetic materials have dramatically shallower skin depths. For steel at 50 Hz, δ is only about 0.6 mm compared to 9 mm for copper.
How is AC resistance calculated for a round wire?
When skin depth δ is less than the wire radius r, the effective conducting area is approximated as π·δ·(2r − δ) — the annular ring within one skin depth of the surface. AC resistance per metre = ρ / effective area. When δ ≥ r, current is uniform and Rac = Rdc.
What Rac/Rdc ratio is considered significant?
A ratio above 1.1 (10% increase) is typically worth noting in audio or power frequency designs. A ratio above 2 represents a doubling of resistance due to skin effect, which is highlighted in the calculator with a yellow warning background. RF engineers generally account for skin effect whenever the wire diameter exceeds two skin depths.
At what frequency does skin effect matter for household wiring?
For 2 mm diameter copper wire at 50 Hz (EU) or 60 Hz (US), the skin depth is roughly 9.4 mm — much larger than the wire radius of 1 mm. So skin effect is negligible at power frequencies for standard household wire gauges. It becomes important for large-diameter busbars, transformer windings, and motor conductors.
How does skin effect affect RF coil design?
At radio frequencies (MHz range), copper skin depth is only 20–70 µm. For solid copper wire, only the outer shell carries significant current, so the additional metal in the wire interior contributes resistance without conductance. RF coils therefore use hollow tubing, silver-plated conductors, or Litz wire (many fine insulated strands) to maximise the surface area carrying current.
What is the proximity effect and how does it relate to skin effect?
The proximity effect is a related phenomenon where the magnetic field of a nearby conductor distorts current distribution in an adjacent conductor, again increasing AC resistance. The skin effect calculator models only the self-field skin effect for a single isolated round wire. Proximity effect requires more complex calculations involving the geometry of multiple conductors.