What is the skin effect?

The skin effect is the tendency of AC current to flow near the surface of a conductor rather than through the entire cross-section. At higher frequencies, the current concentrates in a thin layer called the skin depth, increasing the effective resistance of the conductor.

How do you calculate skin depth?

Skin depth δ = √(ρ / (π × f × μ₀)), where ρ is resistivity (Ω·m), f is frequency (Hz), and μ₀ = 4π×10⁻⁷ H/m (permeability of free space for non-magnetic materials). For copper at 1 MHz, δ ≈ 66 µm.

Why does skin effect matter in electronics?

At high frequencies, skin effect increases conductor resistance, causing higher losses in RF circuits, transformers, and inductors. It is important for PCB trace design at RF frequencies, audio cable design above 10 kHz, and transformer winding design.

How can I reduce skin effect losses?

Use Litz wire (stranded wire with individually insulated strands) for high-frequency inductors. In PCB design, use multiple thinner copper layers or surface-plated vias. Hollow conductors are also used in high-power RF applications since the inner conductor carries little current.

Skin Effect Calculator

Calculate skin depth in copper, aluminum, and silver conductors at any frequency.

Component Values

Conductor Material

Frequency

Wire Diameter (optional, mm)

Results

Skin Depth (δ)66.01 µm

Skin Depth (µm)66.01 µm

δ = skin depth (current zone)

Skin Depth Reference Table

Frequency	Skin depth (Copper)	Skin depth (Aluminum)
50 Hz	9.335 mm	11.95 mm
1 kHz	2.087 mm	2.673 mm
10 kHz	660.1 µm	845.2 µm
1 MHz	66.01 µm	84.52 µm
10 MHz	20.87 µm	26.73 µm
1 GHz	2.087 µm	2.673 µm

The skin effect is the concentration of AC current near the surface of a conductor. At DC, current distributes uniformly across the cross-section. As frequency increases, electromagnetic induction pushes current toward the surface. The depth at which current density falls to 1/e (about 37%) of its surface value is called the skin depth δ.

Skin depth is δ = √(ρ / (π × f × μ₀)), where ρ is resistivity and μ₀ = 4π×10⁻⁷ H/m. For copper at 1 MHz, δ ≈ 66 µm. At 100 MHz, δ ≈ 6.6 µm. The effective resistance of the conductor increases with frequency because only the thin skin layer carries current.

Skin effect is critical in RF coil design, transformer winding optimization, and high-frequency PCB trace analysis. Litz wire (stranded with individually insulated strands) is used in high-frequency inductors to maximize the surface area and minimize effective resistance at the operating frequency.

Skin Depth Formula

δ = √(ρ / (π × f × μ₀))

Key Points

δ = √(ρ/(π×f×μ₀)) — skin depth decreases with frequency
Copper at 50 Hz: δ ≈ 9.3 mm (not significant)
Copper at 1 MHz: δ ≈ 66 µm (significant in thin conductors)
Skin effect increases AC resistance vs DC resistance
Litz wire reduces skin effect in HF inductors

Applications

RF coil and inductor winding design
High-frequency PCB trace sizing
Transformer winding loss estimation
Litz wire gauge selection

Practical Examples

Copper wire at 1 MHz

1 mm diameter copper wire (r = 500 µm) at 1 MHz. Skin depth δ ≈ 66 µm — much less than radius, so strong skin effect.

δ = 66/√(1×10⁶) × 1000 = 66 µm · Rac/Rdc ≈ r/(2δ) = 500/132 = 3.8×

PCB trace at 100 MHz

Copper PCB trace at 100 MHz. Skin depth drops to 6.6 µm — only the outer 6.6 µm of copper carries current.

δ = 66/√(100×10⁶) × 1000 = 6.6 µm · Use wide, flat traces or silver coating for RF

Skin effect formulas

Skin depth:  δ = √(2ρ / (ω × μ))  =  √(ρ / (π × f × μ₀ × μᵣ))

Where:
ρ = resistivity (Ω·m)   μ₀ = 4π×10⁻⁷ H/m   μᵣ = relative permeability
ω = 2πf (rad/s)         f = frequency (Hz)

AC resistance:  Rac ≈ Rdc × (r / (2δ))  for δ << r

Skin depth reference table

Frequency	Skin Depth (copper)	Skin Depth (aluminum)	Application
50 Hz	9.38 mm	11.9 mm	Power mains
60 Hz	8.57 mm	10.9 mm	Power mains (US)
1 kHz	2.10 mm	2.66 mm	Audio amplifiers
10 kHz	0.66 mm	0.84 mm	Switching PSU
100 kHz	0.21 mm	0.27 mm	SMPS, inverters
1 MHz	0.066 mm	0.084 mm	RF circuits
10 MHz	0.021 mm	0.027 mm	HF radio
100 MHz	6.6 µm	8.4 µm	VHF, FM radio
1 GHz	2.1 µm	2.7 µm	Microwave, WiFi

More design examples

Litz wire need for 100kHz flyback transformer

Copper skin depth at 100kHz = 0.21mm. Standard 1mm wire (r=0.5mm >> δ).

Use litz wire with strand diameter < 0.4mm (< 2δ) to minimize AC resistance.

Power cable at 50Hz (9.38mm skin depth)

Standard 50mm² cable (r=4mm). Since r << δ, skin effect is negligible at 50Hz.

Skin effect only matters above ~5kHz for typical power cables.

Design tip: Skin effect becomes significant when conductor radius > 2× skin depth. For PCB traces at >1MHz: use thin, wide traces instead of narrow, thick ones. Gold plating (2–5µm) is sufficient at microwave frequencies (δ_gold ≈ 2.5µm at 1GHz).

Did you know? At 60 Hz (mains frequency), the skin depth in copper is about 8.5 mm — so solid copper conductors thicker than ~17 mm carry no additional current in their core. At 1 GHz (microwave), skin depth is only 2 µm, which is why RF coaxial cables use thin copper plating over steel or aluminium cores.