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).

Skin depth of copper vs frequency

These are the numbers people actually look up. Copper skin depth follows δ ≈ 0.0652/√f metres (f in Hz), so every decade of frequency shrinks δ by about 3.16×. Below the table are the same six anchor frequencies you'll meet in practice.

Frequency	Copper skin depth (δ)
50 Hz	9.2 mm
1 kHz	2.1 mm
100 kHz	206 µm
1 MHz	66 µm
100 MHz	6.6 µm
1 GHz	2.1 µm

At 1 MHz copper sits at 66 µm. Aluminium is worse at the same frequency (≈82 µm, because it's more resistive), and silver actually edges out copper at ≈64 µm — one of the few places where the extra cost of silver plating buys you a measurable win. For the full background, see Wikipedia's article on the skin effect.

The practical rule: above ~50 MHz, more copper barely helps

Here's where people get burned. Above roughly 50 MHz, adding copper thickness barely lowers AC resistance — the current rides in the top few µm and ignores everything underneath. Spend money on plating the surface, not on a thicker conductor.

On a board this shows up early. Standard 1 oz copper is 35 µm thick, and skin depth drops below that figure above about 4 MHz — so a 1 oz PCB trace is already "thicker than the skin" for anything in the HF band and up. Once skin depth falls below the conductor radius, AC resistance climbs in proportion to √f: quadruple the frequency, double the resistance. That's the slope that wrecks the Q of an air-core coil or the loss budget of a feedline.

AC resistance scaling

Once δ < conductor radius: Rac ∝ √f. 1 oz copper (35 µm) ≥ δ above ~4 MHz; from there, thickness past one skin depth is dead weight.

Proximity effect and Litz wire

Skin effect is only half the story in a wound component. Put two conductors side by side carrying AC and their fields push each other's current to one side of the copper — the proximity effect. In a tightly-wound inductor or transformer it's often worse than skin effect alone, because the inner turns sit in the field of every turn around them. Designing a multi-layer coil at high frequency means fighting both effects at once.

The fix is Litz wire: many thin, individually insulated strands twisted so each one spends an equal share of its length near the surface and buried in the middle. No single strand hogs the skin region. You'll find it in SMPS transformers and Qi wireless-charging coils, roughly the 50 kHz–2 MHz range. Above a few MHz the strand insulation and twist overhead stop paying off, and people switch to flat copper foil or plated tube instead. If you're sizing the conductor itself, the wire gauge calculator gives you the DC starting point before skin and proximity effects load it up.

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.