Skin Depth Calculator | Copper at Any Frequency

What Is Skin Depth and Why Does It Matter?

Skin depth (δ) is the distance from a conductor’s surface at which current density drops to 1/e (about 37 %) of its surface value. For annealed copper at 1 GHz, δ is roughly 2.1 µm — far thinner than a standard 1 oz (35 µm / 1.4 mil) copper foil. This means that at microwave frequencies, most of your copper carries almost no current; conductor loss is governed by the thin skin layer, not the full cross-section.

Understanding skin depth lets you make three practical decisions: whether thicker copper actually reduces loss at your operating frequency, how much surface roughness matters, and when exotic plating (ENIG, ENEPIG, immersion silver) helps or hurts. The formula is straightforward, and the calculator below gives you an instant answer for any metal and frequency.

Skin Depth Formula

The classical skin depth for a good conductor is:

δ = 1 / √(π · f · μ · σ)

• δ — skin depth (m)
• f — frequency (Hz)
• μ — magnetic permeability (H/m); for copper, μ ≈ μ₀ = 4π × 10⁻⁷ H/m
• σ — electrical conductivity (S/m); annealed copper σ = 5.8 × 10⁷ S/m

Because δ scales as 1/√f, doubling the frequency reduces skin depth by about 29 %. That inverse-square-root relationship is the reason conductor loss rises steadily with frequency, even on the same trace geometry.

Skin Depth Calculator

Enter your conductor material (or type a custom conductivity) and operating frequency. The tool returns skin depth in µm, mil (1 mil = 25.4 µm), and meters, so you can compare the result directly against your copper foil thickness.

Try copper at 2.4 GHz: you should see δ ≈ 1.33 µm. A 1 oz copper trace is 35 µm thick — roughly 26 skin depths. Beyond about 3–5 skin depths the additional copper carries negligible current, so going from 1 oz to 2 oz at 2.4 GHz does almost nothing for RF loss. The benefit of heavier copper at gigahertz frequencies is mechanical and thermal, not electrical. At 100 MHz, however, δ ≈ 6.6 µm, and 0.5 oz foil (17.5 µm) is only about 2.7 skin depths — here, bumping to 1 oz does measurably lower loss.

Skin Depth Reference Table

Gold and aluminum have lower conductivity than copper (σ_Au ≈ 4.1 × 10⁷ S/m, σ_Al ≈ 3.5 × 10⁷ S/m), so their skin depths are slightly larger and their surface-resistivity losses are higher at the same frequency.

Copper Weight, Thickness, and Skin Depth

PCB copper is specified by weight per unit area: 1 oz/ft² corresponds to 35 µm (1.4 mil) of deposited copper. When choosing copper weight for an RF board, the question is whether the foil is thick enough to contain several skin depths at your lowest operating frequency. Use the converter below to translate between oz, µm, and mil, then compare with the skin depth result above.

If your design runs at 5.8 GHz Wi-Fi, δ ≈ 0.87 µm, and even half-ounce copper (17.5 µm) is about 20 skin depths — electrically plenty. But at 10 MHz in an HF radar receiver, δ ≈ 20.9 µm, so half-ounce foil is less than one skin depth; stepping up to 1 oz or even 2 oz genuinely reduces conductor loss. The rule of thumb: if your foil is thinner than about 3 δ, adding copper helps electrically; above 5 δ, the return is negligible.

How Skin Effect Drives RF PCB Conductor Loss

At high frequencies the effective resistance per unit length of a trace is:

R_s = 1 / (σ · δ) (Ω/square)

This surface resistance rises as √f. For a microstrip line the total conductor loss (α_c in dB/length) depends on R_s, the trace width, and the characteristic impedance. A narrower 50 Ω line on a thinner dielectric concentrates current in a smaller perimeter and suffers more loss — a direct consequence of skin depth physics.

Surface Roughness Amplifies Loss

Electrodeposited copper has an RMS surface roughness (Rq) of roughly 1–6 µm depending on foil type. Standard ED foil is around 2–3 µm Rq. At 10 GHz, skin depth is 0.66 µm — smaller than the roughness features. Current must follow the peaks and valleys, increasing the effective path length and loss. The Hammerstad-Jensen roughness correction factor can add 30–80 % extra conductor loss at millimeter-wave frequencies. Low-profile (LP) and very-low-profile (VLP) foils with Rq below 1 µm are essential above about 10 GHz. Laminate vendors like Rogers specify compatible foil profiles for each high-frequency grade.

Plating Finish Matters

At 28 GHz and above, the plating on pads and transmission lines is within the skin depth. ENIG puts a 3–5 µm nickel layer (σ_Ni ≈ 1.4 × 10⁷ S/m, also ferromagnetic with μ_r ≈ 100–600) beneath 0.05 µm of gold. Nickel’s much higher permeability shrinks its skin depth to below 0.1 µm at a few GHz, and its low conductivity raises R_s dramatically. For RF signal traces, immersion silver or ENEPIG (which limits the nickel-phosphorus layer) are preferred. Avoid ENIG on any trace carrying millimeter-wave signals.

Practical Design Rules Derived from Skin Depth

1. Copper weight selection: Ensure foil thickness ≥ 3 δ at the lowest signal frequency. Below that threshold, heavier copper reduces loss; above it, the benefit is thermal only.
2. Foil roughness: When δ drops below the foil Rq (typically above 3–5 GHz for standard ED foil), switch to LP or VLP foil to control extra conductor loss.
3. Plating: Keep lossy or magnetic metals (nickel, tin) off RF signal traces. Prefer immersion silver, OSP, or hard gold for transmission lines above 5 GHz.
4. Ground plane integrity: Skin effect applies to reference planes too. A ground plane thinner than 3 δ at the lowest frequency can increase return-path resistance and raise both loss and crosstalk between adjacent traces.
5. Via transitions: Barrel plating on vias is typically 20–25 µm. At frequencies where δ is much smaller, the via barrel resistance is not the bottleneck — but the annular ring finish is. Use the same plating guidance as for traces. For thermal management of high-power RF stages, a thermal via array calculator helps size the via field independently of skin-depth concerns.

Skin Depth in Antenna and Radar Design

Patch antennas, feed networks, and Wilkinson power dividers all rely on low-loss transmission lines whose performance is bounded by conductor loss. At 77 GHz automotive radar frequencies, copper skin depth is only 0.24 µm; surface quality dominates. Designers pair VLP copper with low-Df laminates (e.g., RO3003, Df = 0.001 at 10 GHz) and tightly control etch profiles to keep conductor loss predictable.

When calculating link budgets, the conductor loss derived from skin depth feeds directly into the overall noise figure. Even a fraction of a dB matters in a radar range equation, where receive-path loss reduces maximum detection distance by the fourth-root of the loss ratio.

Relationship Between Skin Depth and Wavelength

Skin depth and free-space wavelength both depend on frequency, but they scale differently: λ ∝ 1/f while δ ∝ 1/√f. At 1 GHz, λ₀ = 300 mm but δ_Cu = 2.1 µm — a ratio of about 140,000:1. This enormous gap is why conductors that are electrically thin (small fraction of λ) can still be many skin depths thick, and why skin depth rather than wavelength is the controlling dimension for conductor loss.

FAQ

What is the skin depth of copper at 1 GHz?

Approximately 2.1 µm (0.083 mil) for annealed copper with conductivity 5.8 × 10⁷ S/m. This is well below the thickness of any standard PCB copper foil, so conductor loss at 1 GHz is entirely surface-dominated.

Does increasing copper thickness reduce RF loss?

Only if the existing foil is thinner than about 3 skin depths at the operating frequency. Above 5 skin depths, additional copper has no measurable effect on RF conductor loss. At 5 GHz and above, even half-ounce copper is far thicker than needed electrically.

Why does ENIG increase loss at millimeter-wave frequencies?

The 3–5 µm nickel barrier layer in ENIG is ferromagnetic (μ_r up to several hundred) and has low conductivity (σ ≈ 1.4 × 10⁷ S/m). Its skin depth is extremely small, and its surface resistance is much higher than copper’s. At 28 GHz and above, current flows almost entirely in this lossy nickel layer, raising trace loss significantly. Prefer immersion silver or ENEPIG for RF traces.

How does surface roughness interact with skin depth?

When the RMS roughness of the copper foil is comparable to or larger than the skin depth, current must follow the surface contour, increasing the effective path length. This can add 30–80 % extra conductor loss at millimeter-wave frequencies. Low-profile and very-low-profile foils (Rq < 1 µm) mitigate this effect. The Hammerstad-Jensen model is the most common correction applied in EM solvers.