Eddy Current Skin Depth (Standard Depth of Penetration)
Eddy currents weaken exponentially with depth. The standard depth of penetration (δ) — where current density falls to 37% of the surface value — sets how deep an eddy-current test can reliably see and which frequency to choose. Too high a frequency and you only read the surface; too low and you lose resolution. This tool computes δ so you select frequency on physics, not guesswork.
How it works
δ = 1/√(π·f·μ·σ). In practical units, δ(mm) ≈ 50·√(ρ / (μr·f)), with resistivity ρ in µΩ·cm and frequency f in Hz. Lower conductivity (higher ρ), lower permeability, and lower frequency all increase penetration. Practical inspection depth is roughly 3δ (current density ~5% of surface). Choose test frequency so the flaw of interest sits within ~1–2 δ for good sensitivity and phase separation.
Formula
δ = 1 / √(π·f·μ·σ) ≈ 50 · √( ρ[µΩ·cm] / ( μr · f[Hz] ) ) mm
δ = 1 / √(π·f·μ·σ) ≈ 50 · √( ρ[µΩ·cm] / ( μr · f[Hz] ) ) mmWorked example
Aluminium (ρ ≈ 2.82 µΩ·cm, µr = 1) at 100 kHz: δ = 50·√(2.82 / (1 × 100000)) = 50·√(2.82e-5) = 50 × 0.00531 = 0.27 mm. Effective depth ≈ 3δ ≈ 0.8 mm. To find a flaw 1 mm deep you would drop frequency (e.g. to ~10 kHz, tripling δ).
| Variable | Value |
|---|---|
| input: material | Aluminium (2.82 µΩ·cm) |
| input: frequency | 100 |
| output: sdp_mm | 0.27 |
| output: eff_depth_mm | 0.80 |
When to use this tool
Use when selecting EC test frequency for surface vs. subsurface flaws, designing a multi-frequency setup, inspecting heat-exchanger tubes, or explaining why a deeper flaw needs a lower frequency.
Limitations
Where this calculator stops being accurate:
- Ferromagnetic materials (carbon steel) have high, variable µr — δ becomes very small and readings are dominated by permeability noise; saturation or alternative methods are usually needed.
- Uses nominal resistivity; alloy, temper, and temperature shift conductivity (and thus δ).
- δ is the 37% depth, not a hard limit — sensitivity degrades progressively; ~3δ is a practical effective limit.
- Lift-off, edge effect, and probe design also constrain real-world depth response.
Frequently Asked Questions
How deep can eddy current testing actually inspect?
Reliable response extends to roughly three standard depths of penetration (3δ), where current density is about 5% of the surface value. Beyond that, sensitivity falls off too far for dependable detection. Because δ depends on frequency, conductivity, and permeability, "how deep" always reduces to choosing the right frequency for the material and flaw depth.
Why does carbon steel give such a shallow skin depth?
Carbon steel is ferromagnetic with relative permeability in the tens to hundreds. Since δ scales as 1/√µr, a µr of 100 shrinks penetration by 10× versus a non-magnetic metal. That, plus permeability variation creating large background noise, is why conventional EC on ferrous material is mostly a surface-crack method — subsurface work uses magnetic saturation, remote-field, or other techniques.
How do I pick the test frequency?
Target the flaw depth within about 1–2 δ for the best amplitude and phase separation. Compute δ at a trial frequency; if the flaw sits much deeper than ~3δ, lower the frequency (δ rises as 1/√f). For surface cracks you can use a higher frequency for resolution. Tube inspection and multi-layer parts often run two or more frequencies to separate signals.
References & Standards Cited
- ASTM E2884 — Standard Guide for Eddy Current Testing of Electrically Conducting Materials Using Conformable Sensor Arrays.
- ASTM E309 — Standard Practice for Eddy-Current Examination of Steel Tubular Products Using Magnetic Saturation.
- ASNT, Electromagnetic Testing (ET) Classroom Training — depth of penetration.
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Founder of NDT Connect and Atlantis NDT. 15+ years in industrial inspection across oil & gas, petrochemical, and offshore. ASNT Level III certified across five methods. Drives platform standards for the NDT Connect marketplace.