Calculator
Formula Used
Skin depth: δ = sqrt(2 / (ω μ σ)) = 1 / sqrt(π f μ σ)
Angular frequency: ω = 2πf
Effective permeability: μ = μ0 μr, where μ0 = 4π × 10^-7 H/m
Temperature corrected conductivity: σT = σref / [1 + α(T - Tref)]
Amplitude at depth x: A% = 100e^(-x / δ)
Power at depth x: P% = 100e^(-2x / δ)
Depth for chosen amplitude: x = -δ ln(A% / 100)
Depth for chosen power: x = -(δ / 2) ln(P% / 100)
How to Use This Calculator
- Select a material preset or keep custom input.
- Enter the excitation frequency and choose its unit.
- Choose conductivity or resistivity as the material property.
- Enter relative permeability for the material condition.
- Add temperature data when hot operation matters.
- Enter a remaining percentage for amplitude or power depth.
- Add sample thickness to estimate remaining field and power.
- Press calculate, then export the result as CSV or PDF.
Example Data Table
| Material | Frequency | Conductivity | μr | Approximate Skin Depth |
|---|---|---|---|---|
| Copper | 60 Hz | 58 MS/m | 1 | 8.532 mm |
| Copper | 100 kHz | 58 MS/m | 1 | 0.209 mm |
| Aluminum | 10 kHz | 35 MS/m | 1 | 0.851 mm |
| 304 Stainless Steel | 10 kHz | 1.45 MS/m | 1.02 | 4.138 mm |
| Carbon Steel | 1 kHz | 6 MS/m | 100 | 0.650 mm |
Understanding Eddy Current Depth of Penetration
What This Calculator Estimates
Eddy current testing and induction heating depend on how deep changing magnetic fields enter a conductor. The useful depth is called skin depth. It is also called standard depth of penetration. At one skin depth, field amplitude falls to about 36.8 percent of the surface value. Power density falls faster, because it follows the square of the field.
Why Frequency Matters
Frequency has a strong effect. Higher frequency gives a smaller depth. Lower frequency reaches deeper regions. This is why surface crack inspection often uses higher frequency. Wall thickness checks use lower frequency. The calculator accepts hertz, kilohertz, megahertz, and gigahertz. It also shows the reverse frequency needed for a target depth.
Material Effects
Conductivity and magnetic permeability also control penetration. Copper has high conductivity, so depth is small at high frequency. Stainless steel has lower conductivity, so depth can be larger. Ferromagnetic steels may have high relative permeability. That can make depth much smaller. Steels vary with alloy, heat treatment, stress, and magnetization. Use measured values when accuracy matters.
Temperature Correction
Conductivity changes with temperature. For many metals, conductivity drops as temperature rises. The calculator applies a linear correction using a temperature coefficient. This is useful for hot coils, induction heating, brake rotors, billets, and bus bars. Set the coefficient to zero when no correction is wanted.
Attenuation Depth
One skin depth is not always enough. You may need the depth where amplitude is 10 percent, 5 percent, or 1 percent of the surface value. The tool can compute that depth. It can also use a power based percentage. Power based penetration is smaller for the same remaining percentage.
Practical Use
Results are estimates. Edge effects, coil geometry, probe lift off, surface roughness, coatings, and nearby parts can change readings. Laminated, plated, and layered materials need special care. Nonlinear magnetic behavior can also shift the answer. Use the calculator for planning, comparison, and documentation. Validate critical work with calibration blocks or measured samples.
Interpreting Outputs
The result panel gives skin depth in meters, millimeters, micrometers, and mils. It reports power remaining at a chosen thickness. Use these values to choose test frequency, predict heating concentration, or compare candidate materials before detailed simulation or probe setup.
FAQs
What is eddy current depth of penetration?
It is the depth where an alternating electromagnetic field drops to a defined fraction of its surface value. Standard skin depth uses 36.8 percent amplitude.
Is skin depth the same for every metal?
No. It changes with conductivity, magnetic permeability, and frequency. Temperature and alloy condition can also change the final value.
Why does higher frequency reduce penetration?
Higher frequency increases induced current concentration near the surface. The field decays faster, so the calculated penetration depth becomes smaller.
What does relative permeability do?
Higher relative permeability usually reduces penetration depth. Ferromagnetic steels can therefore have much smaller depth than nonmagnetic materials.
Should I use conductivity or resistivity?
Use whichever value is available. The calculator converts resistivity into conductivity before applying the skin depth formula.
What is the temperature coefficient field?
It adjusts conductivity for temperature. Set it to zero when temperature correction is unknown or not needed.
What is attenuation depth?
It is the depth where amplitude or power reaches your chosen remaining percentage. It may be more useful than one standard skin depth.
Can this replace calibration blocks?
No. Use it for planning and comparison. Critical inspection work should be checked with standards, samples, or validated measurement procedures.