Free · Physics models
Conductive Skin Depth Estimate
Estimate electromagnetic penetration depth using frequency, resistivity and relative magnetic permeability.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
At 1 GHz, the retained copper preset gives skin depth about 2.062 µm.
δ = √[ρ/(π f μ0 μr)], retaining μ0 ≈ 4π × 10⁻⁷ H/m.
Worked example
Enter these known values and leave the other values blank.
- Frequency (f)
- 1 GHz
- Resistivity (ρ)
- 1.678 μΩ·cm
- Relative permeability (μ==r==)
- 0.999991
- Skin depth (δ)
- 2.0617 μm
Assumptions and limitations
- Good-conductor, planar skin-effect approximation with frequency-independent resistivity and permeability.
- Copper preset resistivity is 1.678 × 10⁻⁸ Ω·m and relative permeability 0.999991. Material properties vary with temperature and frequency.
- The conventional approximation μ0 = 4π × 10⁻⁷ H/m is retained; μ0 is no longer exact in the revised SI.
- Enter known quantities and clear the unknown to use available inverse branches. Locks retain supplied values. Consistency messages cover fully visible equations; identities with hidden dependencies may require a manual consistency check. Preset values are illustrative approximations, and unit selectors preserve the underlying quantity.
Common questions
How do I solve for a different quantity?
Clear that quantity and supply enough independent known values. Some outputs are one-way or tied to a selected preset, so they cannot determine every input.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.