HomeCalculatorsElectricalRF & MicrowaveSkin Depth Calculator
Electrical calculator

Skin Depth Calculator

Compute electromagnetic skin depth δ = √(ρ/(π·f·μ)) for conductors. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 2/2 declared partitions (nominal, invalid-domain) · Matrix
Known limitations
  • Good-conductor approximation; SI only
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Electromagnetic skin depth.
Scope
Good conductor; bulk μr
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity
2/2 property · digest 29a379f1211f
Legacy regression
6/6 tests · Production surface contract 4/4
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review
Internal · Pass · electrical-engineer
Named expert review
Not performed
CVP suite
2/2 golden · 2/2 CVP boundary · 2/2 invalid · 2/2 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
Sources
  • Jackson / RF handbook skin effect — Skin depth
  • NIST / electromagnetics handbook — Skin effect in good conductors
Sources
Evidence
2 legacy golden · 2 legacy boundary · legacy regression suite · 2/2 oracle-backed golden · 2/2 invalid · Artifact integrity PASS · CalculatorX electrical review
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Skin depthδ = √(ρ / (π·f·μ0·μr))
iμ0 = 4π×10⁻⁷ H/m. Good conductor / plane-wave approximation.

How to use

1

Enter frequency

f > 0 in Hz.

2

Enter resistivity ρ and relative permeability μr

Example copper ρ ≈ 1.68×10⁻⁸ Ω·m; μr = 1 for non-magnetic metals.

3

Read skin depth δ

δ = √(ρ/(π·f·μ0·μr)).

Example calculations

Common configurations with formula and result.

ϟ

Cu @ 1 MHz

ρ=1.68e-8 · μr=1 · f=1e6

√(ρ/(πfμ))
≈65.2 µm

Skin Depth calculator specification

Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-08-08

Calculation status

Review policy · Evidence · Reviewed by CalculatorX electrical review (electrical-engineer)

Definition
Skin depth δ = √(ρ/(π·f·μ)) with μ = μ0·μr. Most AC current flows within roughly a few skin depths of the surface.
What it calculates
Electromagnetic skin depth.
Inputs
  • f_Hz
  • rho_ohm_m
  • mur
Outputs
  • delta_m
  • delta_um
Formula
δ=√(ρ/(πfμ))
Assumptions
  • Good conductor; bulk μr
Units
  • Hz, Ω·m → m
Boundary conditions
  • f,ρ,μr ≤0 → VALUE_MUST_BE_POSITIVE
Example
Cu 1 MHz → ~65 µm
Validation cases

1 published on this page · 6/6 tests · Production surface contract 4/4 · View evidence

  • f=1e6 rho=1.68e-8 mur=1 → delta≈65.2e-6 m
Sources
  • Jackson / RF handbook skin effect — Skin depth
    Supports: δ=√(2ρ/ωμ) equivalent form
  • NIST / electromagnetics handbook — Skin effect in good conductors
    Supports: δ=√(ρ/πfμ) form
Last reviewed
2026-08-08
Reviewed by
CalculatorX electrical review (electrical-engineer)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute RF skin depth.

Supported and not supported

Supported — Plane-wave skin depth for good conductors · API electrical.rf.skin_depth

Not supported — Waveguides, anomalous skin effect, plated stacks

Agent / API notes

Capability id: electrical.rf.skin_depth · tool id: skin-depth · pin 1.0.0.

Errors: MISSING_REQUIRED_INPUT, VALUE_MUST_BE_POSITIVE, INVALID_MODE.

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Frequently asked questions

Key distinctions behind the calculation.

What resistivity for copper?

Annealed copper is often taken as ≈1.68×10⁻⁸ Ω·m at room temperature.