Reference depth calculator

How deep the induced current flows, for a given material and frequency. This is the number that decides whether you are surface hardening or through heating.

Reference depth

2.01mm

0.079 in

86% of heating within: 4.02 mm
Frequency: 30 kHz
Band: Medium frequency

How this is calculated

Reference depth follows the standard relation:

δ = √( ρ / (π · f · μ_r · μ₀) )

where ρ is electrical resistivity in ohm-metres,f is frequency in hertz, μ_ris relative magnetic permeability and μ₀ is the permeability of free space, 4π × 10⁻⁷ H/m.

At the reference depth, induced current density has fallen to about 37 percent of its surface value. Around 86 percent of the total heating occurs within twice that depth.

What this does not tell you

This is not case depth. Reference depth is where the energy goes in. Case depth is how deep the metallurgy changed, which also depends on power density, heating time and how far heat conducted inward before the quench.
Permeability is not a constant. For magnetic steel it varies with field strength and with temperature, so the cold-steel figures are working estimates, not precise values.
Resistivity rises as the part heats. The reference depth therefore increases during the cycle, before jumping again at the Curie point.
Geometry is ignored. The relation assumes a flat semi-infinite surface. Small diameters, edges and corners all behave differently.

Use this to choose a frequency band and sanity-check a supplier's proposal. Do not use it as a heat treatment specification. For machines built around the case depth you need, see our induction hardening machines.

Now send us the part.

A calculator narrows the frequency band. Your component, its material, the case depth you need and your production rate settle the machine. Send those four and you will get a real answer.

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