What units does this converter support?

It converts between H/m absolute permeability and relative permeability μ_r, which is dimensionless.

What formula is used?

The converter uses μ = μ_r × μ₀ and μ_r = μ / μ₀, with μ₀ approximately 1.25663706×10⁻⁶ H/m.

Can I enter zero or negative values?

Zero is allowed because the input must be non-negative. Negative values are not supported.

What is the relative permeability of vacuum?

Vacuum has a relative permeability μ_r of 1, corresponding to approximately 1.25663706×10⁻⁶ H/m.

How precise can the displayed result be?

You can choose between 0 and 14 decimal places.

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Magnetic Permeability Converter (H/m ↔ relative μ_r)

Convert magnetic permeability (μ) between absolute permeability in henry per metre (H/m, SI unit; equivalently N/A² or T·m/A) and relative permeability μ_r (dimensionless). Vacuum permeability μ₀ = 4π×10⁻⁷ H/m ≈ 1.25663706×10⁻⁶ H/m (defined pre-2019; since the 2019 SI redefinition it is a measured quantity with relative uncertainty 1.6×10⁻¹⁰, so the 4π×10⁻⁷ form is still exact for all engineering purposes). Relations used: μ = μ_r × μ₀ and μ_r = μ / μ₀ (magnetic susceptibility χ_m = μ_r − 1). Reference: vacuum μ_r = 1, copper 0.999994 (diamagnetic), aluminum 1.000022 (paramagnetic), iron ≈ 5000 (ferromagnetic).

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2 examples

Iron: μ_r = 5000 → H/m ≈ 6.2831853×10⁻³

μ = μ_r × μ₀ = 5000 × 4π×10⁻⁷ = 6.2831853×10⁻³ H/m. Typical relative permeability of 99.8% iron (ferromagnetic).

{"result":"5000 relative = 0.0062831853 H/m. All units: H/m=0.0062831853, relative=5000.","metadata":{"input":{"inputUnit":"relative","value":5000,"outputUnit":"H/m"},"result":{"outputValue":0.0062831853,"outputUnit":"H/m","H/m":0.0062831853,"relative":5000}}}

Vacuum: μ_r = 1 → H/m ≈ 1.2566371×10⁻⁶

μ = 1 × 4π×10⁻⁷ = 1.2566371×10⁻⁶ H/m. By definition the vacuum permeability μ₀.

{"result":"1 relative = 0.000001256637061436 H/m. All units: H/m=0.000001256637061436, relative=1.","metadata":{"input":{"inputUnit":"relative","value":1,"outputUnit":"H/m"},"result":{"outputValue":0.000001256637061436,"outputUnit":"H/m","H/m":0.000001256637061436,"relative":1}}}

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4 options

SettingsAdjust formats, ranges, numbers, and modes.4

Input unitselectOptionalValuenumberRequiredPermeability in the selected Input unit. Must be non-negative.Output unitselectOptionalDecimal PlacesnumberOptional

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Magnetic Permeability Converter (H/m ↔ relative μ_r)

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Examples

1. Convert iron's relative permeability to H/m

2. Convert vacuum permeability

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