# 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).

> Canonical page: https://elysiatools.com/en/tools/permeability-converter

- **Category:** Math & Numbers

- **Keywords:** magnetic permeability, permeability, henry per metre, H/m, relative permeability, μ_r, mu_r, vacuum permeability, μ₀, mu_0, magnetic susceptibility, N/A², electromagnetism, permeability conversion

## Overview

Convert magnetic permeability between absolute permeability in H/m and relative permeability μ_r. Enter a non-negative value, choose the input and output units, and set the displayed decimal places from 0 to 14.

## Inputs

- **Input unit** (select)
- **Value** (number): Permeability in the selected Input unit. Must be non-negative.
- **Output unit** (select)
- **Decimal Places** (number)

## When to use

- Convert a material's relative permeability μ_r into absolute permeability in H/m for electromagnetic calculations.
- Convert an absolute permeability value in H/m into dimensionless relative permeability.
- Check reference values such as vacuum or typical iron permeability using a consistent conversion.

## How it works

- Enter a non-negative permeability value.
- Select whether the input is H/m or relative μ_r.
- Choose the desired output unit: H/m or relative μ_r.
- Set decimal places from 0 to 14 and read the JSON result.

## Use cases

- Electromagnetism coursework requiring conversions between μ_r and SI permeability.
- Magnetic material comparisons using dimensionless relative permeability values.
- Engineering calculations that require permeability in H/m, N/A², or the equivalent SI form.

## Frequently asked questions

### 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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