Elysia Tools

Browse tools, examples, visual explainers, and topic guides from one clear workspace.

Top Categories

Hubs

Language
ZHESPTRUFRDEEN

Elysia Tools

Navigation

Math & Numbers

Magnetic Permeability Converter (H/m ↔ relative μ_r)

· Last updated：2026-08-02

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).

Execution

Run this tool

Fill in the form, run the tool, and review the result in one place.

Samples

Examples that match this tool

Related

Continue with connected tools and hubs

Written by the Elysia Tools team

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category
Math & Numbers
Input types
select, number
Output type
json
Sample coverage
4
API ready
Yes

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.

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

  1. 1Enter a non-negative permeability value.
  2. 2Select whether the input is H/m or relative μ_r.
  3. 3Choose the desired output unit: H/m or relative μ_r.
  4. 4Set 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.

Examples

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

Electrical engineering student

Background

A student is using a typical relative permeability of approximately 5000 for iron in a magnetic circuit calculation.

Problem

The calculation requires absolute permeability in H/m rather than relative permeability.

How to use

Set Input unit to relative, enter 5000, choose H/m as the Output unit, and set Decimal Places to 10.

Input unit: relative; Value: 5000; Output unit: H/m; Decimal Places: 10

Outcome

The converter returns approximately 0.0062831853 H/m.

2. Convert vacuum permeability

Physics learner

Background

A physics learner wants to verify the SI value associated with vacuum relative permeability.

Problem

The learner needs the H/m value corresponding to μ_r = 1.

How to use

Set Input unit to relative, enter 1, choose H/m as the Output unit, and set Decimal Places to 12.

FAQ

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.

Home
Tools3201
Samples593
Visualizations465
Viewers103
Hubs233
Tags333
Images, Audio & Video657

Image, audio, and video processing, conversion, and optimization tools

Math, Date & Finance644

Calculators, numerics, date logic, statistics, and finance tools

Design & Color297

Color, layout, graphics, visual styling, and design helper tools

Text & Writing209

Writing, cleanup, formatting, extraction, and text analysis tools

Developer & Web193

Developer utilities, networking, web debugging, and automation helpers

Conversion & Encoding175

Format, file, archive, unit, and encoding conversion tools

FLAC/WAV Source Screening and Evidence Handoff
Self-Hosted Giveaway Widget Review and Embed Handoff
Stripe Promo Code Batch Review and Import Preflight
Batch Photo Culling Review and Editing Shortlist Handoff
UI Screenshot Structure Review and Development Handoff

© 2026 Elysia Tools. All rights reserved.

DocsPricingAboutTerms of ServicePrivacy PolicyCookiesContact
Python

Web Image Processing Python Samples

Web Python image processing examples using PIL/Pillow including reading, saving, resizing, and format conversion

Java

Android Image Processing Java Samples

Android Java image processing examples including reading/saving images, scaling, and format conversion

Kotlin

Android Image Processing Kotlin Samples

Android Kotlin image processing examples including reading/saving images, scaling, and format conversion

Rust

Web Image Processing Rust Samples

Web Rust image processing examples including image read/save, scaling, and format conversion

Math & Numbers

Absolute Value Calculator

Calculate the absolute value of positive, negative, or decimal numbers and explain the sign relationship

Math & Numbers

Air Changes per Hour (ACH, n = Q/V)

Compute the air change rate (ACH / n) of a room from the outdoor supply airflow Q and the room volume V: n = Q/V (1/h). Three modes: solve ACH (given Q and V), solve airflow (given n and V), or solve volume (given n and Q). Flow in m³/s/m³/h/CFM, volume in m³/ft³/L. Also reports the well-mixed single-zone purge time to reach a target residual fraction ε (default 1%): t = −ln(ε)/n hours.

Math & Numbers

Bar to PSI

Convert bar to pounds per square inch with configurable decimal precision

Math & Numbers

Bearing Life L10 Calculator

Calculate the basic rating life of a rolling bearing: L10 = (C/P)^p, with p = 3 for ball bearings and p = 10/3 for roller bearings. When a speed is provided, converts to L10h in operating hours.

Input unit: relative; Value: 1; Output unit: H/m; Decimal Places: 12

Outcome

The converter returns approximately 0.000001256637061436 H/m.