# Units for magnetic properties

*You may also be interested in our common units and conversions page*

Symbol | Gaussian & cgs emu^{a} | Conversion factor, C^{b} | SI & rationalized mks^{c} | |
---|---|---|---|---|

Magnetic flux density, magnetic induction | B | gauss (G)^{d} | 10^{-4} | tesla (T), Wb/m^{2} |

Magnetic flux | Φ | maxwell (Mx), G·cm^{2} | 10^{-8} | weber (Wb), volt second (V·s) |

Magnetic potential difference, magnetomotive force | U, F | gilbert (Gb) | 10/4π | ampere (A) |

Magnetic field strength, magnetizing force | H | oersted (Oe),e Gb/cm | 10^{3}/4π | A/m^{f} |

(Volume) magnetization^{g} | M | emu/cm^{3 h} | 10^{3} | A/m |

(Volume) magnetization | 4πM | G | 10^{3}/4π | A/m |

Magnetic polarization, intensity of magnetization | J, I | emu/cm^{3} | 4π × 10^{-4} | T, Wb/m^{2 i} |

(Mass) magnetization | σ, M | emu/g | 1 4π × 10 ^{-7} | A·m^{2}/kgWb·m/kg |

Magnetic moment | m | emu, erg/G | 10^{-3} | A·m^{2}, joule per tesla (J/T) |

Magnetic dipole moment | j | emu, erg/G | 4π × 10^{-10} | Wb·m^{i} |

(Volume) susceptibility | χ, κ | dimensionless, emu/cm^{3} | 4π (4π) ^{2} × 10^{-7} | dimensionless henry per meter (H/m), Wb/(A·m) |

(Mass) susceptibility | χ_{ρ}, κ_{ρ} | cm^{3}/g, emu/g | 4π × 10^{-3}(4π) ^{2} × 10^{-10} | m^{3}/kgH·m ^{2}/kg |

(Molar) susceptibility | χ_{mol}, κ_{mol} | cm^{3}/mol, emu/mol | 4π × 10^{-6}(4π) ^{2} × 10^{-13} | m^{3}/molH·m ^{2}/mol |

Permeability | µ | dimensionless | 4π × 10^{-7} | H/m, Wb/(A·m) |

Relative permeability^{j} | µ_{r} | not defined | — | dimensionless |

(Volume) energy density, energy product^{k} | W | erg/cm^{3} | 10^{-1} | J/m^{3} |

Demagnetization factor | D, N | dimensionless | 1/4π | dimensionless |

- Gaussian units and cgs emu are the same for magnetic properties; the defining relation is B = H + 4πM
- Multiply a number in Gaussian units by C to convert it to SI (e.g., 1 G × 10
^{-4}T/G = 10^{-4}T) - SI (Système International d’Unités) has been adopted by the National Bureau of Standards. Where two conversion factors are given, the upper one is recognized under, or consistent with, SI and is based on the definition B = µ
_{0}(H + M), where µ_{0}= 4π × 10^{-7}H/m. The lower one is not recognized under SI and is based on the definition B = µ_{0}H + J, where the symbol I is often used in place of J. - 1 gauss = 10
^{5}gamma (γ) - Both oersted and gauss are expressed as cm
^{-1/2}·g^{1/2}·s^{-1}in terms of base units - A/m was often expressed as “ampere-turn per meter” when used for magnetic field strength
- Magnetic moment per unit volume
- The designation “emu” is not a unit
- Recognized under SI, even though based on the definition B = µ
_{0}H + J; see footnote c - µ
_{r}= µ/µ_{0}= 1 + χ, all in SI; µ_{r}is equal to Gaussian µ - B · H and µ
_{0}M · H have SI units J/m^{3}; M · H and B · H/4π have Gaussian units erg/cm^{3}

*Goldfarb, R. and Fickett, F. (1985), Units for magnetic properties:, National Institute of Standards and Technology, Gaithersburg, MD, [online], https://doi.org/10.6028/NBS.SP.696 (Accessed August 3, 2023)*