Magnetic Field Converter — tesla, gauss, oersted, weber

The magnetic field converter above handles the three quantities that people casually lump together as "magnetic field" and which are, in fact, distinct: magnetic flux density B, magnetic field strength H, and magnetic flux Φ. Each has its own SI unit, its own centimetre-gram-second unit, and its own set of conversion factors. Mixing them is the single most frequent source of magnetics errors, and it is why this tool asks you to choose the quantity before it will show you any units.

Arb Digital publishes this converter as part of a free technical reference library. Factors are taken from the SI definitions in the BIPM Brochure and the conversion tables in NIST Special Publication 811, with the exact CGS relationships preserved and the magnetic constant carried at its current CODATA value rather than the pre-2019 exact form.

What This Magnetic Field Converter Does

In flux density mode it converts between tesla, its decimal submultiples down to nanotesla, gauss, milligauss, kilogauss, the geophysical gamma, and webers per square metre. In field strength mode it works in amperes per metre, kiloamperes per metre, amperes per centimetre and millimetre, ampere-turns per inch, oersted and gilbert per centimetre. In flux mode it covers weber, its submultiples, the maxwell, the line, the kiloline and the volt-second.

The headline figure is your requested conversion. The four panels beneath it always show the same quantity in the SI unit, the corresponding CGS unit, a useful submultiple, and one genuinely related quantity computed for free space, so you can see at a glance what field strength corresponds to a given flux density without opening a second tool.

How to Use It

1. Pick the quantity. If your unit is tesla or gauss, choose flux density. If it is A/m or oersted, choose field strength. If it is weber or maxwell, choose flux.
2. Enter the value. Magnetic quantities span an enormous range, so scientific notation input such as 5e-5 for the Earth field is fully supported.
3. Choose the from and to units. The lists only contain units valid for the selected quantity, which makes an invalid cross-quantity conversion impossible.
4. Read the four supporting panels for the SI value, the CGS value, a convenient submultiple, and the free-space equivalent of the paired quantity.
5. Use Swap to reverse the direction and sanity-check that you have not inverted the factor.

The Formula and How It Is Calculated

Each unit is stored as a multiplier to the SI unit for its quantity, so the conversion is result = value × factor(from) ÷ factor(to) with a single trip through the SI base. The tesla is the SI unit of magnetic flux density, defined as one weber per square metre, or one kilogram per second squared per ampere. The gauss is the corresponding CGS-Gaussian unit, and the relationship is exact: 1 T = 10⁴ G. The weber is the SI unit of magnetic flux, and the maxwell is its CGS counterpart at exactly 10⁻⁸ Wb.

Field strength is where the arithmetic stops being decimal. The SI unit is the ampere per metre, and the oersted is defined so that 1 Oe = 1000 ÷ 4π A/m, which is approximately 79.5774715 A/m. That factor of 4π is a fossil of the rationalisation choice made when the SI was constructed, and it is the reason so many magnetics conversions are not round numbers. Both the BIPM SI Brochure and NIST Special Publication 811 tabulate these CGS-to-SI relationships.

B Versus H: Why Gauss and Oersted Are Not the Same Thing

In a vacuum, one gauss of flux density corresponds numerically to one oersted of field strength, and generations of engineers have used the two words interchangeably because of it. Inside any material other than vacuum, that equivalence breaks down completely.

Magnetic field strength H describes the field produced by free currents: turns of wire, amperes, and geometry. Magnetic flux density B describes the total field actually present, including the contribution of the material's own magnetisation. In free space they are linked by B = μ₀H. Inside a ferromagnetic core the material adds its own magnetisation, and B can be thousands of times larger than μ₀H for the same driving current. A soft ferrite might reach 0.3 T of flux density at a field strength of only 50 A/m. That ratio is the material's permeability, and it is neither constant nor linear, which is why B-H curves are drawn as loops rather than straight lines.

The Magnetic Constant Is No Longer Exact

Before May 2019, μ₀ was defined as exactly 4π × 10⁻⁷ N/A², because the ampere itself was defined through the force between current-carrying wires. The 2019 revision of the SI redefined the ampere in terms of the elementary charge, which flipped the situation: the elementary charge is now exact and μ₀ became an experimentally determined quantity.

The current recommended value is about 1.25663706212 × 10⁻⁶ N/A², which differs from 4π × 10⁻⁷ only in the tenth significant figure. For every practical engineering purpose the old value remains perfectly usable, and this converter uses the CODATA value so that the free-space cross-conversion panel is technically correct. The lesson worth carrying is broader: a constant being "exact" is a statement about the definitional structure of the unit system, not about nature, and those definitions do change. Values are published and maintained by the NIST reference on constants, units and uncertainty.

Real Field Magnitudes, From Nanotesla to Tens of Tesla

Magnetic quantities span roughly fifteen orders of magnitude in ordinary technical work, which is why so many different units survive. The Earth's field at the surface runs between roughly 25 and 65 microtesla, or 0.25 to 0.65 gauss, and geophysicists measure its variations in nanotesla, historically called gamma. A refrigerator magnet sits near 5 millitesla. The permanent magnets in a hard disk actuator or a modern motor reach 1 to 1.4 tesla at the pole face.

A clinical MRI scanner operates at 1.5 or 3 tesla, and research systems exceed 10 tesla. The strongest continuous laboratory magnets reach the mid-40s in tesla. At the other extreme, the magnetic signals from the human brain measured in magnetoencephalography are a few femtotesla, roughly a billionth of the Earth's field, which is why those instruments live inside multi-layer shielded rooms. Keeping the exponent straight matters more here than in almost any other unit family, and the scientific notation converter is a useful companion when the numbers get small.

Flux Versus Flux Density: Area Is the Difference

Magnetic flux Φ is flux density integrated over an area. One weber is one tesla acting over one square metre. This distinction matters enormously in transformer and inductor design, because the voltage induced in a winding depends on the rate of change of flux, not flux density, while core saturation depends on flux density, not flux.

The practical consequence is that a designer can trade core area against flux density to hit a target flux. Doubling the core cross-section halves the flux density needed for the same flux, which is exactly how a core is kept out of saturation without changing the turns count. When a datasheet quotes a saturation figure it will be in tesla or gauss; when it quotes a volt-second product it is describing flux in webers. Confusing the two leads to cores that saturate at a fraction of the expected load. Cross-sectional areas can be converted in the area converter.

Full Magnetic Unit Conversion Tables

Magnetic flux density, one unit expressed in tesla:

Magnetic field strength, one unit expressed in amperes per metre:

Magnetic flux, one unit expressed in webers:

Common Mistakes to Avoid

• Converting gauss to oersted with a factor of one — that equality only holds in vacuum, and inside a magnetic material B and H differ by the permeability, which can be a factor of thousands.
• Mixing up weber and tesla — the weber is total flux, the tesla is flux per unit area, and the difference between them is the core cross-section.
• Reading gamma as anything other than a nanotesla — the geophysical gamma is exactly 1 nT, not a separate scale.
• Assuming permeability is constant — ferromagnetic materials saturate, so a B-to-H conversion using a single permeability figure fails at high field.
• Still treating the magnetic constant as exactly 4π × 10⁻⁷ — since the 2019 SI revision it is a measured value, though the difference is far below engineering significance.

Related Free Tools From Arb Digital

Magnetics calculations pull in several other quantities. Convert core cross-sections in the area converter, winding and gap dimensions in the length converter, switching rates in the frequency converter, core loss in the power converter, and stored energy in the energy converter. Very large and very small magnitudes are easier to read through the scientific notation converter, and the general unit converter covers the rest.

Frequently Asked Questions

This converter is a unit reference only. Magnetic exposure limits, shielding design, and equipment safety clearances should be assessed against the applicable standards and the manufacturer documentation for your installation.