Magnetic Field Converter

A magnetic field converter translates measurements of magnetic phenomena between three related families of units. The flux density (B) family measures how much magnetic field passes through a surface area; it is reported in tesla (SI), gauss (CGS), and their prefixes plus the geophysics gamma. The flux (Φ) family measures the total field through an area; it is reported in weber (SI) and maxwell (CGS). The field strength (H) family measures the magnetising field inside a material; it is reported in ampere per metre (SI) and oersted (CGS). This converter keeps each panel in sync through its own pivot unit and exposes a free-space bridge between B and H, while making clear that the three families are not interchangeable.

How to Use the Magnetic Field Converter

1. Type a value into any of the six fields in the Flux density panel, tesla, millitesla, microtesla, gauss, milligauss, or gamma. The other five update instantly through the tesla pivot.
2. Type a value into either field in the Magnetic flux panel, weber or maxwell. The other field updates instantly through the weber pivot.
3. Type a value into either field in the Field strength panel, A/m or oersted. The other field updates instantly through the A/m pivot.
4. Read the Free-space bridge panel to see what the equivalent B would be at the current H, or vice versa, in vacuum only. The bridge uses µ₀ = 4π × 10⁻⁷ H/m exactly (NIST 2019 redefinition).
5. Use the Reference field magnitudes cards as a sanity-check table, they are not input fields. Real measurements vary with specimen, distance, and instrument.
6. The three panels do NOT auto-sync to each other. Converting B to H in a medium requires knowing the permeability; converting B to Φ requires knowing the area through which B passes.

The Conversion Factors

Magnetic flux density, pivot tesla. Every flux-density unit is an exact multiple of the tesla:

• 1 T = 1 T (the SI unit)
• 1 mT = 1e-3 T
• 1 µT = 1e-6 T
• 1 G = 1e-4 T, i.e. 1 T = 10 000 G exactly
• 1 mG = 1e-3 G = 1e-7 T
• 1 γ (gamma) = 1 nT = 1e-9 T

The 10 000 factor between tesla and gauss is exact by the SI definition; the gauss is named after Carl Friedrich Gauss and was the standard CGS flux-density unit before the SI was adopted. The gamma (γ) survives in geophysics, where Earth's field is naturally quoted in nanotesla.

Magnetic flux, pivot weber. Every magnetic flux unit is an exact multiple of the weber:

• 1 Wb = 1e8 Mx, i.e. 1 Wb = 100 000 000 maxwell exactly
• 1 Mx = 1e-8 Wb

The weber is named after Wilhelm Eduard Weber; the maxwell is named after James Clerk Maxwell. One weber is the flux that, linking a circuit of one turn, would produce an EMF of one volt if it were reduced to zero at a uniform rate in one second. 1 Wb = 1 V·s exactly.

Magnetic field strength, pivot A/m. Every field-strength unit is an exact multiple of the ampere per metre:

• 1 A/m = (4π × 10⁻³) Oe, i.e. 1 Oe = 1000 / (4π) A/m exactly
• 1 Oe ≈ 79.57747154594767 A/m (rounded)

The factor 4π enters by the CGS electromagnetic definition, in which the oersted is the field strength at the centre of a circular coil of unit radius carrying a unit current. The 4π propagates through B = µ₀ · H in CGS, where µ₀ = 1 in CGS-Gaussian and the oersted emerges naturally. In SI, µ₀ = 4π × 10⁻⁷ H/m exactly, so 1 Oe = (1/µ₀) × 1 A/m × 1e-3 = 1000/(4π) A/m.

The free-space bridge, B = µ₀ · H. In vacuum (or in air to a very good approximation), magnetic flux density and field strength are related by:

B = µ₀ · H, where µ₀ = 4π × 10⁻⁷ H/m exactly (NIST 2019 SI redefinition)

So 1 A/m in vacuum corresponds to B = (4π × 10⁻⁷) T ≈ 1.2566 µT. And 1 Oe in vacuum corresponds to B = (4π × 10⁻⁷) × (1000/(4π)) T = 10⁻⁴ T = 1 G, recovering the famous "in free space, B in gauss equals H in oersted" rule of thumb. This is exact only in vacuum. Inside any magnetic material, B = µ₀ · (H + M) where M is the magnetisation, and B and H diverge by the permeability.

Worked Examples

Example 1, 1 T to gauss. 1 T = 10 000 G exactly. Reverse: 10 000 G × 1e-4 T/G = 1 T. Round trip is exact.

Example 2, 50 µT to gauss. 50 µT × 1e-6 T/µT × 1e4 G/T = 0.5 G. This is the right order of magnitude for the Earth's field in the mid-latitudes.

Example 3, 1 mT to gauss. 1 mT × 1e-3 T/mT × 1e4 G/T = 10 G exactly.

Example 4, 1 Wb to maxwell. 1 Wb × 1e8 Mx/Wb = 1e8 Mx exactly. This is the flux that would induce 1 V for 1 s in a single-turn coil.

Example 5, 1 A/m to oersted. 1 A/m × (1 Oe / 79.57747154594767 A/m) ≈ 0.01256637 Oe. The factor 4π/1000 enters here by the CGS definition of the oersted.

Example 6, 1 T to oersted in vacuum. In free space, B = µ₀ · H, so 1 T corresponds to H = 1 / (4π × 10⁻⁷) A/m ≈ 795 774.72 A/m ≈ 10 000 Oe. This is why "B in gauss equals H in oersted" is exact only in vacuum.

Where Magnetic Field Conversion Shows Up

MRI and medical imaging. Clinical MRI scanners use superconducting magnets in the range of roughly 1.5 to 3 T, with field homogeneity specified in parts-per-million of the central field. Older papers and equipment manuals sometimes quote in gauss, the conversion is exactly 1 T = 10 000 G.

Electrical machines and power engineering. Transformer cores, motor armatures, and inductor cores are designed using B-H curves of electrical steel. The flux linking a coil of N turns is Φ = N · B · A, where A is the cross-section in square metres; a 1.5 T flux density in a 10 cm × 10 cm iron core yields 0.015 Wb per turn.

Geophysics and prospecting. Earth's magnetic field is on the order of 25 to 65 µT at the surface, varying with latitude, geology, and solar activity. Aeromagnetic surveys for mineral exploration report anomalies in nanotesla or gamma (1 γ = 1 nT). Magnetometers for navigation and archaeology resolve fractions of a nanotesla.

Data storage. Hard-disk write heads generate fields on the order of 1 T at the recording medium to flip the magnetisation of grains only a few nanometres across. The field strength is always reported in tesla, never in gauss in this context.

Permanent magnets. Neodymium-iron-boron magnets (N52 grade, the strongest commercial) produce surface fields on the order of 0.2 to 0.5 T. Ferrite (ceramic) magnets are about an order of magnitude weaker, around 0.02 to 0.05 T at the surface. Surface field is always less than the remanence B_r of the material because of the open magnetic circuit.

Particle accelerators and scientific instruments. Cyclotrons, synchrotrons, and Hall-effect setups use fields from a few hundred millitesla up to several tesla. NMR spectrometers for chemistry operate in the 7 to 23 T range; research instruments push to 30 T with resistive magnets and higher with hybrid designs.

Common Mistakes

Treating "magnetic field" as a single quantity. Engineers and scientists use "magnetic field" loosely for both B and H. They are not the same. B (tesla, gauss) is flux density. H (A/m, oersted) is the applied field. In vacuum they coincide via B = µ₀ · H; in materials they diverge, and only H enters the constitutive relation as the "cause" while B is the "effect".

Assuming B in gauss and H in oersted are always interchangeable. They coincide exactly only in vacuum. In a magnetic material with relative permeability µ_r = 5000 (transformer steel), B = µ₀ · µ_r · H, and a 1 Oe applied field corresponds to B = 5000 G, not 1 G.

Confusing gauss with tesla by a factor of 10 or 100. The most common numerical error is mixing up the 10 000 conversion (T ↔ G) and the 100 000 000 conversion (Wb ↔ Mx). Always double-check: 1 T = 10 000 G exactly, but 1 Wb = 100 000 000 Mx.

Forgetting that flux is flux density times area. Φ = B · A only when B is uniform and perpendicular to area A. Reporting a "flux of 1 Wb" without specifying the area tells you nothing about the field strength; 1 Wb through 1 m² is 1 T, but 1 Wb through 1 mm² is 1000 T.

Using gamma without specifying. "Gamma" persists in geophysics and magnetometry literature; outside those communities it is rarely seen. Always write "γ = 1 nT" the first time you use it, to remove ambiguity.

Treating prefixes as the same. mT, µT, nT, and G are all flux-density units but they differ by large factors. 1 mT = 10 G exactly, but 1 µT = 10 mG exactly, and 1 gamma = 1 nT = 0.01 mG.

Frequently Asked Questions

Why are there three different magnetic units families?

Because the underlying physics has three related-but-distinct quantities. Flux density B (tesla, gauss) measures how much magnetic field passes through a unit area and generates forces on moving charges. Flux Φ (weber, maxwell) is the integral of B over an area and governs Faraday's law of induction. Field strength H (A/m, oersted) is the magnetising field produced by free currents and enters the constitutive relation B = µ₀ · (H + M). Mixing them is the single most common conceptual error in introductory electromagnetism.

Is 1 gauss equal to 1 oersted?

Only in free space. The exact relationship in vacuum is 1 G = 1 Oe because of the way the CGS oersted and the CGS gauss were defined. Inside any magnetic material with relative permeability different from 1, B and H diverge by the permeability, and the equality no longer holds. A 1 Oe magnetising field in iron with µ_r = 5000 produces B = 5000 G, not 1 G.

How do I convert B to H in vacuum?

Use B = µ₀ · H, with µ₀ = 4π × 10⁻⁷ H/m exactly (NIST 2019 redefinition). So H (in A/m) = B (in T) / (4π × 10⁻⁷) ≈ B (in T) × 795 774.72. Equivalently, in vacuum, B in gauss equals H in oersted exactly. Inside magnetic materials you cannot convert without knowing the permeability; the relationship B = µ₀ · µ_r · H requires µ_r.

Why is the gamma used in geophysics?

The gamma (γ) is a non-SI unit defined as 1 γ = 1 nT. It survives in geophysics because Earth's field and its anomalies are naturally on the order of tens of thousands of gammas (50 000 γ = 50 µT). Modern SI practice prefers nanotesla, but gamma remains common in aeromagnetic surveys and magnetometry papers.

What is the difference between weber and tesla?

A weber is a unit of magnetic flux (the total field through an area), and a tesla is a unit of flux density (flux per unit area). 1 Wb = 1 T · m² exactly. So 1 T over 1 m² gives 1 Wb, while the same 1 T over 1 mm² gives 1e-6 Wb. The two units are linked but not interchangeable; flux density describes the strength of the field, flux describes how much of that field is captured by a particular surface.

Why is 1 T = 10 000 G exactly?

Because the SI definition of the tesla is the weber per square metre (T = Wb/m²) and the gauss was defined in the CGS system as the maxwell per square centimetre (G = Mx/cm²). The conversion 1 Wb = 1e8 Mx and 1 m² = 1e4 cm² together give 1 T = 1 Wb/m² = 1e8 Mx / 1e4 cm² = 1e4 G exactly. The factor is exact, not approximate.

Can this calculator be used for professional or scientific work?

Yes. The conversion factors are exact by international definition and are reproduced from NIST SP 811, the BIPM SI Brochure, ISO 80000-6, and IEC 60050-121. The converter's results are mathematically correct to the full precision of the inputs. For high-stakes work (medical, regulatory, scientific publication), cross-check with a domain expert and consult the original references.

How often are the magnetic-unit definitions updated?

Rarely. The 2019 SI redefinition made µ₀ = 4π × 10⁻⁷ H/m exact, which eliminated the last small uncertainty in the conversion factors. The CGS legacy units (gauss, maxwell, oersted) are fixed by definition relative to their SI counterparts. The geophysics gamma remains 1 nT by long convention. Updates only occur when the SI itself is redefined.

References

• NIST Special Publication 811, Guide for the Use of the International System of Units (SI). The authoritative US reference for SI usage, unit conversion, and the exact definitions of derived units including the tesla, weber, and the factors relating gauss, maxwell, oersted, and their SI equivalents.
• BIPM SI Brochure (9th edition), The International System of Units (SI). The canonical definition of the SI units, including the conventions for magnetic units and the post-2019 exact value of µ₀.
• ISO 80000-6, Quantities and units, Part 6: Electromagnetism. The international standard for the quantities, symbols, and units of electromagnetism, including magnetic flux density (B, T), magnetic flux (Φ, Wb), magnetic field strength (H, A/m), and B = µ₀ · H in vacuum.
• IEC 60050-121, International Electrotechnical Vocabulary, Part 121: Electromagnetism. The IEC's authoritative terminology for electromagnetism, defining the tesla, weber, gauss, maxwell, oersted, and related quantities.
• ICRU Report 33, Quantities and Units of Radiation Dosimetry. Establishes the gamma (γ) as 1 nT in the geophysics and dosimetry literature.
• NIST 2019 SI redefinition, The 2019 redefinition of the SI base units fixed µ₀ = 4π × 10⁻⁷ H/m exactly (previously measured), so the conversions between SI and CGS magnetic units are now exact without any experimental uncertainty.