Magnetic Flux Density Converter

Magnetic flux density, denoted B and sometimes called magnetic induction or simply the B-field, measures the density of magnetic flux lines passing perpendicularly through a unit area of surface. It is defined as B = Φ/A (flux per unit area) for uniform fields, and more generally as the vector field satisfying ∇·B = 0 (Gauss's law for magnetism). The SI unit is the tesla (T), equal to one weber per square meter (Wb/m²) or equivalently one volt-second per square meter (V·s/m²). The tesla is named after Nikola Tesla. Magnetic flux density is one of the most important quantities in electrical engineering, materials science, medical imaging, and geophysics.

The gauss (Gs or G) is the CGS unit of magnetic flux density: 1 T = 10,000 Gs. The gauss remains in widespread use in the permanent magnet industry (where typical surface fields are expressed in hundreds to thousands of gauss), in scientific literature (particularly in the USA), and in older European literature. Earth's magnetic field at the surface is approximately 0.25–0.65 gauss (25,000–65,000 gamma) depending on location. A strong ceramic ferrite magnet produces 2000–4000 gauss at its surface; NdFeB magnets can reach 6000–14,000 gauss.

The weber per square meter is exactly equal to the tesla (1 Wb/m² = 1 T), making this unit interchangeable and useful for showing the relationship between flux (Wb) and flux density explicitly. The weber per square centimeter = 10,000 T — an astronomically large unit rarely encountered in practice, since it would represent an incredibly dense magnetic field. It appears in unit conversion tables for completeness.

The maxwell per square centimeter is numerically equal to the gauss (1 Mx/cm² = 1 Gs = 10⁻⁴ T), since the maxwell is the CGS unit of flux and the square centimeter is the CGS area unit. Similarly, line per square centimeter = gauss. The maxwell per square meter = 10⁻⁴ T — equivalent to the gauss re-expressed with SI area units. These relationships reflect the CGS system's use of different area conventions compared to SI.

The gamma (γ) = 1 nanotesla (nT) = 10⁻⁵ gauss is the unit used in geomagnetic surveys. Earth's total magnetic field intensity ranges from about 25,000 gamma near the equator to 65,000 gamma near the poles. Magnetic anomaly maps used in mineral exploration depict local variations of tens to thousands of gamma superimposed on this global field. Aeromagnetic surveys flown at 100–300 m altitude can resolve anomalies of 1–10 gamma associated with iron ore bodies, nickel–copper sulfide deposits, and kimberlite pipes (diamond sources).

In MRI technology, the main magnetic field B₀ must be extremely uniform — better than 5 ppm over the imaging volume — to produce diagnostic quality images. The superconducting magnets in clinical scanners (1.5 T and 3 T) are shimmed to achieve this uniformity using both passive iron shims and active superconducting shim coils. Gradient coils produce rapidly switched fields of 20–80 mT/m on top of B₀ for spatial encoding. The line per square inch unit (1 line/in² ≈ 1.55 × 10⁻⁵ T) and weber per square inch (1 Wb/in² ≈ 1550 T) appear in older American electrical engineering standards and patent literature.

In particle physics accelerators, dipole bending magnets steer the particle beam using fields of 1–9 T (in superconducting magnets). The LHC at CERN uses 8.33 T NbTi superconducting dipoles operating at 1.9 K. The proposed Future Circular Collider (FCC) would use 16 T Nb₃Sn magnets. Magnetic rigidity — the product B × r (flux density times bending radius) in T·m — characterizes the momentum of a charged particle in a magnetic field: p [GeV/c] = 0.3 × B [T] × r [m].

In data storage and magnetic recording, the coercivity of recording media (the B field needed to reverse magnetization) was historically specified in gauss or oersteds. Modern hard disk recording media have coercivities of 3000–5000 Oe (≈ 0.3–0.5 T) in the recording layer. Write heads must produce fields exceeding this coercivity — typically 10,000–20,000 Oe — in the write gap. Converting between tesla and gauss is routine in hard disk engineering.

This magnetic flux density converter supports all 11 units: tesla, weber/m², weber/cm², weber/in², maxwell/m², maxwell/cm², maxwell/in², gauss, line/cm², line/in², and gamma — instantly and precisely to 12 significant digits, completely free.