Magnet calculator: convert units and calculate magnetic fields
Two tools in one: the converter translates magnetic units using the factors from the NIST table, including between magnetic flux density B and magnetic field strength H. The field calculator determines the field of conductors, coils and permanent magnets and shows it as a field plot and as a profile along the axis.
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Abbreviations and symbols on this page (20)
- B
- Magnetic flux density (induction), unit tesla (T). The effect of the field, e.g. force on currents.
- H
- Magnetic field strength, unit A/m. The cause of the field, e.g. from current and turns.
- Φ
- Magnetic flux: B × area, unit weber (Wb).
- M
- Magnetization: magnetic moment per volume, unit A/m.
- m
- Magnetic moment of a magnet or a coil, unit A·m².
- µ0
- Magnetic constant: 1.25663706212 × 10⁻⁶ N/A² (CODATA 2018). Links B and H in vacuum.
- µr
- Relative permeability of a material: air about 1, iron many hundreds to thousands. B = µ0 µr H.
- Br
- Remanence: flux density a permanent magnet retains in the material. Outside, at the pole face, the field is lower.
- (BH)max
- Maximum energy product of a magnetic material, unit kJ/m³ or MGOe; a measure of its strength.
- T, mT, µT
- Tesla, millitesla, microtesla: SI unit of flux density. 1 mT = 0.001 T.
- G
- Gauss, older unit of flux density: 1 G = 0.0001 T, so 10,000 G = 1 T.
- Oe
- Oersted, older unit of field strength: 1 Oe ≈ 79.58 A/m.
- Wb
- Weber, SI unit of magnetic flux: 1 Wb = 1 V·s.
- Mx
- Maxwell, older unit of flux: 1 Mx = 10⁻⁸ Wb.
- emu
- Electromagnetic unit, older unit of magnetic moment: 1 emu = 0.001 A·m².
- MGOe
- Megagauss-oersted, older unit of energy product: 1 MGOe ≈ 7.958 kJ/m³.
- NdFeB
- Neodymium-iron-boron: material of the strongest commercially available permanent magnets.
- N42, 35H …
- Grade designation of neodymium magnets: the number roughly equals (BH)max in MGOe, the letter the temperature class (none = up to 80 °C, M 100 °C, H 120 °C, SH 150 °C per data sheet). Y35 etc. are ferrite grades.
- NIST
- National Institute of Standards and Technology (USA); source of the conversion factors.
- CODATA
- Committee on Data for Science and Technology: publishes the recommended values of the fundamental physical constants.
1. Convert units
Enter a value and unit; all other units of the same quantity appear instantly. Factors from the NIST table “Units for magnetic properties”.
| T | 1 |
| mT | 1,000 |
| µT | 1,000,000 |
| nT | 1.0000e+9 |
| G | 10,000 |
| mG | 1.0000e+7 |
| kG | 10 |
| Wb/m² | 1 |
| A/m | 795,775 |
| kA/m | 795.775 |
| A/cm | 7,957.75 |
| Oe | 10,000 |
| kOe | 10 |
- 1 T = 10,000 G; 1 mT = 10 G.
- 1 Oe = 1000 ÷ (4π) A/m ≈ 79.58 A/m ≈ 0.796 A/cm; conversely 1 A/cm ≈ 1.257 Oe.
- In air B = µ0 H: there 1 G numerically equals 1 Oe, and 1 T is about 795,775 A/m.
- µ0 = 1.25663706212 × 10⁻⁶ N/A² (CODATA 2018). Since the 2019 SI redefinition, µ0 is a measured value that differs from 4π × 10⁻⁷ by less than one part in a billion.
2. Calculate the magnetic field
Choose an arrangement and enter the dimensions. The calculation uses the formulas for the symmetry axis; the field plot shows the cross-section.
Axially magnetized disc or rod. Field on the axis at distance z in front of the pole face (formula from supermagnete.de).
| Flux density B in front of the pole face | 251.1 mT |
| in gauss | 2,511 G |
| Field strength H in air | 199,800 A/m · 2,511 Oe |
| Remanence Br (used) | 1.31 T |
B = Br ÷ 2 · [ (D + z) ÷ √(R² + (D + z)²) − z ÷ √(R² + z²) ], R = d ÷ 2Formula
Units (NIST): 1 G = 10⁻⁴ T, 1 Oe = 1000 ÷ (4π) A/m, 1 Mx = 10⁻⁸ Wb, 1 emu = 10⁻³ A·m², 1 emu/cm³ = 10³ A/m, 1 MGOe = 10⁵ ÷ (4π) J/m³. B = µ0 µr H. Wire B = µ0 I ÷ (2π r); circular loop on the axis B = µ0 N I R² ÷ (2 (R² + z²)^1.5); solenoid B = µ0 N I ÷ (2 L) · [(z + L/2) ÷ √(R² + (z + L/2)²) − (z − L/2) ÷ √(R² + (z − L/2)²)]; toroid core B = µ0 µr N I ÷ (2π r); Helmholtz centre B = (4/5)^1.5 µ0 N I ÷ R. Cylindrical magnet on the axis B = Br ÷ 2 · [(D + z) ÷ √(R² + (D + z)²) − z ÷ √(R² + z²)].
Example
A neodymium disc magnet N42 (Br about 1.3 T), Ø 20 mm, 10 mm thick, has about 0.25 T on the axis 5 mm in front of the pole face. A circular loop with 100 turns, R = 20 mm, 1 A, gives 2.9 mT at a distance of 5 mm. 1 T equals 10,000 G; in air 1 T corresponds to about 795,775 A/m or 10,000 Oe.
Notes
- The magnet formulas apply only on the symmetry axis of an axially magnetized magnet (supermagnete.de). For points off the axis, the field plot shows a model with equivalent surface currents; exact values come from field simulations (e.g. FEMM).
- Br is the remanence inside the material, not the field at the surface. Directly on the pole face of a long rod the field is about Br ÷ 2, less for flat discs.
- The values for magnet grades are ranges from a retailer table (supermagnete.de); the datasheet of your own magnet takes precedence. Neodymium permanently loses strength above its temperature limit.
- Coils: calculated without an iron core; µr only acts in the toroid core and in the ideal long solenoid. An open core amplifies much less than µr.
- Strong magnets pinch fingers, shatter when they collide and interfere with pacemakers; keep them away from storage media and cards.