Convert magnetomotive force (MMF) between ampere-turns, kiloampere-turns and gilberts.
Magnetism • 5 units
All 5 units on the Magnetomotive Force Converter are defined against the Ampere-turn (At), so each result is one conversion factor away from a single reference rather than the end of a chain of roundings.
The conversion this page is most often opened for is ready before you type anything: 1 At = 1.256637 Gb. Change either side and every row in the table recalculates with it.
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As with magnetic field strength, the SI-to-CGS conversion here carries a 4π: one ampere-turn is about 1.2566 gilberts, and one gilbert is roughly 0.7958 At. The ampere row and the ampere-turn row are numerically the same because turns are a dimensionless count, so a single-turn loop carrying 200 A and a 200-turn coil carrying 1 A appear identically in this table.
Magnetomotive force earns its keep through the magnetic circuit analogy, where flux equals magnetomotive force divided by reluctance. A core presenting 2 × 10⁵ ampere-turns per weber of reluctance, driven by 500 At, carries 2.5 mWb. Working this way turns a magnetic design into the same arithmetic as a resistive network, with reluctances in series adding just as resistances do.
The consequence that governs real designs is that the airgap usually dominates. Because the relative permeability of electrical steel runs into the thousands, even a short gap can present more reluctance than the entire iron path around it, so introducing a millimetre of air can multiply the ampere-turns needed to reach a given flux many times over. That is why relay and solenoid pull-in force falls off so sharply with distance, and why inductors are deliberately gapped when the goal is to store energy rather than to maximise inductance.
Quick reference — 1 Ampere-turn (At) is equal to:
| Ampere | A | 1 |
| Kiloampere-turn | kA·t | 0.001 |
| Milliampere-turn | mA·t | 1,000 |
| Gilbert | Gb | 1.256637 |
5 units of magnetomotive force, each a fixed multiple of the At. The table spans 1,000,000:1, from mA·t (0.001 At) to kA·t (1000 At). Conversion is one multiplication into the base unit and one division out of it, with no lookup table and no approximation.
value_to = value_from × (factor_from ÷ factor_to)1 At = 1 At1 A = 1 At1 kA·t = 1000 At1 mA·t = 0.001 At1 Gb = 0.795775 Atwhere:
Assumptions: Factors are exact definitions. Full double precision is carried internally and rounding is applied only for display.
Result25 At = 31.4159 Gb
Magnetomotive force is what drives flux around a magnetic circuit, and its unit — the ampere-turn (At) — says exactly how it is produced: current multiplied by the number of turns carrying it.
The practical consequence is that coil design has one degree of freedom. A 200-turn coil at 1 A and a 100-turn coil at 2 A produce the same 200 ampere-turns and, in the same core, the same flux. What differs is everything else: the 100-turn version needs thicker wire, dissipates four times the resistive heat at the same wire gauge, and fits a different space. The gilbert, the CGS equivalent, is about 0.7958 At and turns up in older magnetics texts.