Magnetomotive Force Converter (ampere-turn, gilbert)

Understanding the magnetomotive force converter — concept and principle

Magnetomotive force (MMF) is the "driving pressure" that pushes magnetic flux around a magnetic circuit, in the same way that voltage pushes current around an electric circuit. It is used when designing electromagnets, relays, solenoids, transformers and motor windings. This converter switches between ampere-turns (A·t), kiloampere-turns and the CGS unit, the gilbert (Gb).

More turns can replace more current; the gilbert is the older CGS unit with a 4π factor.

How it is calculated

For a coil, MMF is F = N × I, where N is the number of turns and I the current in amperes. Values are converted to ampere-turns and then to the target unit: result = value × (A·t per "from" unit) ÷ (A·t per "to" unit). The factors are:

1 kiloampere-turn = 1,000 A·t
1 Gb = 10 ÷ (4π) A·t ≈ 0.7957747 A·t
so 1 A·t = 4π ÷ 10 Gb ≈ 1.256637 Gb

The principle

Every turn of wire carrying current adds to the magnetising effect, so 100 turns at 1 A act like 1 turn at 100 A; both give 100 A·t. This follows from Ampère's circuital law: going once around a closed path, the magnetic field strength H summed along the path equals the total current enclosed, which for a coil is N × I. A magnetic circuit then follows Hopkinson's law, F = Φ × ℛ, where ℛ is the reluctance (the magnetic equivalent of resistance). In SI the "turns" are a pure count, so the official SI unit of MMF is simply the ampere. The gilbert comes from the CGS electromagnetic system, where the equations carry a factor 4π; that is where 4π ÷ 10 comes from.

Worked example

Inputs: value = 1, from ampere-turns, to gilberts.
1 A·t × 1 ÷ (10 ÷ 4π) = 4π ÷ 10 = 1.256637061 Gb.
In kiloampere-turns: 1 ÷ 1,000 = 0.001.

How to read the result

MMF on its own does not tell you the field; you also need the path. Field strength along a magnetic path of length l is H = F ÷ l in A/m (the CGS counterpart is the oersted, Gb/cm). A coil of 500 turns carrying 2 A gives 1,000 A·t; around a 0.2 m core path that is about 5,000 A/m if the core is uniform. A larger number means a stronger magnetising push, but the resulting flux depends on the core material and any air gaps.

Common mistakes

Forgetting that MMF scales with turns as well as current; doubling the turns at the same current doubles the MMF.
Using 1.257 instead of 0.796 (or the reverse) when going from gilberts to ampere-turns.
Confusing MMF (A·t) with field strength H (A/m or oersted), which is MMF per unit length.

Keep in mind: The simple F = N × I and magnetic circuit model ignore leakage flux, fringing at air gaps and core saturation. Real coil and magnet designs require detailed analysis and appropriate safety margins.

Frequently asked questions

How many gilberts is one ampere-turn?

4π ÷ 10 ≈ 1.256637 Gb.

Why does SI list MMF in amperes rather than ampere-turns?

A turn count has no unit, so N × I is measured in amperes. "Ampere-turn" is kept in practice as a reminder that the turns have been multiplied in.

How do I get the current I need for a given MMF?

Divide the required ampere-turns by the number of turns: I = F ÷ N.

Sources: BIPM, The International System of Units (SI Brochure), 9th edition, 2019 · NIST Special Publication 811 (2008), Appendix B · IEC 60050-121, International Electrotechnical Vocabulary: Electromagnetism

Checked 8 Nov 2026. Factors from the SI Brochure (BIPM, 9th ed.) and NIST Special Publication 811 (2008), Appendix B.