Magnetomotive Force Converter
Convert magnetomotive force (MMF) between ampere-turn, kiloampere-turn, milliampere-turn, abampere-turn and gilbert. Pick a source and a target unit, enter a value and read the result instantly.
Select two units to see the conversion factor.
Magnetomotive force is not magnetic field strength. MMF is in ampere-turns (a total), while field strength H is in ampere-turns per meter. Use the Magnetic Field Strength Converter for H.
Magnetomotive Force Formula
Every MMF unit is a fixed multiple of one reference unit, the ampere-turn (At). To convert, multiply the value by the size of the source unit in ampere-turns, then divide by the size of the target unit in ampere-turns. The abampere-turn is exactly 10 At, and the gilbert is exactly 10 ÷ (4π) At, about 0.7957747 At. SI prefixes are exact powers of ten.
What Is Magnetomotive Force?
Magnetomotive force (MMF), written F, is the quantity that drives magnetic flux around a magnetic circuit, in the same way that electromotive force drives current around an electric circuit. For a coil it equals the number of turns multiplied by the current: F = N × I. Its SI unit is the ampere-turn (At). Because a turn is a pure count, the ampere-turn has the same dimension as the ampere, and the two are numerically equal when one turn is counted.
A coil of 200 turns carrying 0.5 A therefore produces an MMF of 100 At. That MMF, divided by the reluctance of the magnetic path, gives the flux: Φ = F ÷ R. A larger MMF, from more turns or more current, produces more flux in the same circuit.
The CGS unit is the gilbert (Gi), equal to 10 ÷ (4π) ampere-turns, or about 0.796 At, so 1 At is about 1.2566 Gi. The abampere-turn is the electromagnetic CGS unit of current counted per turn and equals exactly 10 At. Kiloampere-turns and milliampere-turns cover large electromagnets and small sensor coils.
MMF is a total quantity for a whole path. It should not be confused with magnetic field strength H, which is MMF per unit length (ampere-turns per meter), or with flux density B, which is measured in tesla or gauss.
Supported Units
This converter supports the following 5 magnetomotive force units. The last column shows how many ampere-turns one unit equals.
| Unit | Symbol | Value in At |
|---|---|---|
| Ampere-turn | At | 1 |
| Kiloampere-turn | kAt | 1,000 |
| Milliampere-turn | mAt | 0.001 |
| Abampere-turn | abAt | 10 |
| Gilbert | Gi | 0.7957747155 |
How to Use the Magnetomotive Force Converter
- Type the magnetomotive force in the value box. Decimals and scientific notation such as 0.0025 or 2.5e-3 are accepted.
- Choose the From unit and the To unit.
- The result appears instantly, or press Convert Now. Very large or very small results are shown in scientific notation.
- Use Swap Units to reverse the conversion, Copy Result to copy the answer, open Show this value in all units for a full list, and Clear to start again.
Step-by-step by hand
- Find the size of each unit in the common base unit (At): 1 Gi = 0.7957747155 At and 1 At = 1 At.
- Divide the source size by the target size to get the conversion factor: 0.7957747155 ÷ 1 = 0.7957747155, so 1 Gi = 0.7957747155 At.
- Multiply by your value: 125 Gi × 0.7957747155 = 99.47183943 At.
Magnetomotive force cannot be negative in this tool, so only zero and positive numbers are accepted; the sign of an MMF only gives its direction.
Common MMF Conversions
- CGS to SI: 125 Gi equals 99.47183943 At.
- SI to CGS: 100 At equals 125.6637061 Gi.
- Coil design: 200 turns × 0.5 A is 100 At, which is 0.1 kAt or 100,000 mAt.
- Large electromagnet: 12 kAt equals 12,000 At.
- Abampere-turn: 3 abAt equals 30 At, and 1 abAt equals 12.56637061 Gi.
- Small sensor coil: 450 mAt equals 0.45 At.
Ampere-turn to Gilbert – Common Values
Quick reference for frequently used values
| Ampere-turn | Gilbert | Abampere-turn | Kiloampere-turn |
|---|---|---|---|
| 0.1 | 0.1256637061 | 0.01 | 0.0001 |
| 1 | 1.256637061 | 0.1 | 0.001 |
| 5 | 6.283185307 | 0.5 | 0.005 |
| 10 | 12.56637061 | 1 | 0.01 |
| 50 | 62.83185307 | 5 | 0.05 |
| 100 | 125.6637061 | 10 | 0.1 |
| 500 | 628.3185307 | 50 | 0.5 |
| 1,000 | 1,256.637061 | 100 | 1 |
| 10,000 | 12,566.37061 | 1,000 | 10 |
Where and Why This Conversion Is Used
- Electromagnet, solenoid and relay design: the ampere-turns needed to reach a force or flux are calculated in At.
- Transformers, inductors and motors: magnetic-circuit calculations (the magnetic equivalent of Ohm’s law) use MMF and reluctance.
- Older textbooks and data sheets: CGS sources use gilbert, so values are converted to SI.
- Teaching physics and electrical engineering: comparing SI and CGS magnetic units.
Important Differences Between Related Magnetic Quantities
- Magnetomotive force, F (ampere-turn, gilbert): the “driving force” of a magnetic circuit, F = N × I.
- Magnetic field strength, H (A/m, oersted): magnetomotive force per unit length of the magnetic path.
- Magnetic flux density, B (tesla, gauss): how strong the resulting magnetic field is, and the flux per unit area. In a material B = μ × H.
- Magnetic flux, Φ (weber, maxwell): the total magnetic field passing through an area, Φ = B × A.
These four quantities have different dimensions, so none of them can be converted into another by a unit factor. Moving between them needs extra information such as a length, an area or the permeability of the material. Each converter here only changes units within one quantity. See the Magnetomotive Force Converter, Magnetic Field Strength Converter, Magnetic Flux Converter and Magnetic Flux Density Converter.