Magnetomotive Force Converter

Magnetomotive Force (also known as MMF, Magnetic Excitation Potential, Magnetic Potential Difference, or Ampere-Turn Driving Force, symbolized by &mathcal;F or F_m) measures the quantitative magnetic potential difference that drives magnetic flux through a magnetic circuit, analogous to electromotive force (voltage) driving current in an electric circuit (&mathcal;F = N · I = Φ · &mathcal;R = ∮ H · dl, where N is coil turn count, I is current in amperes, Φ is total magnetic flux in webers, &mathcal;R is magnetic reluctance, H is magnetic field strength, and dl is differential path length). Across industrial electric motor stator windings, relay solenoid actuators, power distribution transformer core excitation, magnetic levitation (Maglev) coils, and superconducting MRI magnet design, magnetomotive force is categorized across three major engineering unit families: International System of Units (SI metric fundamental: Ampere-Turn / At, Kiloampere-Turn / kAt, Milliampere-Turn / mAt), CGS Electromagnetic System units (Gilbert / Gi), and CGS Absolute Electromagnetic units (Abampere-Turn / abAt).

Our free online Magnetomotive Force Converter provides instant, high-precision conversions across all SI metric, CGS Gilbert, and electromagnetic coil MMF units:

• Gilbert (Gi) to Ampere-Turns [CGS to SI Standard]: Multiply Gilberts by 0.7957747151 (1 Gilbert = 10 ÷ 4π At = 0.795775 Ampere-turns ⇒ 1 At = 4π ÷ 10 Gi = 1.256637061 Gilberts).
• Kiloampere-Turns to Ampere-Turns & Gilberts [Motor & Transformer Standard]: Multiply kAt by 1,000.0 (1 kAt = 1,000.0 At = 1,256.637 Gi = 100.0 abAt ⇒ 1 At = 0.001 kAt).
• Abampere-Turns (abAt) to Ampere-Turns & Gilberts [CGS Electromagnetic Standard]: Multiply abAt by 10.0 (1 abampere-turn = 10.0 Ampere-turns = 12.56637 Gilberts ⇒ 1 At = 0.10 abAt).
• Milliampere-Turns to Ampere-Turns [Precision Actuator Standard]: Multiply mAt by 0.001 (1 mAt = 0.001 At = 0.0012566 Gi ⇒ 1 At = 1,000.0 mAt).

Master Magnetomotive Force Conversion Table

The table below displays exact mathematical conversion relationships, SI Ampere-Turn (At) multipliers, and Gilbert (Gi) equivalents relative to 1 Ampere-Turn (1 At = 0.001 kAt = 1,000 mAt = 0.10 abAt = 1.256637 Gi):

Step-by-Step Solenoid Relay & MRI Magnet MMF Calculation Example

To calculate the magnetomotive force (&mathcal;F) produced by a solenoid actuator relay coil wound with 500 turns carrying 0.10 Amperes of current (N = 500 turns, I = 0.10 A), and calculate the MMF generated by a superconducting 1.5-Tesla MRI magnet coil wound with 3,000 turns carrying 500 Amperes (N = 3,000 turns, I = 500 A) into Ampere-Turns (At), Kiloampere-Turns (kAt), and Gilberts (Gi):

Step 1 (Solenoid Relay MMF Calculation): &mathcal;F = N · I = 500 turns × 0.10 A = 50.0 Ampere-Turns (50.0 At)

Step 2 (Solenoid Relay Gilberts Conversion): &mathcal;F = 50.0 At × 1.256637061 = 62.83185 Gilberts (62.83 Gi) = 5.0 abAt

Step 3 (MRI Magnet MMF Calculation): &mathcal;F = 3,000 turns × 500 A = 1,500,000 Ampere-Turns (1.50 × 106 At)

Step 4 (MRI Magnet kAt & Gilberts Conversion): &mathcal;F = 1.50 × 106 At ÷ 1,000 = 1,500.0 Kiloampere-Turns (1,500.0 kAt); &mathcal;FGi = 1.50 × 106 × 1.256637061 = 1,884,955.59 Gilberts (1.885 × 106 Gi)

Thus, the solenoid relay coil generates an MMF of 50.0 At (62.83 Gi), while the MRI magnet core generates a massive 1,500.0 kAt (1.885 × 10⁶ Gi).

Real-World Electromagnetic System & Magnetic Circuit Benchmarks

Below is a comparative reference chart showing magnetomotive force values (&mathcal;F) across relays, motors, transformers, and MRI magnets:

History & Physics: 1600 William Gilbert vs 1885 Hopkinson’s Magnetic Ohm Law (&mathcal;F = Φ · &mathcal;R)

1600 William Gilbert & The Gilbert Unit (1 Gi = 0.795775 At)

Named in honor of 16th-century English physician and natural philosopher William Gilbert (author of De Magnete in 1600, widely considered the founder of magnetic science), the Gilbert (Gi) was officially established by the International Electrotechnical Commission (IEC) in 1930 as the CGS unit of magnetomotive force: 1 Gi = 10 ÷ 4π Ampere-turns ≈ 0.7957747 At.

1885 John Hopkinson & Hopkinson’s Law (&mathcal;F = Φ · &mathcal;R)

In 1885, English engineer and physicist John Hopkinson derived Hopkinson’s Law, the magnetic circuit equivalent of Ohm’s Law: &mathcal;F = Φ · &mathcal;R (where &mathcal;F is magnetomotive force in Ampere-turns, Φ is magnetic flux in Webers, and &mathcal;R = l ÷ (μ · A) is magnetic reluctance). Hopkinson’s equation allowed electrical engineers for the first time to design efficient electric motors and transformers using predictable magnetic circuit laws.

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Frequently Asked Questions (FAQ)

How do you convert Ampere-Turns (At) to Gilberts (Gi)?

To convert Ampere-Turns to Gilberts, multiply At by 1.256637061 (4π ÷ 10). For example, 100 At × 1.256637 = 125.6637 Gilberts (125.66 Gi).

How do you convert Gilberts (Gi) to Ampere-Turns (At)?

To convert Gilberts to Ampere-Turns, multiply Gi by 0.795774715 (10 ÷ 4π). For example, 500 Gi × 0.795775 = 397.887 Ampere-Turns (397.89 At).

How do you convert Kiloampere-Turns (kAt) to Ampere-Turns (At)?

To convert Kiloampere-Turns to Ampere-Turns, multiply kAt by 1,000. For example, 18.0 kAt × 1,000 = 18,000.0 Ampere-Turns (18,000 At).

Is 1 Abampere-Turn (abAt) equal to 10 Ampere-Turns (At)?

Yes! 1 Abampere-Turn (abAt) in the CGS electromagnetic system equals exactly 10 Ampere-Turns (10 At = 12.56637 Gilberts).