Magnetomotive Force (MMF

Magnetic Circuits, Hopkinson's Law & MMF Metrology

Magnetomotive Force is the magnetic analogue of electromotive force (voltage), driving magnetic flux through a magnetic circuit:

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• Universal MMF Conversion Formulas (SI & CGS Standards)**:

1 Ampere-turn (At) = 0.4π Gilberts (Gb) ≈ 1.256637 Gb = 10^-3 kAt = 0.10 abAt

1 Gilbert (Gb) = (10) / (4π) At ≈ 0.795775 At = 795.775 mAt

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• Hopkinson's Magnetic Ohm's Law & Core Intensity Equations**:

Φ = FR (Hopkinson's Law Magnetic Flux in Webers, Wb)

H = Fl_core

R = l_coreμ_r μ_0 A

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• Standard Magnetic Circuit Benchmarks**:

• Ferrite SMPS Core: 50.0 At 62.83 Gb High-frequency power transformer

• Solenoid Relay Actuator: 500.0 At 628.32 Gb Φ = 1.0 mWb

• EV Traction Motor Stator: 2,500.0 At = 2.50 kAt 3,141.6 Gb

• Superconducting MRI Coil: 250.0 kAt = 250,000 At 314,159 Gb

How to Use This Calculator

Enter your Magnetomotive Force (MMF / ℱ = N·I) (e.g. 500 in ℱ), From Magnetomotive Force Unit — choose from Ampere-turns (At = A - SI Base Standard), Gilberts (Gb = 1/(0.4π) At ≈ 0.7958 At - CGS Unit), Kiloampere-turns (kAt = 1,000 At - Heavy Machinery), To Magnetomotive Force Unit — choose from Gilberts (Gb), Ampere-turns (At), Kiloampere-turns (kAt), Core Magnetic Reluctance (ℛ in A/Wb) (e.g. 500000 in A/Wb), Mean Magnetic Path Length (l_core in meters) (e.g. 0.20 in m), and Magnetic Circuit & Actuator Benchmark — choose from Custom Magnetomotive Force, Industrial Contactor Solenoid (500.0 At = 500 Turns @ 1A) → 628.32 Gilberts | Flux Φ = 1.00 mWb | H = 2,500 A/m, Ferrite Flyback Transformer (50.0 At = 50 Turns @ 1A) → 62.83 Gilberts | High-frequency power core. Verify your units match the formula standard (SI vs imperial) before entering values.

The Formula

Multipliers to SI Base Unit Ampere-turns (At = A)

Worked Example

An electromechanical engineer designing an industrial contactor wound with 500 turns carrying 1.0 Amp calculates the coil generates 500 Ampere-turns (628.3 Gilberts) of MMF, delivering 1.0 mWb of magnetic flux across a 500,000 A/Wb core reluctance.

Understanding Your Result

Force in Newtons (N): 1 N = 1 kg·m/s². Reference values: 1 kg object at Earth's surface weighs 9.81 N, atmospheric pressure 101,325 Pa (N/m²). Pressure benchmarks: car tire 30–35 psi (207–241 kPa), blood pressure systolic 120 mmHg (16 kPa), deep sea at 3,000m depth ~300 atm (30 MPa). Torque = Force × moment arm length — doubling the wrench length doubles the torque for the same applied force. Always verify whether gauge or absolute pressure is required for the application.