Transformer EMF Equation

E = 4.44 · f · N · Bmax · A

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Result
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Formula

E = 4.44 × f × N × Bmax × A

Description

The transformer EMF equation gives the RMS voltage induced in a winding from the supply frequency, the number of turns, the peak magnetic flux density in the core, and the core cross-sectional area. The constant 4.44 is 2π/√2 and arises because the induced EMF is proportional to the rate of change of a sinusoidal flux. It is the fundamental relationship used to design transformer windings and to choose a core that will not saturate at the operating voltage and frequency.

Variables

  • E — RMS winding voltage (V)
  • f — Supply frequency (Hz)
  • N — Number of turns
  • Bmax — Peak flux density in the core (T)
  • A — Core cross-sectional area (m²)

Practical Notes

Keep Bmax below the core material saturation limit (typically 0.3–0.4 T for ferrite, 1.2–1.5 T for silicon steel). Running a transformer at lower frequency raises the required turns or flux density, which is why a 50 Hz transformer is larger than a 60 Hz one of the same rating.

Related Concepts

All Magnetics & Transformers formulas →
Transformer EMF Equation Transformer VA Rating Transformer Voltage Regulation Transformer Current Ratio Transformer Copper Loss Transformer Iron (Core) Loss Transformer Turns-per-Volt Transformer Impedance Matching

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