Transformer EMF Equation

E = 4.44 · f · N · Bmax · A

Quick answer

This calculator solves E = 4.44 × f × N × Bmax × A for RMS Voltage. With Frequency 1 kHz, Number of Turns 0.5, Peak Flux Density 0.5 T, Core Area 10 cm², the result is 1.11 V. It solves in 5 directions, so you can enter the values you have and get the one you need.

Calculator

RMS Voltage (V)
—

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.

Symbols and units

Symbol Meaning Default unit Accepted units
E RMS Voltage V pV, nV, µV, mV, V, kV
f Frequency Hz Hz, kHz, MHz, GHz
N Number of Turns — —
Bmax Peak Flux Density T G, mT, T
A Core Area cm² mm², cm², m²

Step by step

  1. 1. What you know: Frequency 1 kHz, Number of Turns 0.5, Peak Flux Density 0.5 T, Core Area 10 cm²
  2. 2. The relation: E = 4.44 × f × N × Bmax × A
  3. 3. Substitute: f = 1 kHz, N = 0.5, Bmax = 0.5 T, A = 10 cm²
  4. 4. Result: RMS Voltage = 1.11 V

Worked examples

Minimum range

Given: Frequency 5 Hz, Number of Turns 0.025, Peak Flux Density 10 G, Core Area 10 mm²

Result: RMS Voltage = 5.55 nV

Low range

Given: Frequency 50 Hz, Number of Turns 0.25, Peak Flux Density 10 mT, Core Area 1 cm²

Result: RMS Voltage = 55.5 µV

Typical

Given: Frequency 1 kHz, Number of Turns 0.5, Peak Flux Density 0.5 T, Core Area 10 cm²

Result: RMS Voltage = 1.11 V

High range

Given: Frequency 20 kHz, Number of Turns 0.8, Peak Flux Density 1.5 T, Core Area 100 cm²

Result: RMS Voltage = 1.066 kV

Maximum range

Given: Frequency 0.2 MHz, Number of Turns 8, Peak Flux Density 15 T, Core Area 0.1 m²

Result: RMS Voltage = 10660 kV

Solving for each variable

Solve for RMS Voltage

Frequency 5 Hz, Number of Turns 0.025, Peak Flux Density 10 G, Core Area 10 mm² → 5.55 nV

Solve for Frequency

RMS Voltage 0.33 V, Number of Turns 0.025, Peak Flux Density 10 G, Core Area 10 mm² → 0.2973 GHz

Solve for Number of Turns

RMS Voltage 0.33 V, Frequency 5 Hz, Peak Flux Density 10 G, Core Area 10 mm² → 1.49 × 10⁶

Solve for Peak Flux Density

RMS Voltage 0.33 V, Frequency 5 Hz, Number of Turns 0.025, Core Area 10 mm² → 59460 T

Solve for Core Area

RMS Voltage 0.33 V, Frequency 5 Hz, Number of Turns 0.025, Peak Flux Density 10 G → 594.6 m²

How RMS Voltage changes with Frequency

Frequency (input) RMS Voltage (result)
100 Hz 111 mV
0.25 kHz 0.2775 V
0.5 kHz 0.555 V
0.75 kHz 0.8325 V
1 kHz 1.11 V
1.5 kHz 1.665 V
2 kHz 2.22 V
4 kHz 4.44 V
7 kHz 7.77 V
10 kHz 11.1 V

The same result in other units

Unit Value
µV 1110000
mV 1110
V 1.11
kV 0.00111

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Frequently asked questions

How do you calculate Transformer EMF Equation?

Use E = 4.44 × f × N × Bmax × A. With Frequency 1 kHz, Number of Turns 0.5, Peak Flux Density 0.5 T, Core Area 10 cm², RMS Voltage works out to 1.11 V.

How do you calculate transformer emf?

Rearrange for RMS Voltage: with Frequency 50 Hz, Number of Turns 0.25, Peak Flux Density 10 mT, Core Area 1 cm², RMS Voltage is 55.5 µV.

What is the formula for Transformer EMF Equation?

The formula is E = 4.44 × f × N × Bmax × A. 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.

How do you find Frequency when you know the other values?

Rearrange for Frequency: with RMS Voltage 0.33 V, Number of Turns 0.025, Peak Flux Density 10 G, Core Area 10 mm², Frequency is 0.2973 GHz.

How do you find Number of Turns when you know the other values?

Rearrange for Number of Turns: with RMS Voltage 0.33 V, Frequency 5 Hz, Peak Flux Density 10 G, Core Area 10 mm², Number of Turns is 1.49 × 10⁶.

What units does Transformer EMF Equation use?

RMS Voltage is shown in µV, mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

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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