Faraday's Law Calculator (Induced EMF)
By Santaji GadepatilinUpdated November 2, 2026
Faraday's law of induction says that a changing magnetic flux through a coil induces a voltage proportional to the number of turns and the rate of change. This Faraday's law calculator works out the change in flux, the average induced EMF and the resulting current — see Faraday's law of electromagnetic induction and Lenz's law for the direction of the induced current.
How to use the Faraday’s law calculator
Enter the coil’s number of turns and area, the initial and final magnetic flux density through it, the time over which the change happens and the resistance of the circuit. The calculator returns the change in flux, the average induced EMF (magnitude) and the current that flows.
Faraday’s law formula
ε = −N × ΔΦ ÷ Δt · ΔΦ = A × (B2 − B1) · I = ε ÷ R
Example
A 200-turn coil of 50 cm² is placed in a field that rises from 0 to 0.4 T in 20 ms; the circuit resistance is 10 Ω:
- ΔΦ = 0.005 m² × 0.4 T = 0.0020 Wb
- ε = 200 × 0.0020 ÷ 0.02 = 20 V
- I = 20 ÷ 10 = 2 A
Induced EMF for a 1 mWb flux change
| Turns | in 10 ms | in 100 ms | in 1 s |
|---|---|---|---|
| 1 | 0.1 V | 0.01 V | 0.001 V |
| 10 | 1 V | 0.1 V | 0.01 V |
| 50 | 5 V | 0.5 V | 0.05 V |
| 100 | 10 V | 1 V | 0.1 V |
| 500 | 50 V | 5 V | 0.5 V |
| 1000 | 100 V | 10 V | 1 V |
Where Faraday’s law is used
- Generators and alternators: a rotating coil sees a sinusoidal flux, giving an EMF of N Φmax ω.
- Transformers: the same changing flux links both windings, so the voltages divide in the turns ratio — see the transformer turns ratio calculator.
- Magnetic flow meters: a conducting liquid moving through a magnetic field produces a voltage proportional to its velocity (ε = B D v).
- Inductive kick: switching off a coil collapses its flux quickly and induces a large voltage spike.
Frequently asked questions
What is Faraday's law?
The induced EMF equals the rate of change of magnetic flux linkage, ε = −N dΦ/dt. The minus sign (Lenz's law) means the induced current opposes the change that caused it.
What is magnetic flux?
Φ = B × A × cos θ, in webers (1 Wb = 1 T·m²), where θ is the angle between the field and the normal to the coil. This calculator assumes the field is perpendicular to the coil (cos θ = 1).
How can I increase the induced voltage?
Use more turns, a larger coil area, a stronger field or a faster change. Doubling any one of them doubles the EMF.
What about a conductor moving through a field?
A straight conductor of length L moving at speed v across a field B has a motional EMF ε = B L v — the same law applied to the area it sweeps.