Faraday’s Law Induced EMF Calculator

Understanding the Faraday's law induced EMF calculator — concept and principle

This calculator finds the voltage (electromotive force, EMF) induced in a coil when the magnetic field through it changes, using Faraday's law of induction. It helps estimate the output of pickup coils, simple generators and inductive sensors, and check induction homework.

The flux changes by 0.001 Wb in 0.1 s; with 100 turns that gives 1 V.

How it is calculated

Faraday's law states that the induced EMF equals the number of turns times the rate of change of magnetic flux: ε = −N · ΔΦ / Δt. For a uniform field B perpendicular to a flat coil of area A, the flux is Φ = B · A, so ΔΦ = (B₂ − B₁) · A.

N (turns): every turn links the same flux, so the voltages of all turns add up.
B₁, B₂ (tesla): initial and final flux density.
A (cm²): converted to m² by multiplying by 10⁻⁴.
Δt (s): how long the change takes. The calculator reports the average EMF over that interval as a positive magnitude.

The principle

A changing magnetic flux creates a circulating electric field, which pushes charges around the wire loop. The faster the flux changes, the stronger this push, which is why the EMF depends on ΔΦ/Δt and not on Φ itself: a strong but constant field induces nothing. The minus sign is Lenz's law: the induced current flows in the direction that opposes the change that produced it, a consequence of energy conservation. Flux is measured in webers (1 Wb = 1 T·m²), and 1 Wb/s equals 1 volt.

Worked example

Field change: B₂ − B₁ = 0.5 − 0 = 0.5 T.
Area: 20 cm² × 10⁻⁴ = 0.002 m².
Flux change per turn: ΔΦ = 0.5 × 0.002 = 0.001 Wb.
Rate of change: 0.001 / 0.1 s = 0.01 Wb/s.
EMF: ε = 100 × 0.01 = 1 V.

Each point is the calculator re-run with only “Time (s)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Time (s)	EMF (V)
0.025	4
0.05	2
0.075	1.333333333
0.1	1
0.125	0.8
0.15	0.6666666667
0.2	0.5

How to read the result

The value is an average over Δt. If the field changes non-uniformly (for example a magnet passing a coil), the instantaneous peak can be several times higher. Doubling the turns or the area doubles the EMF; halving the time also doubles it. The EMF is the open-circuit voltage; once a load draws current, coil resistance and inductance reduce the voltage at the terminals.

Common mistakes

Entering the area in m² when the field expects cm² (an error of 10,000×).
Using only the final field instead of the change B₂ − B₁.
Forgetting the angle: if the field is tilted by θ from the coil's axis, the effective flux is B·A·cos θ.
Multiplying the flux change by N when reporting flux; flux is per turn, N only multiplies the EMF.

Keep in mind: The formula assumes a uniform field over the whole coil area and a linear change in time. Real magnets, iron cores and fast transients need field mapping or simulation.

Frequently asked questions

Why is there a minus sign in Faraday's law?

It expresses Lenz's law: the induced current opposes the change in flux. The calculator shows the size of the EMF, so the sign is dropped.

Does a constant strong magnet induce voltage?

No. Only a change in flux induces EMF, whether from changing B, changing area, or rotating the coil.

How does a generator use this law?

A rotating coil sees the flux B·A·cos(ωt) change continuously, producing a sinusoidal EMF with peak N·B·A·ω.

Sources: Halliday, Resnick and Walker, Fundamentals of Physics, chapter on induction and inductance · Griffiths, Introduction to Electrodynamics, section on Faraday's law

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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