Faraday's Law EMF Calculator
Find the electromotive force induced in a coil using Faraday's law of electromagnetic induction.
Wb
Wb
s
Magnitude of the voltage induced across the coil
- 1
Change in flux ΔΦ = Φf − Φi
0.05 − 0.01 = 0.04 Wb - 2
Rate of flux change ΔΦ ÷ Δt
0.04 ÷ 0.1 = 0.4 Wb/s - 3
Signed EMF = −N × (ΔΦ/Δt)
−200 × 0.4 = -80 VThe minus sign (Lenz's law) means the induced EMF opposes the flux change. - 4
Induced EMF magnitude
|-80| = 80
How does this calculator work?
Faraday's law gives induced EMF as EMF = -N × (Phi_f - Phi_i) / dt. Enter the coil turns, the initial and final magnetic flux in webers, and the time interval in seconds. The calculator returns the EMF magnitude in volts plus the rate of flux change, modelling the average EMF over the interval.
Formula
How this is calculated
Faraday's law of induction states that a changing magnetic flux through a coil induces an electromotive force (EMF). The induced EMF equals the number of turns N multiplied by the negative time rate of change of the magnetic flux: EMF = -N × dPhi/dt. Here Phi is the magnetic flux measured in webers (Wb), where one weber equals one tesla times one square metre.
The inputs are the number of turns N (dimensionless), the initial flux Phi_i and final flux Phi_f in webers, and the time interval dt in seconds over which the flux changes. The calculator first computes the change in flux dPhi = Phi_f - Phi_i, then the average rate of change dPhi/dt, and finally multiplies by -N to obtain the signed EMF. The magnitude is reported as the main result because the sign only encodes direction (Lenz's law: the induced EMF opposes the change that produced it).
This model assumes a uniform, average rate of flux change over the interval; for non-linear flux variation it gives the time-averaged EMF rather than the instantaneous value. The time interval must be non-zero to avoid division by zero. A larger number of turns, a larger flux change, or a shorter time interval all increase the induced EMF.
Frequently asked questions
The minus sign reflects Lenz's law: the induced EMF acts to oppose the change in flux that creates it. The magnitude is what matters for the voltage value, so the calculator highlights it.
Magnetic flux must be in webers (Wb). One weber equals one tesla multiplied by one square metre, so for a uniform field B over area A, Phi = B × A.
It gives the average EMF over the time interval, since it uses the total flux change divided by the total time. For the instantaneous EMF you would need the derivative dPhi/dt at a specific moment.
Also known as
TG we-Calculate Editorial Team. (2026). Faraday's Law EMF Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/faraday-law-emf-calculator
TG we-Calculate Editorial Team. "Faraday's Law EMF Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/faraday-law-emf-calculator.
TG we-Calculate Editorial Team, "Faraday's Law EMF Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/faraday-law-emf-calculator
@misc{wecalculate_faraday_law_emf_calculator, title = {Faraday's Law EMF Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/faraday-law-emf-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?