Calculate induced electromotive force (EMF), flux change, field change, motional EMF, or AC generator voltage using Faraday's law of induction ($\mathcal{E} = -N \cdot \Delta\Phi / \Delta t$).
Quick Presets:
Inputs
Number of wire loops in the coil (N > 0).
Change in magnetic flux through one loop (positive = increasing, negative = decreasing).
Duration of flux change (Δt > 0).
V
Desired electromotive force in volts.
Ω
Specify circuit resistance to compute induced current (I), charge (Q), and power (P).
Results & Analysis
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Enter inputs above to calculate.
Inputs
Number of wire loops in the coil.
Change in magnetic field strength over time.
Area of a single loop.
m
Height of rectangular coil.
deg (°)
0° = Field perpendicular to loop plane (max flux). 90° = Field parallel to loop (zero flux).
Duration of field change (Δt > 0).
V
Desired electromotive force in volts.
Ω
Specify circuit resistance to compute induced current (I), charge (Q), and power (P).
Results & Analysis
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Enter inputs above to calculate.
Inputs
Uniform magnetic field strength.
Length of straight conductor rod moving through field.
Speed of conductor rod relative to magnetic field.
deg (°)
90° = Motion perpendicular to field lines (max EMF). 0° = Motion parallel to field lines (zero EMF).
V
Desired motional electromotive force in volts.
Ω
Specify circuit resistance to compute motional current (I) and power dissipation (P).
Results & Analysis
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Enter inputs above to calculate.
Inputs
Number of wire loops in the rotating armature.
Uniform stator field strength.
Area of single rotating coil loop.
Coil rotation speed in Hertz (cycles per second).
V
Desired peak alternating voltage.
Ω
Connected load resistance to compute peak/RMS AC current and average AC power.
Results & Analysis
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Enter inputs above to calculate.
Interactive Visualizer & Vector Diagram
Step-by-Step Mathematical Breakdown
Select a tab and enter valid inputs to view the detailed mathematical substitution breakdown.
4 min read3 steps7 terms3 examples6 FAQsEMF = -N (dPhi/dt)
Faraday's law of induction explains how generators, transformers, and induction chargers all work: a changing magnetic flux through a coil induces a voltage, and more turns or a faster change both mean more voltage.
Choose From Flux Change if you already know how much the magnetic flux changed, From Field & Area if you know the change in field strength over a fixed loop area, or Motional EMF if a conductor is physically moving through a field.
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Enter the coil and change values
Fill in the number of turns and the relevant change values — flux, or field and area, or field, rod length, and velocity. The calculator updates instantly as you type.
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Read the induced EMF
The result card shows the induced EMF magnitude in volts, along with the exact equation used. The interpretation line reminds you that the sign, by Lenz's law, always opposes the change that caused it.
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Reference
Formula & Methodology
3 formulas▸
Faraday's law — flux change
EMF = -N (dPhi/dt)
The induced EMF in a coil of N turns equals the negative rate of change of magnetic flux through one loop. The minus sign is Lenz's law: the induced EMF drives a current that opposes the flux change producing it. This calculator reports the magnitude, |EMF| = N |dPhi| / dt.
Flux from field and area
Phi = B A cos(theta)
Magnetic flux through a loop is the field strength times the loop area times the cosine of the angle between the field and the loop's normal. With the field perpendicular to the loop (theta = 0), a change in field strength alone changes the flux by dPhi = A dB, giving EMF = N A |dB| / dt.
Motional EMF
EMF = B L v
A straight conductor of length L moving at speed v through a perpendicular magnetic field B has free charges pushed along its length by the magnetic force, producing an EMF equal to the product of field, length, and velocity — the same physics as Faraday's law, viewed from the moving conductor's frame.
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General reference
Trust, Methodology & Sources
Written by Calculover Editorial Team · Updated 2026-07-31▸
Editorial accountability
Author: Calculover Editorial Team - Editor
Owner: Calculover Editorial Team - Editorial owner
Last reviewed: 2026-07-31
Last verified: 2026-07-31
Methodology
Assumption: Note: Calculations assume uniform magnetic fields and quasistatic field changes. High-frequency electromagnetic radiation, parasitic capacitance, and non-linear magnetic core saturation are excluded.
Limitations & guidance
Professional guidance:
Primary sources
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Glossary
Key Terms Explained
7 terms▸
Faraday's law ↗The physical law stating that a changing magnetic flux through a circuit induces an electromotive force (EMF) in that circuit, with magnitude equal to the rate of flux change times the number of turns.
Induced EMF ↗The electromotive force (voltage) generated in a conductor by a changing magnetic flux, measured in volts. It drives current if the circuit is closed.
Magnetic flux (Phi) ↗A measure of the total magnetic field passing through a surface, equal to field strength times area times the cosine of the angle between the field and the surface's normal, measured in webers (Wb).
Turns (N) ↗The number of loops of wire in a coil. Each additional turn adds another loop's worth of induced EMF, so a coil's total EMF scales linearly with N.
Lenz's law ↗The principle that an induced current always flows in the direction that opposes the change in flux that created it — the source of the minus sign in Faraday's law, and a consequence of energy conservation.
Weber (Wb) ↗The SI unit of magnetic flux. One weber equals one tesla times one square meter, and a flux change of one weber per second across one turn induces one volt.
Electromagnetic induction ↗The broader phenomenon, described by Faraday's law, in which a changing magnetic environment around a conductor generates an electric current or voltage — the operating principle behind generators, transformers, and induction charging.
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Scenarios
Real-World Examples
3 worked examples▸
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Physics student
Coil in a changing field
Turns (N) 100Change in flux (ΔΦ) 0.05 WbTime interval (Δt) 2 s
EMF = N|ΔΦ|/Δt = 100 × 0.05 / 2 = 2.5 V. Because the coil has 100 turns, the same flux change through a single loop produces 100 times the EMF of a one-turn loop.
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Physics student
Conducting rod sliding on rails
Magnetic field (B) 0.5 TRod length (L) 2 mVelocity (v) 3 m/s
EMF = B·L·v = 0.5 × 2 × 3 = 3 V. This is motional EMF — no coil or explicit flux change is needed, since the rod's motion through the field itself changes the enclosed flux over time.
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Engineering student
Doubling the number of turns
Turns (N) 200 (doubled from 100)Change in flux (ΔΦ) 0.05 WbTime interval (Δt) 2 s
EMF = 200 × 0.05 / 2 = 5 V — exactly double the 2.5 V result at 100 turns. Because EMF scales linearly with N, adding more turns is the most direct way to boost a generator or transformer's output voltage for the same flux change.
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Reference
Cite This Calculator
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Use either format to cite this calculator in a paper, report, or resource list.
Faraday's law of induction explains how generators, transformers, and induction chargers all work: a changing magnetic flux through a coil induces a voltage, and more turns or a faster change both mean more voltage. This calculator computes that induced EMF three ways — from a known flux change, from a field change over a fixed area, or from a conductor physically moving through a field.
How the Faraday's Law Calculator works
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The core relationship is EMF = -N (dPhi/dt): the induced EMF equals the number of turns times the rate at which magnetic flux changes through each turn, with a minus sign from Lenz's law indicating the induced EMF opposes that change. When you know the field change instead of the flux change directly, the calculator uses Phi = B A cos(theta) with the field held perpendicular to the loop (cos(theta) = 1), so dPhi = A dB and EMF = N A |dB| / dt. For a conductor moving through a field rather than sitting in a changing one, the equivalent result is the motional EMF, EMF = B L v — the same underlying physics viewed from the moving conductor's reference frame. All three modes report the EMF magnitude in volts.
Inputs and what they mean
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Turns (N) is the number of wire loops in the coil; it multiplies directly into the flux-based results. Change in flux (ΔΦ) and change in field (ΔB) are the total change over the time interval, not a rate — divide by Δt yourself first if you only have an instantaneous rate. Loop area (A) is the area of a single loop, assumed perpendicular to the field. For motional EMF, rod length (L) and velocity (v) assume the rod, field, and velocity are all mutually perpendicular, which is the standard textbook setup and gives the maximum possible EMF for those magnitudes.
Limits and edge cases
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A time interval (Δt) of zero is physically meaningless for an average rate of change, so both flux-based tabs require Δt greater than 0. On the Field & Area tab, the calculator uses ΔΦ = A·ΔB·cos(θ), where θ is measured from the loop normal; if area, angle, and field all change together, compute the total flux change directly instead. The motional EMF formula includes sin(θ) for the angle between velocity and field. The optional resistive statistics use Ohm's law and, for the AC generator, RMS voltage over one cycle; inductance, capacitance, and core saturation are excluded.
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Questions
Frequently Asked Questions
6 questions▸
What's the formula behind the Faraday's Law Calculator?+
The core formula is EMF = -N (dPhi/dt) — the induced EMF equals the number of coil turns (N) times the rate of change of magnetic flux (dPhi/dt) through one loop. The calculator also derives EMF from a field change over a fixed area (EMF = N A |dB| / dt) and from motional EMF (EMF = B L v) for a conductor moving through a field.
Why is there a minus sign in Faraday's law, and does the calculator show it?+
The minus sign is Lenz's law: the induced EMF always drives a current in the direction that opposes the flux change creating it, which is a direct consequence of energy conservation. This calculator reports the EMF magnitude (always positive) and notes the Lenz's-law sign convention in the result's interpretation line rather than displaying a signed number.
What is motional EMF and how is it different from Faraday's law?+
Motional EMF (EMF = B L v) is the voltage induced when a conductor physically moves through a magnetic field, rather than sitting still in a field that's changing. It's the same phenomenon as Faraday's law — the enclosed flux is still changing over time — just viewed from the perspective of the moving conductor instead of a stationary coil.
Why does a faster flux change produce more induced EMF?+
Faraday's law depends on the rate of change of flux, dPhi/dt, not the total change alone. Spreading the same flux change over a shorter time interval increases dPhi/dt, which increases the induced EMF proportionally — this is why rapidly moving a magnet through a coil produces a much larger voltage spike than moving it slowly.
What units does the Faraday's Law Calculator use?+
Flux is in webers (Wb), magnetic field in tesla (T), area in square meters (m²), time in seconds (s), length in meters (m), and velocity in meters per second (m/s). The result, induced EMF, comes out in volts (V) in every mode.
How is magnetic flux related to the field and area?+
Magnetic flux is Phi = B A cos(theta), where B is field strength, A is the loop's area, and theta is the angle between the field and the loop's normal (perpendicular) direction. This calculator assumes the field is perpendicular to the loop (theta = 0, cos(theta) = 1) on the From Field & Area tab, so a change in field strength alone drives the flux change.
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