Magnetic Flux Calculator
The magnetic flux through a loop from the field, its area and the angle it sits at, and the voltage Faraday’s law induces when that flux changes over a time.
Flux is field strength times the area the field passes through, reduced by the cosine of the angle between the field and the loop’s normal: Φ = B A cos θ, in webers.
How the magnetic flux calculator works
Flux is field strength times the area the field passes through, reduced by the cosine of the angle between the field and the loop’s normal: Φ = B A cos θ, in webers. Change the flux — move the magnet, turn the coil, switch the field off — and each turn of the coil develops an EMF equal to the rate of change: ε = N ΔΦ ÷ Δt.
Formula: Φ = B × A × cos θ; ε = N × ΔΦ ÷ Δt
Worked examples
| Inputs | Magnetic flux (Wb) | Note |
|---|---|---|
| 0.5 T through 100 cm², face on | 0.005 | 5 mWb, 5 V induced |
| Loop turned to 60° | 0.0025 | 2.5 mWb |
| Earth’s field (50 µT) through a 1 m² loop | 0.00005 | 50 µWb |
FAQFrequently asked questions
What is the angle measured from?
From the normal — the line perpendicular to the loop. At 0° the field passes straight through and flux is greatest; at 90° the field runs along the plane of the loop and no flux threads it.
Why does a changing flux make a voltage?
Faraday’s law: a changing magnetic flux through a circuit induces an EMF proportional to how fast it changes. It is the principle of every generator, transformer and induction cooktop.
What is flux linkage?
Flux times the number of turns. Each turn of a coil is threaded by the flux, so the induced EMF is N times what a single loop would give.
What is a weber?
One tesla passing through one square metre. Real loops see small fractions: a 0.5 T field through a 100 cm² loop is 5 mWb, and collapsing it in a tenth of a second across 100 turns gives 5 V.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.