Understand flux through coils, plates, and loops quickly. Compare scenarios with conversions and clear outputs. Perfect for labs, motors, generators, and sensor designs everywhere.
Magnetic flux through a flat surface in a uniform field is:
Φ = B × A × cos(θ)
Flux linkage for a coil with N turns: λ = N × Φ.
| Case | B (T) | A (m²) | θ (deg) | Φ (Wb) | Notes |
|---|---|---|---|---|---|
| 1 | 0.25 | 0.020 | 30 | 0.004330127 | cos(30°) reduces flux slightly. |
| 2 | 0.12 | 0.015 | 0 | 0.001800000 | Maximum flux when surface is normal to B. |
| 3 | 0.50 | 0.010 | 90 | 0.000000000 | Zero flux when B is parallel to the surface. |
These examples assume a uniform field and a flat surface.
Magnetic flux, Φ, measures how much magnetic field crosses a surface. It depends on field strength, surface area, and orientation. A larger perpendicular area captures more field lines, increasing Φ. When the field is parallel to the surface, Φ approaches zero.
Real-world magnetic fields vary widely. Earth’s field is about 25–65 µT, which is 0.025–0.065 mT. Small permanent magnets often produce 10–200 mT near the surface. Strong neodymium magnets can exceed 300 mT. Laboratory electromagnets and MRI systems commonly operate around 1.5–3 T.
Flux scales linearly with area. Doubling area doubles Φ if B and θ stay constant. For example, with B = 0.20 T and θ = 0°, a 0.010 m² loop gives Φ = 0.0020 Wb. Increasing the area to 0.050 m² raises flux to 0.010 Wb.
This calculator uses θ between the field vector and the surface normal. The cosine term sets both magnitude and sign. If θ is greater than 90°, cos(θ) becomes negative, indicating the field crosses the surface opposite the chosen normal direction.
Coils multiply the effect through turns. Flux linkage is λ = NΦ, reported in Wb·turn. If Φ = 2.5 mWb and N = 400 turns, then λ = 1.0 Wb·turn. This value is central in inductors, transformers, and machine windings.
In many devices, changing flux produces voltage. Faraday’s law relates induced emf to the time rate of change of flux linkage, |e| = dλ/dt. Increasing rotational speed, using more turns, or enlarging area can increase the induced voltage for generators and sensors.
Area errors are common when shapes are irregular. Use precise dimensions and consistent units. For angle, measure relative to the surface normal, not the surface itself. If θ is near 90°, small angle errors cause large relative changes because cos(θ) changes rapidly.
The formula Φ = BAcos(θ) assumes a uniform magnetic field over a flat surface. For nonuniform fields, you can approximate by splitting the surface into smaller patches and averaging B. For curved surfaces or fringe fields, results should be treated as estimates.
Magnetic flux is measured in webers (Wb). This calculator also shows milliw webers (mWb) and micro webers (µWb) for small values.
Enter the angle between the magnetic field direction and the surface normal. If you only know the angle to the surface plane, subtract it from 90° to get the normal angle.
Flux is signed because it depends on the chosen surface normal. If the field crosses the surface opposite that normal, cos(θ) becomes negative and Φ is negative.
At 90°, the field is parallel to the surface, so cos(90°)=0 and flux is ideally zero. Small measurement errors near 90° can cause noticeable changes in computed flux.
Yes. Choose “Angle (θ)” and enter Φ, B, and A. The calculator uses θ = arccos(Φ/(B·A)) and reports both radians and degrees.
Flux linkage is λ = NΦ, where N is the number of turns. It is a key quantity for inductors and coils because induced voltage depends on how λ changes with time.
The result is exact only for uniform fields over a flat surface. For nonuniform fields, treat it as an approximation and consider dividing the area into smaller regions with different B values.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.