HesapHanem

Magnetic Flux Calculator

Find the magnetic flux through a loop or surface.

How it is calculated

The tool computes Φ = B × A × cos θ. B is the field strength in tesla (T), A is the surface area in square metres (m²), and θ is the angle in degrees between the field direction and the surface normal (the line perpendicular to the surface), not between the field and the surface itself. If the angle is left empty it is taken as 0°, the case where the field passes straight through. The flux is shown in webers (Wb) with four decimals, and again in milliwebers (1 Wb = 1000 mWb) with two decimals. The tool does not stop negative inputs, so a negative flux simply means the field passes through the surface in the opposite direction.

Worked example

A coil of area 0.02 m² sits in a 0.5 T field, tilted so the angle to the normal is 60°. Step 1: B × A = 0.5 × 0.02 = 0.01. Step 2: cos 60° = 0.5. Step 3: Φ = 0.01 × 0.5 = 0.0050 Wb, which equals 5.00 mWb. At 90° the same coil would give 0.0000 Wb, because the field runs parallel to the surface.

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Common mistakes

  • Entering the angle between the field and the surface instead of the angle to the normal; the two differ by 90°, so cos and sin swap.
  • Giving the area in cm² or the field in gauss; the tool expects m² and tesla (1 gauss = 0.0001 T).
  • Multiplying by the number of turns outside the tool; this gives flux through one loop only, and the turns must be added afterwards for flux linkage.
  • Leaving the angle blank and not noticing that it is treated as 0°, which gives the maximum possible flux.

Sources

About this calculator

This calculator finds magnetic flux, Φ = B·A·cosθ, the measure of the total magnetic field passing through a surface, where B is the magnetic field strength, A is the surface area, and θ is the angle between the field lines and the surface's normal vector. Flux is maximum when the field is perpendicular to the surface (θ=0) and zero when the field runs parallel to it (θ=90°) — this quantity is the basis of Faraday's law of electromagnetic induction, since a changing flux is what induces an EMF.

Electrical engineering students use it to work through transformer, generator and inductor problems, and it's foundational for understanding how motors, generators and induction-based sensors work.

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Comments (1)

  • Editorial team

    Weak fields give tiny numbers, so look at the milliweber line when the weber line rounds off. The Earth's field of roughly 0.00005 T through a 1 square metre loop shows 0.0001 Wb, yet the milliweber result reads 0.05 mWb, which is the more faithful figure. A 0.01 square metre coil would round both to zero, so scale the area up and divide afterwards. What field source are you working with?

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