What is the formula for magnetic flux?

Magnetic flux is calculated with Φ = B × A × cos θ, where Φ is flux in webers (Wb), B is the magnetic field strength in tesla (T), A is the surface area in square meters (m²), and θ is the angle between the magnetic field vector and the outward normal to the surface.

The weber (Wb) is the SI unit of magnetic flux. One weber equals one tesla multiplied by one square meter (1 Wb = 1 T·m²). It represents the total magnetic field passing perpendicularly through a given surface area.

Why does cos θ appear in the formula?

Only the component of the magnetic field perpendicular to the surface contributes to flux. The dot product of B and the area vector A naturally produces a cos θ term, where θ is measured between B and the surface normal.

When is magnetic flux maximum and when is it zero?

Flux is maximum when θ = 0°, meaning the field is perpendicular to the surface (cos 0° = 1). Flux is zero when θ = 90°, meaning the field is parallel to the surface and no field lines pass through it (cos 90° = 0).

What is the difference between the angle and the surface normal?

The surface normal is an imaginary line perpendicular to the flat surface. The angle θ in the formula is between the magnetic field vector B and that normal — not the angle between B and the surface itself. If the field is straight through the surface, θ = 0°.

How is magnetic flux used in Faraday's law?

Faraday's law states that the induced EMF in a loop equals the negative rate of change of magnetic flux through the loop (EMF = −ΔΦ/Δt). A changing flux — caused by a changing B, area, or angle — induces a voltage.

Magnetic Flux Calculator

Name: Magnetic Flux Calculator
Availability: InStock
Author: Nham Vu

Enter magnetic field strength, surface area, and angle to calculate magnetic flux using Φ = B × A × cos θ.

Input Values

Magnetic Field Strength (B)

Tesla (T)

Surface Area (A)

m²

Square meters (m²)

Angle θ (field vs. surface normal)

° 0° – 180°

0° (max flux) 90° (zero flux) 180°

Quick Presets

Result

Enter values and click Calculate to see the magnetic flux.

Step-by-Step Breakdown

Breakdown appears after calculation.

Flux Efficiency

Appears after calculation.

Summary

Enter magnetic field strength, surface area, and angle to calculate magnetic flux using Φ = B × A × cos θ.

How it works

Enter the magnetic field strength (B) in tesla.
Enter the surface area (A) in square meters.
Set the angle (θ) between the magnetic field and the surface normal using the slider or input field.
The calculator applies Φ = B × A × cos θ and displays the flux in webers instantly.
A breakdown panel shows B, A, cos θ, and the final result.
Adjust any value to see how flux changes in real time.

Use cases

Physics homework and exam problems involving magnetic flux through a coil.
Calculating induced EMF via Faraday's law (requires flux change over time).
Understanding how orientation affects flux when studying electromagnetic induction.
Lab exercises with solenoids, loops, and varying field angles.
Verifying hand-calculated results for transformer and motor design problems.
Teaching aid to show that flux is maximum when B is perpendicular to the surface (θ = 0°) and zero when parallel (θ = 90°).

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu