# Magnetic Flux Calculator (Φ = BA cosθ)

Calculate magnetic flux with Phi = B x A x cos(theta). Enter magnetic field (Tesla), area (m squared), and angle to find flux in Webers. Essential for Faraday's law.

## What this calculates

Magnetic flux measures how much magnetic field passes through a surface. It is the foundation of electromagnetic induction: changing flux through a coil is what generates voltage in generators, transformers, and wireless chargers. This calculator finds the flux from field strength, area, and the angle between the field and the surface.

## Inputs

- **Magnetic Field (B)** (T) — min 0 — Earth's field: ~50 uT. Fridge magnet: ~5 mT. MRI: 1.5-3 T.
- **Area (A)** (m²) — min 0
- **Angle (θ)** (°) — min 0, max 180 — 0 = field perpendicular to surface (max flux). 90 = parallel (zero flux).

## Outputs

- **Magnetic Flux (Φ)** (Wb) — Magnetic flux in Webers
- **Magnetic Flux** (mWb) — Flux in milliwebers
- **Magnetic Flux** (μWb) — Flux in microwebers
- **cos(θ)** — Cosine of the angle
- **Effective Area** (m²) — A x cos(theta) -- area projected onto the field direction

## Details

## The Formula

**Phi = B x A x cos(theta)**

Where B is the magnetic field in Tesla, A is the area of the surface in m squared, and theta is the angle between the field direction and the line perpendicular to the surface (the surface normal).

### Understanding the Angle

- **theta = 0 degrees:** Field is perpendicular to the surface. Maximum flux. This is a coil face-on to the field.
- **theta = 90 degrees:** Field runs parallel to the surface. Zero flux. No field lines pass through.
- **theta = 45 degrees:** Flux is reduced by cos(45) = 0.707, about 71% of maximum.

### Magnetic Field Strengths

| Source | Strength |
|--------|----------|
| Earth's magnetic field | ~25-65 uT |
| Refrigerator magnet | 5 mT |
| Bar magnet (surface) | 10-100 mT |
| Neodymium magnet | 0.2-1.4 T |
| MRI scanner | 1.5-3 T |
| Large electromagnet | 1-20 T |

### Why Magnetic Flux Matters

Faraday's law says the voltage induced in a coil equals the rate of change of magnetic flux: **EMF = -d(Phi)/dt**. This is the operating principle behind every electric generator, transformer, and induction cooktop. Understanding flux is the first step to understanding all of electromagnetic induction.

### Units: The Weber

One Weber (Wb) equals one Tesla times one square meter. Named after Wilhelm Eduard Weber, it is the SI unit of magnetic flux. In everyday applications, milliwebers (mWb) and microwebers (uWb) are more common since most surfaces and fields are small.

## Frequently Asked Questions

**Q: What is the difference between magnetic field and magnetic flux?**

A: Magnetic field (B, in Tesla) describes the strength and direction of the magnetic influence at a point in space. Magnetic flux (Phi, in Webers) describes how much of that field passes through a specific area. Think of B as rain intensity (inches per hour) and flux as the total rain collected by a bucket (the bucket's opening area matters). Same rain, different collection depending on bucket size and tilt.

**Q: Why does the angle matter?**

A: The angle determines how much of the surface 'faces' the field. At 0 degrees the surface captures the maximum field lines. At 90 degrees the field slides along the surface without passing through it, giving zero flux. This is why generators rotate coils in magnetic fields -- the changing angle continuously changes the flux, inducing alternating voltage.

**Q: What is Faraday's law of induction?**

A: Faraday's law states that a changing magnetic flux through a loop of wire induces a voltage (EMF) equal to the negative rate of change of flux: EMF = -dPhi/dt. If the flux through a 100-turn coil changes by 0.01 Wb in 0.1 seconds, the induced EMF is 100 x 0.01/0.1 = 10 volts. This principle powers generators, transformers, and induction heating.

**Q: Can magnetic flux be negative?**

A: Yes. The sign of flux depends on which side of the surface you define as positive. When theta is between 90 and 180 degrees, cos(theta) is negative, meaning the field passes through the 'back' of the surface. In Faraday's law, the sign of the flux change determines the direction of the induced current (Lenz's law).

---

Source: https://vastcalc.com/calculators/physics/magnetic-flux
Category: Physics
Last updated: 2026-04-08