Magnetic Flux Calculator

How Magnetic Flux Is Calculated

Magnetic flux measures the total magnetic field passing through a given surface area. It determines how much of the magnetic field is “captured” by a loop or coil, which drives electromagnetic induction.

Magnetic Flux Formula: Φ = B × A × cos(θ)

Where:

• Φ (Phi) = magnetic flux in Webers (Wb)
• B = magnetic field strength in Tesla (T)
• A = area of the surface in square meters (m²)
• θ (theta) = angle between the magnetic field direction and the normal to the surface

Special Cases:

• θ = 0° (field perpendicular to surface): Φ = B × A (maximum flux)
• θ = 90° (field parallel to surface): Φ = 0 (no flux passes through)

Worked Example: A circular coil with radius 0.05m is placed in a 0.3 T magnetic field at 30° to the normal:

• A = π × (0.05)² = 7.854 × 10⁻³ m²
• cos(30°) = 0.866
• Φ = 0.3 × 7.854 × 10⁻³ × 0.866 = 2.04 × 10⁻³ Wb = 2.04 mWb

Faraday’s Law Connection: A changing magnetic flux induces a voltage: EMF = −N × ΔΦ/Δt where N is the number of coil turns. This is the operating principle of generators and transformers.

Typical Field Strengths:

• Earth’s magnetic field: ~50 µT (0.00005 T)
• Refrigerator magnet: ~0.01 T
• MRI machine: 1.5–3.0 T
• Neodymium magnet: 1.0–1.5 T

A note on the unit. The weber (Wb) is named after Wilhelm Eduard Weber, a 19th-century German physicist who worked with Carl Friedrich Gauss on the first practical electric telegraph. One weber equals one tesla times one square meter. Older textbooks and CGS-based literature use the maxwell instead, where 1 Wb = 10⁸ maxwells. You’ll occasionally see the maxwell in legacy industrial magnetic-circuit calculations, but SI weber is standard everywhere modern.