Flux. The magnetic flux through a loop measures how much of the magnetic field passes through it: Φ = BA cos θ. The angle θ is between the field and the area vector, which is perpendicular to the loop (the normal), not the angle between the field and the loop itself.

Another way to see it. Only the part of the field that is along the area vector goes through the loop: B cos θ. Or, only the area that faces the field counts: A cos θ, the shape you see when you look along the field. Each of these pictures gives the same flux.

The special angles. At 0° the loop faces the field and the flux is a maximum (BA). At 90° the loop is edge-on, no field passes through it and the flux is zero. At 180° the field goes through the loop from the back and the flux is −BA. The sign tells you which way the field is going through the loop.

Field lines. The crosses show the field going into the page. The density of the lines is proportional to B, and each line stands for 0.1 Wb. The flux through the loop is about 0.1 Wb for every line that passes through it. The count is a whole number, so it is only approximate.

The unit of flux is the weber: 1 Wb = 1 T m².