Meaning

• The absolute or relative size, extent or importance of something.

• An order of magnitude.

• A number, assigned to something, such that it may be compared to others numerically

• Of a vector, the norm, most commonly, the two-norm.

• A logarithmic scale of brightness defined so that a difference of 5 magnitudes is a factor of 100.

• A measure of the energy released by an earthquake (e.g. on the Richter scale).