Following the comments to this answer to another question, what is the difference between size and magnitude?
I know there's a difference, but can someone put it in a nutshell for me?
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Usually, size connotes physical dimensions while magnitude connotes either a numerical measure (particularly a non-linear one) of any sort of amount or metaphorical size.
"What size is that screw?" (Physical dimensions)
"A problem of immense magnitude" (Metaphorical size)
You can also use size to mean metaphorical size, but you usually can't use magnitude alone to mean physical size. (Nobody would say "What's your sneaker magnitude?")
The difference/usage exists mainly in natural sciences (physics)
In mathematics, magnitude, together with direction, describes a vector. For instance, an object is said to have a velocity if it travels in a particular direction (say, "Northeast") at a particular rate (say, "30 knots"). The magnitude of velocity is speed, which does not imply a direction. Only values with a direction are said to have magnitude in this way; scalar values, such as an object's mass, or physical dimension (size) is never described in this way. Of course, there are many other ways that the word 'magnitude' is used