This question is about terminology for physical quantities.

When we talk about magnitude (while talking about scalars and vectors) do we refer to just number or Number along with units?

example: If a person weighs 120 pounds, then "120" is the numerical value and "pound" is the unit.

Which is magnitude? 120? or 120 pounds?


In the book I'm using its written as

The number indicates the magnitude of the scalar quantity and is inversely proportional to the unit chosen.

This statement is wrong. Right? Its not the number alone. Its along with units.

  • 2
    $\begingroup$ Don't get hung up on definitions. It really doesn't matter--- you know what the author means--- your weight in kilos is half your weight in pounds. $\endgroup$ – Ron Maimon Aug 2 '12 at 1:04

After a bit of thinking I myself found the answer.

Let us consider example:

mass of an ant is 1000 milli grams. mass of an elephant is 1 ton.

If just number was taken as magnitude then magnitude of mass of ant would be greater than that of elephant. Which clearly shouldn't be.

So magnitude is number along with units.


You dont give magnitude of pounds, you give magnitude of , say mass (as here). So the magnitude is 120 pounds.


Magnitude is a property of the object, not our description of it; it's the same regardless of what units we use. Writing 10 m/s as 1000 cm/s doesn't change how fast something is travelling. What magnitude the velocity has is a fact about the physical world, not how a human chooses to write it.

  • $\begingroup$ There sure is a difference between 10 m/s and 1000 m/s. Did you mean to change one of the units as well? $\endgroup$ – Jasper Apr 11 '18 at 15:32

@claws. That's wrong. Because you have to always use the official units. For mass is Kg. Neither milligrams nor tons. But coming to the question, usually we put units to magnitude (norm) of a vector. For velocity in English there are two words to distinguish between the vector and its magnitude, respectively "velocity" and "speed", BOTH with units. This is the accepted rule. However, personally I am perplexed in attributing units to magnitude, because for instance, in the case of speed (norm of velocity), a direction (ANY if not a specific one) is always necessary, because in "no direction" only speed = 0 m/s is possible. So, being the norm deprived of direction (and sense) how can it express m/s different from zero? In my opinion magnitude should be a pure number and acquire units only within the FULL vector. The same on cartesian axes: the segment representing magnitude always lies on a line (direction), which, if not considered, should give just a pure number. But again: officially magnitude has units.


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