# Hyphenating complex physical units

I have been reading about writing conventions for scholarly articles recently - specifically, physics - and have learned that when writing units, write them out if they are not associated with a numeric value ("how many meters....?" rather than "it is 5 m long").

But what about more complicated units? Take momentum, which is kg⋅m/s. Do I write "Momentum has units of kilogram-meters per second" or "Momentum has units of kilogram meters per second"?

Wikipedia seems to accept both but prefers no hyphen. Can someone give me a reference which actually states a preference of one over the other?

• The official SI brochure (p. 131) explicitly accepts both spaces and hyphens. The style guides of the American Institute of Physics and of the American Physical Society are both silent on the matter.
– user1635
May 12, 2014 at 20:17
• This is the answer I was looking for - make it an answer! May 12, 2014 at 21:49
• Just nitpicking: it's actually kilogram meters per second, not meter. May 17, 2014 at 21:17
• That could be a whole separate question, since I agree only because that's because what my ears say. I have no idea why that's correct as opposed to "kilograms meter per second" or "kilogram meter per seconds". But anyway, I've changed it. May 19, 2014 at 14:19

As the comment above notes, the SI brochure states:

In both English and in French, when the name of a derived unit is formed from the names of individual units by multiplication, then either a space or a hyphen is used to separate the names of the individual units.

In Section 7.80, "Hyphens and readability," the Chicago Manual of Style advises (emphasis mine):

A hyphen can make for easier reading by showing structure and, often, pronunciation. Words that might otherwise be misread, such as re-creation or co-op, should be hyphenated. Hyphens can also eliminate ambiguity.

On pg. 14, the AIP Style Guide echoes the advice of the Chicago Manual:

Modifiers made up of two or more words are usually hyphenated. When such hyphens forestall ambiguity, they are essential.

The salient quantity in kilogram meter per second is the kilogram-meter; after all, what's being measured is not the meter per second (velocity) or the kilogram per second (my weight gain on weekends), but the kilogram-meter per second.

So to highlight the composite term formed by multiplication, I (and this source) would write:

The kilogram-meter per second (kg · m/s or kg · m · s -1 ) is the standard unit of momentum. Reduced to base units in the International System of Units (SI), a kilogram-meter per second is the equivalent of a newton-second (N · s), which is the SI unit of impulse.

The idea of the hyphen is to say that the two objects either side of it cannot be read separate but in connection to each other. So, sticking to that old logic, the relationship between 'Kilogram' and 'Meters' is best represented with a hyphen than without. Reason: they are a compound. with the hyphen 'Kilogram-meter' (without the 's'), and without it, 'Kilogram meters per second'. Both should be correct but, they hyphen makes it clear that we're talking about the unit in physics.

• I understand the logic underlying this, but since a "kilogram-meter" can only really be made sense of mathematically, I don't think it applies here. Would the units of the gravitational constant be "newton-meter squared per kilogram squared"? How do I know this doesn't refer to (N m)^2/kg^2, or even (Nm^2/kg)^2? Since mathematics is infinitely generalizable, I don't see that using it to find reason in language will be much help. Jun 11, 2014 at 15:49