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Physical quantities often have units, and some units are formed by multiplying or dividing other units. For example, the unit for momentum is kg m s-1 and the unit for impulse is N s.

The question is, how do we pluralize them (during conversation)? For example, which of the following is correct?

1: Its momentum is:
  a. 15 kilogram meter per second
  b. 15 kilograms meter per second
  c. 15 kilogram meters per second
  d. 15 kilogram meter per seconds

2: It receives an impulse of:
  a. 10 newton second
  b. 10 newtons second
  c. 10 newton seconds

3: The gravitational constant is:
  a. 6.67 × 10-11 newton meter squared per kilogram squared
  b. 6.67 × 10-11 newtons meter squared per kilogram squared
  c. 6.67 × 10-11 newton meters squared per kilogram squared
  d. 6.67 × 10-11 newton meter squared per kilograms squared

4: The permeability of free space is:
  a. 4π × 10-7 volt second per ampere per meter
  b. 4π × 10-7 volts second per ampere per meter
  c. 4π × 10-7 volt seconds per ampere per meter
  d. 4π × 10-7 volt second per amperes per meter
  e. 4π × 10-7 volt second per ampere per meters

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  • Have you tried looking around for a respectable source guiding on this? In other words, have you tried to find an answer by yourself first?
    – Kris
    Commented Mar 24, 2015 at 13:21
  • @Kris Tried googling, couldn't find anything. All I could find was that symbols for units are not pluralized (which is obvious) and plural forms for units that are not derived from other units (which are obvious).
    – user12205
    Commented Mar 24, 2015 at 14:56

1 Answer 1

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Units always receive the plural immediately before the "per":

Its momentum is 15 kilogram meters per second
It receives an impulse of 10 newton seconds
The gravitational constant is 6.67 × 10-11 newton meters squared per kilogram squared
The permeability of free space is 4π × 10-7 volt seconds per ampere per meter

This is because the unit is a compound unit (kilogram metre, newton second...) and it is then distributed across another dimension.

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  • correct. Several kilogram-meters (think of multiplied units as one quantity) may fit into one second (think of divided units as what the quantity is normated to, i.e. "how many X can i fit in 1 Y ? ---> A*X/Y .... where 'A' is the amount or coefficient).
    – Matthaeus
    Commented Mar 24, 2015 at 9:41
  • Please cite the source. (Incidentally, it is not correct. Incidentally, it is not quite what the OP asked.)
    – Kris
    Commented Mar 24, 2015 at 13:15
  • @Kris No source other than O-level education, erm, some time ago. If you think that another answer should be provided, please do that.
    – Andrew Leach ♦
    Commented Mar 24, 2015 at 13:18
  • @Kris I believe "Units always receive the plural immediately before the "per"" is the answer to what I asked.
    – user12205
    Commented Mar 24, 2015 at 15:02

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