# Plurals for multiplied units

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

• 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). Commented Mar 24, 2015 at 14:56

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.

• 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). 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. 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. Commented Mar 24, 2015 at 15:02