# 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 Mar 24 '15 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 Mar 24 '15 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). – Matthaeus Mar 24 '15 at 9:41
• Please cite the source. (Incidentally, it is not correct. Incidentally, it is not quite what the OP asked.) – Kris Mar 24 '15 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 Mar 24 '15 at 13:18
• @Kris I believe "Units always receive the plural immediately before the "per"" is the answer to what I asked. – user12205 Mar 24 '15 at 15:02