Having taken my wife's 20 year old Nissan in for it's MOT test last week, I was looking at the results of the emissions test, and noticed that the Hydrocarbon reading was 6ppm - with a limit of 200. I was wondering how that compares to the more recent standards, but they're all measured in g/km - is there an easy way to convert between them?
Yes, there is a way, if the g/km is referring to hydrocarbons and not to CO2 (if it's referring to CO2 they are measuring different things).
You need to calculate how much exhaust gases the engine produces for one kilometer. You can do that based on fuel consumption because the amount of air going through the engine is dependent on the amount of fuel for stoichiometric gasoline engines. Then multiply the amount of exhaust gases by 6/(1000*1000), and you get the amount of hydrocarbons per km.
It ain't easy. I don't now have time to do example calculations here, but I'll see if I in the near future have time to do some example calculation. If I do, I'll edit and update my answer.
They are measuring two different things, so you can't convert them.
The MOT test results show how efficiently the engine is burning fuel - i.e. all the fuel that goes into the combustion chamber either gets burned, or decomposed in the catalytic converter.
The g/km numbers are effectively measuring fuel consumption, for the purpose of making the annual road tax less for "small cars" than for big ones. IMO that is just a political game, and increasing fuel tax by a small amount would be a fairer way to achieve the same thing - but the road haulage industry won't accept that idea, and it does have side effects for international road haulage where you can buy your fuel in the cheapest country but distribute your contribution to road maintenance costs where you drive, not where you paid the fuel tax.
It is also gamed by the car manufacturers. If a higher tax band starts at 140g CO2/km, there are a large number of car models which "officially" produce no more than 139. How very convenient, for marketing purposes - it eliminates the criterion as a factor in consumer choice.
A 50 cc motor scooter and a 5 liter stretch limo both have the same hydrocarbon limit on the emissions test, but obviously one produces much more CO2 per km travelled than the other.