The ZOE Range Rule

ZOE Range = (1000 / Speed) 2

– where Range is in km and Speed in km/hr, and Speed is from 30km/hr to 140km/hr


I found the data provided by Nosig in Maximising Range in a ZOE very interesting, particularly with regard to how ZOE range is affected by speed. Having done some line fitting on it I believe I have discovered a useful method of predicting the maximum range achievable for a given speed for the ZOE.

To a good approximation it can be summarised by the equation above. In other words, to work out the approximate maximum range at a particular speed you just divide the speed into 1000 and square the result!

This ‘ZOE Range Rule’ is actually simple enough to do in your head while driving along (at least roughly) so you can choose an appropriate speed if required to get to a particular destination – here are some examples:

  • Range at 125km/hr (78mph) = (1000/125)^2 = 8*8 = 64km (40 miles)
  • Range at 100km/hr (62mph) = (1000/100)^2 = 10*10 = 100km (62 miles)
  • Range at 50km/hr (31mph) = (1000/50)^2 = 20*20 = 400km (250 miles)


The second one is particularly easy to remember – the ZOE can travel about 100km at 100km/hr. That’s not an impressive range – but drop the speed and the range can go up hugely.

Of course, these predicted ranges are all approximate and represent the best achievable range (i.e. travelling at constant speed on level ground). With further experimentation and data gathering it should be possible, firstly, to validate and refine the approximate rule above and, secondly, to make a more general model to calculate range taking into account more key variables (e.g. type of route, altitude changes, number of passengers, etc.).