Depends on the amount of time you're prepared to spend putting them on and off the potty, tbh. I think all these stories that grannies love to tell about fully-trained 1yo actually involved putting the on the pot every hour on the hour. Which is probably useful if you're washing terry nappies by hand, but probably less useful in an age where you have a washing machine and want to have a life outside toddler pottying.
My dd1 was dry during the day before her 2nd birthday. We started putting her on the potty at 18 months and she got the idea very quickly, and was in pants at about 21 months. But you do have to put the hours in, and with 2nd and 3rd children I simply didn't have the time to spend 20 mins umpteen times a day trying to persuade an 18 month old to perform.
If you're taking trained to mean 'capable of recognising when they need to go and asking in sufficient time to get to the loo without accident', then I would have thought you'd be talking closer to age 3.
Personally, I've found the best compromise between the hassle of nappies and the hassle of pottying is to do cold turkey at 2 and a quarter. But you do have to put them on regularly, since at that age, "Mummy I need a wee" generally means, "Mummy, I've just wet my pants." 