So how many hours of sleep should a toddler have? Well it varies from child to child, and even from day to day in the same child. Toddlers sleep an average of twelve hours a day in the 3rd year, but that's an average that takes into account those who sleep only 10 hours and those who sleep 14, those who nap and those who don't.
If your toddler has recently given up his afternoon nap, you can expect him to be sleepier and crankier than usual until his body adjusts to his new shut-eye schedule. But as long as he is able to function well on the sleep he is getting you can rest assured he is getting enough. If he is not functioning up to par, continue to be tired and cranky, consider moving bedtime ahead a bit to compensate for the nap he's nixed.
My son is usually in bed between 8 and 8:30pm and he wakes up before 7am. And then he takes a nap for at least 2 hours every afternoon. So he's getting at least 13 hours of sleep total. I am careful about him not missing two naptimes in a row, otherwise he won't function really well that will stress me out too.