What is the smallest bird in the world?

The bee hummingbird of Cuba, about five centimetres long and under two grams - lighter than a small coin, and lighter than some of the larger insects it gets mistaken for. Its nest is the size of a thimble and its eggs are about the size of a coffee bean.

Being that small is metabolically brutal. Its heart runs above 1,200 beats a minute in flight, its wings beat up to 80 times a second, and it must feed every ten or fifteen minutes through the day, visiting hundreds of flowers. It lives so close to starvation that every night it enters torpor, letting its body temperature fall towards the air temperature and its heart rate drop to a fraction of normal, essentially hibernating until morning.

There is a hard floor here and it is close. Below a certain size a warm-blooded animal loses heat faster than it can possibly eat to replace it, because surface area grows more slowly than volume shrinks. The bee hummingbird and the Etruscan shrew are both sitting at roughly that limit, from opposite ends of the vertebrate family, which is why nothing warm-blooded is smaller.