There are roughly 2 billion children worldwide. However, assuming Santa doesn't visit the children of Hindu, Muslim, Jewish, atheist and so on parents, that leaves the 35 per cent or thereabouts whose parents consider themselves Christian. That's still an impressive 700,000,000 children in a night. Assuming three children per household, that's 233,000,000 stops for Santa and his sleigh.
If we assume that the 233,000,000 good Christian households are distributed evenly around the world , and the planet's surface area is 510,000,000km (and for the sake of simple calculations we are going to treat the Earth as a square map, rather than a globe), then each stop between households will be around 1.47km (0.91 miles) apart. Santa will therefore have to travel a total of 342,510,000km (212,030,000 miles).
If he's clever about it, and travels from east to west with the Sun, maximising his available night-time, Santa has about 32 hours to work with (assuming children sleep for eight hours, he has 24 hours plus those eight to finish). Travelling 342,510,000km in 32 hours equates to a speed of 10,703,437.5km/hr (6,650,807.72mph), or a little under 1,800 miles per second, assuming he takes no time actually to deliver the presents or stop for any comfort breaks.
http://www.telegraph.co.uk/topics/christmas/6859529/Father-Christmass-Christmas-Eve-in-figures.html
