Things seem to be crashing down to Earth all over the place at the moment, what with the house of the suitably named Comette family getting hit by an egg-sized meteorite, last month's Nasa satellite falling somewhere off the west coast of America and Lars von Trier envisioning Earth colliding with an even larger planet in Melancholia. It prompts the question: what are the actual chances of something solid dropping from space and landing on our heads?

Let's start with natural stuff. The US National Research Council (NRC) has released the riveting Defending Planet Earth: Near-Earth Object Surveys and Hazard Mitigation Strategies, which tells us that around 100 tonnes of "very small objects", mainly dust, drops on Earth every day. There is no recent record of anyone killed by bigger bits, although a few cars in the US have been damaged this century and one, the famous Peekskill meteorite car, has toured the world.

Fortunately, Nasa's Near Earth Object Programme is watching over us so we can find, for example, that object 2009TM8, about 10 metres across, is due to pass closer than the moon on Monday 17 October. Airbursts from objects only 30 metres across can be serious – the one over Siberia in 1908 devastated the area of a large city – the NRC estimate a one in 200 chance per year of this happening somewhere on Earth.

The biggest recent scare was from Apophis, which is around 200 metres across. When it was discovered in 2004, it was estimated there was a 2.7% chance of impact in 2029, but new information has shown we're safe after all. The current frontrunner is 2011AG5, which is 140 metres across and has a cumulative impact probability of around 2% between 2040 and 2047.

Nasa is tracking over 800 objects of more than 1km across, and anything with a diameter of over 3km is considered a global catastrophic risk. Still, a clash with debris of that calibre is only expected to happen every few million years: the NRC stoically points out that "while this apocalyptic possibility is extraordinarily unlikely to happen in the lifetime of anyone living now, traditional approaches to preparing for disaster would become irrelevant". Have they not heard of Bruce Willis?

What about man-made junk? About 5,400 tonnes worth of rubbish has come back down over the last 40 years and there have been 28 re-entries of satellites so far this year. So far nobody has been injured, even when 40 tonnes rained down on the US after the Columbia shuttle broke up – Nasa afterwards estimated that there was a one in four chance someone would have been hit.

When the remnants of the Upper Atmosphere Research Satellite (UARS) came to Earth last month Nasa said there was a "one in 3,200 chance of anyone being hit". Where did they get this number from?

The satellite had been up 20 years, stopped working in 2005 and weighed 5,700kg, about the size and weight of a double-decker bus. Nasa said it would break into 26 objects that would survive re-entry, weighing 532kg in total, about the weight of eight washing machines. These would be spread over about 300 miles, but cover a total damage area of around 22 sq metres (around three parking places), but they had no idea where it would land. As one commentator said, you'd think these boffins would have better control of their satellites – it's not rocket science.

The largest object weighed 158kg, about the weight of an adult gorilla (though that sounds a bit soft – better to think of a couple of washing machines tied together, travelling at 100mph). This does not sound encouraging, but the Earth is a big place with a surface area of 500,000,000 sq km, and so assuming the bits can land anywhere, there is around a one in 20,000,000,000,000 chance of any particular square metre being hit.

If an individual makes a target of say around 1 sq metre, then assuming a random landing place there is around a one in 20,000,000,000,000 chance of them being hit – that's the same chance as flipping a coin 44 times in a row and it coming up heads every time. Or slightly better than the chance of winning the lottery twice in a row.

But there are 6,700,000,000 people on Earth, and so the chance of anybody at all being hit is 6,700,000,000/20,000,000,000,000 which is one in 3,000, very close to Nasa's quoted figure of one in 3,200. So really this is a back-of-an-envelope calculation.

The chances of hitting anyone is so low because people don't cover much of the Earth. It may not seem like that when you are jammed against a stranger's armpit on the northern line, but as anyone taking an intercontinental flight will notice, this globe is covered by an awful lot of not-very-much. If each of us take our 1 sq metre, that's 6,700 sq km, which is only 1/80,000 of the Earth's surface. So if everyone in the world went to the Glastonbury festival, they would only take up Somerset and Wiltshire combined (although you can't even start to imagine the state of the toilets).