A Fermi-question: Are there more stars than grains of sand?

This claim is pretty popular in the web and obviously cannot be answered by counting grains or stars. Thats what physicists call a Fermi-question. It deals with problems/questions where we dont have at all/enough measurement data to calculate a exact result, but can make a approximation based on plausibility, general knowledge and common sense.

When trying to answer this question give out a approximated number of grains of sand on earth and stars in the universe, the assumptions the approximation is based and the rough error of your approximation so everybody can compare the quality & plausibility of different answers.

• Is it me or this sounds like an exam question for Astronomy course?:) – Tigran Khanzadyan Jul 31 '11 at 23:30
• It comes off as a bit patronizing to me to remind us to support our answers by saying where they come from, to explain what a Fermi problem is, to say what you expect from the answers. We're your peers, not your students. – Mark Eichenlaub Oct 4 '12 at 2:54
• @MarkEichenlaub I removed it, this was a astronomy.se (seeded) question to get more traffic and at that time the community was lacking questions, votes,... well unfortunately its closed now – Hauser Oct 4 '12 at 11:14

From http://www.hawaii.edu/suremath/jsand.html the estimate for the grains of sand is 7.5 x 10^18 or 7.5 billion billion.

From http://www.faqs.org/faqs/astronomy/faq/part8/section-3.html the estimate for the number of stars in our own galaxy is between 2 x 10^11 and 6 x 10^11 stars.

From http://www.faqs.org/faqs/astronomy/faq/part8/section-4.html the lower end estimate for the number of galaxies in the visible universe is 8 x 10^10 galaxies.

So:
Sand grains: ~7.5e18
Stars (low estimate): 2e11 * 8e10 = 16e21

That gives ~2000 stars per grain of sand for the low estimate of the number of stars. Although, isn't the Milky Way on the medium to big size as far as galaxies go? If so then multiplying the number of stars in our galaxy by the number of galaxies isn't correct. However, the number used, 2e11, was on the low end so and even using something like 1e10 as an estimate of the average number of stars per galaxy still gives ~100 stars per grain of sand.

"Space is big. You just won't believe how vastly, hugely, mind- bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space." -- Douglas Adams

• I think there is a big underestimate of the amount of sand in all the beaches. A cubic kilometer contains 10^18 cubic mm, and any decent volcanic eruption gives a cubic kilometer of dust and ash. I would think there must be at least 1,000 cubic km of sand lying around. – Pete Jackson Jul 31 '11 at 17:53
• The link calculates grains of sand on beaches. Most of the volcanic sand you mention is probably at the bottom of the ocean or mixed into sandy loam soils. Always important to define your terms. – Andrew Aug 9 '11 at 3:13
• Don't you mean 2000 stars per grain of sand in the first part of your answer – user9711 Jun 7 '12 at 1:23

There's a pretty good analysis on CosmologyScience.com that describes the uncertainty and measures actual beach sand. It gives lots of sciencey references and is persuasive that sand outnumbers stars.

• I think the difference with the previous estimate comes partly in a) that it uses 1mm^3 sand grainswhereas as we all know sand can be very fine, 2)the perimeter of the earth as an estimate for beaches, whereas shores are fractal and the earth has a surface – anna v Oct 4 '12 at 4:05