Which Is More Numerous: Grains of Sand on Beaches or Stars in the Universe?
― Stars win by tens of times or more. But they lose to the molecules in one glass of water
You may have heard that there are more stars in the universe than grains of sand on Earth's beaches. Nobody can count them, but we can estimate both with multiplication alone. Try it, and stars do win. And closer to home, there is something that outnumbers the stars by a wide margin.
You are at the seaside in summer. You scoop up a handful of sand, and the grains trickle through your fingers.
Looking around, you see the beach stretching for kilometres. Beyond it, similar beaches lie all over the world.
At night, you look up from the same beach and see stars across the whole sky. So which really is more numerous, the grains of sand or the stars?
Two multiplications decide the contest
A grain of sand is tiny, but a beach has a limited size. Multiply the beach's length, width and depth to get its volume, then divide by the volume of one grain. That gives a rough count of grains. The answer is about 10 to the power of 20.
Our Milky Way is thought to hold more than 100 billion stars. The visible universe contains hundreds of billions of galaxies or more. Multiply them and you pass 10 to the power of 22.
10 to the 20 and 10 to the 22. Both are numbers too big to imagine, but a difference of just 2 in the exponent means a factor of 100. That is the most interesting part of this contest.
How do you count the grains of sand on a beach?
Counting them one by one is impossible. So we build the answer by multiplying things whose sizes we know. This kind of estimating is called a Fermi estimate.
The world's coastlines add up to about 360,000 kilometres. One survey suggests that roughly 30% of that is sandy beach. If we assume a beach 50 metres wide and sand 5 metres deep, the world's beach sand comes to about 27.5 billion cubic metres.
A single grain of sand is about 0.5 millimetres across. A box of one cubic metre holds about 8 billion such grains. Multiply the two, and the grains on the world's beaches come to about 2 × 10 to the 20, or roughly 200 quintillion.
Look at Figure 1. Each step to the right on the horizontal scale means ten times more. Move the slider to change the grain size and see how the count moves.
If the grains are half the size, there are eight times as many. That is because volume is length multiplied by itself three times. Even if every beach were made of very fine sand, the count would only approach the lower end of the star estimate. It would still not overtake the star estimate's range.
How do you count the stars in the universe?
Stars cannot be counted one by one either. So we use a two-step multiplication. First, the number of stars in one galaxy. The Milky Way is estimated to have 100 billion to 400 billion stars.
Next, the number of galaxies in the part of the universe we can see with telescopes. This is put at several hundred billion to about 2 trillion, and researchers disagree on the estimate. Take the low side: 100 billion galaxies, each with 100 billion stars, gives 10 to the 22 stars.
Compare that with about 2 × 10 to the 20 grains of sand, and stars outnumber them by about 45 times. With higher estimates, the gap widens to tens of thousands of times. "Stars outnumber sand grains" is a conclusion that does not easily fall apart, however you choose your estimates.
Think of one glass of water, 180 millilitres. It holds about 6 × 10 to the 24 water molecules. That is more than even the upper end of the star estimate. When things are too small to see, their numbers grow by orders of magnitude.
This article counted only seaside beaches. Vast deserts hold far more sand than beaches do. If desert sand is included, the estimate swells by thousands of times, and the contest with the stars becomes too close to call. The answer changes depending on "how far you count as sand".
Summary
Even things that cannot be counted can be estimated: split them into parts of known size and multiply. The sand grains on the world's beaches number about 10 to the 20, and the stars in the universe 10 to the 22 or more. And the molecules in one glass of water exceed even the stars.
Numbers we cannot count can still be compared by multiplication.
What outnumbers the stars in the universe is in your glass.
You can read about the nature of sand grains themselves in Why does dry sand crumble but wet sand hold together? For how starlight reaches your eye, try How many particles of light does the human eye need to know it has seen something?
- Take one level teaspoon (5 millilitres) of dry sand and spread it on a sheet of black paper.
- With a toothpick, separate a small heap about the size of a grain of rice and count its grains. Then estimate by eye how many times larger the rest of the sand is than that heap.
- "Grains in the small heap × how many times larger" gives the grains in a teaspoon. You should get thousands to tens of thousands.
This is the smallest possible practice for a Fermi estimate. You will also see how much the answer changes with the size of the grains.
For those who want to know more ― terms, formulas and links to textbooksEach part is labelled by level, from middle-school science to university-level courses
- Middle schoolCovered in middle-school science
- High schoolCovered in high-school basic chemistry and earth science
- High school+Advanced high-school material, or textbook sidebars
- UniversityUniversity courses not taught in high school (sedimentology, astronomy)
- ResearchNot yet settled even at university level; researchers are still working on it
Middle schoolTerms: this phenomenon has names
- Sand: In earth science, grains from about 1/16 mm to 2 mm across are called sand. Finer material is mud, and coarser material is gravel.
- Galaxy: A huge group of stars and gas held together by gravity. Our Sun is one of the stars in the Milky Way.
- Fermi estimate: A way to find an approximate value for a quantity you cannot measure directly, by splitting it into a multiplication of known quantities.
Middle schoolHigh schoolChecking with formulas: estimating sand grains and stars
The number of sand grains is "total volume ÷ volume of one grain," and the number of stars is "stars in one galaxy × number of galaxies." Writing big numbers as powers of 10 makes the work easier, because when you multiply you just add the exponents.
| In symbols | N ＝ ( L × W × H ) ÷ d³ ／ N★ ＝ n × G |
| In words | Grains of sand = volume of beach ÷ volume of one grain. Stars = stars in one galaxy × number of galaxies |
| Where the formulas come from | Volume is a sum of small pieces, so dividing the whole by the size of one grain gives a count (ignoring gaps between grains). For stars, it is a multiplication of how many similar groups there are |
| Symbol | Meaning and unit |
| L | Total length of the world's beaches (m) |
| W | Width of a beach (m) |
| H | Depth of the sand (m) |
| d | Diameter of one grain. Each grain is treated as a cube with side d (mm) |
| n, G | Stars in one galaxy, number of galaxies (count) |
| Length of the world's coastlines | about 360,000 km |
| Share that is sandy beach | one survey gives about 31% |
| Beach width and sand depth (assumed) | width 50 m, depth 5 m |
| Diameter of a sand grain | 0.5 mm |
| Stars per galaxy, number of galaxies (low side) | both 100 billion, that is, 10 to the 11 |
| Molecules in 1 mole (18 grams) of water | about 6.0 × 10 to the 23 (Avogadro constant) |
| Length of beaches (km) | 360000 × 0.31 ≒ 110000 |
| Convert to metres | 110000 × 1000 ＝ 110000000 |
| Area of beaches (m²) | 110000000 × 50 ＝ 5500000000 |
| Volume of sand (m³), about 27.5 billion | 5500000000 × 5 ＝ 27500000000 |
| Volume of one grain (mm³), midway | 0.5 × 0.5 ＝ 0.25 |
| Volume of one grain (mm³) | 0.25 × 0.5 ＝ 0.125 |
| Grains in 1 m³ (1 billion mm³) | 1000000000 ÷ 0.125 ＝ 8000000000 |
| Grains of sand: the number parts of 2.75 × 10 to the 10 and 8 × 10 to the 9 | 2.75 × 8 ＝ 22 |
| Same, the exponent part of the 10s (addition) | 10 + 9 ＝ 19 |
| Stars: exponents of 10 to the 11 × 10 to the 11 | 11 + 11 ＝ 22 |
| How many times more stars than sand (10 to the 22 ÷ 2.2 × 10 to the 20) | 100 ÷ 2.2 ≒ 45 |
| Moles in a glass of water (180 g) | 180 ÷ 18 ＝ 10 |
| Water molecules (number part; 10 to the 23 is attached) | 10 × 6.0 ＝ 60 |
The sand comes to 22 × 10 to the 19, or about 2.2 × 10 to the 20 grains. Stars number 10 to the 22 or more, about 45 times the sand. Water molecules come to 60 × 10 to the 23, or about 6 × 10 to the 24, which is more than the upper limit of the star estimate (10 to the 24).
High schoolHigh school+Where is the estimate shakiest?
High schoolThe number of grains is inversely proportional to the cube of the diameter. If the diameter differs by a factor of 10, the count differs by a factor of 1000. Sand fineness varies a lot from beach to beach, so grain size is what affects this estimate most. The slider in Figure 1 lets you feel that sensitivity.
High school+Real sand grains are rounded, not cubes, and gaps between them are said to take up about 30–40% of the volume. Allowing for the gaps reduces the count a little, but by less than a factor of 2. In a contest of orders of magnitude, the assumptions about depth and width matter far more.
UniversityGrain-size distribution, and how galaxies are counted
In sedimentology, sand size is called "grain size" and is described by the share of weight caught by sieves (the grain-size distribution). A logarithmic scale called the phi scale is also used. In astronomy, researchers count the galaxies in deep-space images and, from the number at each brightness (the luminosity function), add in the faint galaxies that do not show up. The size of the observable universe itself is a quantity set by the history of cosmic expansion.
📖 Derivations and further reading: Fermi estimate (Wikipedia) ／ Observable universe (Wikipedia)
ResearchWhat is still not well understood
- How many galaxies are in the universe. In 2016 an estimate of "2 trillion" appeared, but since then some reports, based on measurements of the sky's darkness, have suggested far fewer.
- The exact area of the world's beaches. Studies using satellite images to find the share of sandy beach are advancing, but how deep the sand goes varies greatly from place to place, and there is no consolidated data.
- Whether beaches are growing or shrinking. Changes in the sand carried by waves and rivers, and in the sand people remove, have led to reports that many beaches are thinning, and the overall picture is still being studied.
In other words, this article too is "an explanation of what is known so far." The numbers in the estimates may change, but the order-of-magnitude relation that "stars outnumber beach sand grains" is unlikely to be overturned any time soon.
Links to textbooks (by level)
| Level | Subject and unit | Where in this article |
|---|---|---|
| Middle school | Science "Changes in the Earth" (gravel, sand, mud), Maths "Volume" | Definition of sand, volume of a beach |
| High school | Basic Chemistry "Amount of substance (mole)", Earth Science "Galaxies and the Universe" | Number of water molecules, stars in a galaxy |
| High school+ | How grains pack and the gaps between them | Correction for gaps |
| University | Sedimentology (grain-size distribution), Astronomy (luminosity function) | Ways to make the estimate more accurate |
| Research | Total number of galaxies, changes in beaches | Numbers that still have a wide range |
| ― | Connection to daily life | A feel for big numbers as "10 to the something" |
- Luijendijk, A. et al. (2018) The State of the World's Beaches. Scientific Reports 8, 6641
- CIA, The World Factbook (length of the world's coastlines)
- Conselice, C. J. et al. (2016) The Evolution of Galaxy Number Density at z < 8 and Its Implications. The Astrophysical Journal 830, 83
- Avogadro constant (Wikipedia, Japanese)
- National Astronomical Observatory of Japan (国立天文台), ed., Rika Nenpyo (理科年表, Chronological Scientific Tables), Maruzen Publishing
※This article is a science explainer for general readers. The figures given are rough guides to help you understand how things work. The width and depth of beaches are assumptions made for explanation, and real values differ greatly from place to place.