# Can anyone verify this analogy....? **URL:** \ **Category:** Factual Questions\ **Created:** [September 9, 2002, 8:26am UTC](https://boards.straightdope.com/t/can-anyone-verify-this-analogy/127624 "2002-09-09T08:26:31Z")\ **Posts on this page:** 12\ **Page:** 1
**Author:** ![Aro](https://avatars.discourse-cdn.com/v4/letter/a/b3f665/32.png) [@Aro](https://boards.straightdope.com/u/Aro)\ **Post date:** [September 9, 2002, 8:26am UTC](https://boards.straightdope.com/t/can-anyone-verify-this-analogy/127624/1 "2002-09-09T08:26:31Z")
I have been reading a book, in which the following quote appeared: _“There are more molecules in a glass of water thean there are glasses of water in the oceans…”_ Is this correct, or merely bad poetic science? If it is correct, how small a {measure} of water would ‘equal’ (approximately) the number of {that measure} in the oceans? A thimble-full? A tea-spoon? A single raindrop? Less? Thanks… ---
**Author:** ![Peanuthead](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/peanuthead/32/360_2.png) [@Peanuthead](https://boards.straightdope.com/u/Peanuthead)\ **Post date:** [September 9, 2002, 9:52am UTC](https://boards.straightdope.com/t/can-anyone-verify-this-analogy/127624/2 "2002-09-09T09:52:48Z")
Sounds kind of like “How many angels can dance on the head of a pin”, and won’t last too long in this forum. But if you really want to know… There are exactly 887,563,947,568,547.3 glasses of water in the oceans. ---
**Author:** ![Sublight](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@Sublight](https://boards.straightdope.com/u/Sublight)\ **Post date:** [September 9, 2002, 10:00am UTC](https://boards.straightdope.com/t/can-anyone-verify-this-analogy/127624/3 "2002-09-09T10:00:17Z")
Well, one mole (6 x 10[sup]23[/sup] molecules) of water would weigh 18 grams and take up 18ml of space. A glass holding 360ml (about the size of a 10oz. can) would therefore contain 20 moles, or 1.2 x 10[sup]25[/sup] molecules. 1.2 x 10[sup]25[/sup] of these glasses of water would have a volume of 4.3 x 10[sup]27[/sup]ml, or 4.3 x 10[sup]9[/sup]km[sup]3[/sup], which would make a solid sphere of water with a diameter of about 1000km. The Earth has a radius of 10,000km, and a surface area of about 1 billion km[sup]2[/sup], 70% of which is covered by water. If we assume an average depth of 2km, that gives a volume of 1.4 x 10[sup]9[/sup]km[sup]3[/sup]. So, the number of molecules in a glass of water is greater than the number of glasses of water in the ocean, but only by a factor of about three. Considering how many assumptions and approximations I’ve made, they can be called essentially equal. Now all you need is someone who can show what mistakes I’ve inevitably made and give you the real answer. ---
**Author:** ![Sublight](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@Sublight](https://boards.straightdope.com/u/Sublight)\ **Post date:** [September 9, 2002, 10:04am UTC](https://boards.straightdope.com/t/can-anyone-verify-this-analogy/127624/4 "2002-09-09T10:04:18Z")
Btw, my figure of 2km for the average depth of the ocean was rectally-derived, so if anyone knows the real figure, use that instead. ---
**Author:** ![Aro](https://avatars.discourse-cdn.com/v4/letter/a/b3f665/32.png) [@Aro](https://boards.straightdope.com/u/Aro)\ **Post date:** [September 9, 2002, 10:11am UTC](https://boards.straightdope.com/t/can-anyone-verify-this-analogy/127624/5 "2002-09-09T10:11:16Z")
Thanks \*\* Sublight \*\*, Even within the obvious necessity for guesswork and approximations, it seem the quote DOES have some credence to real figures. (Well, close enough for me) I just liked how it sounded as an analogy, and just wanted to check it out before repeating it, and thus perpetuating any further ignorance. 🙂 BTW, **Peanuthead** , as this was a question with a (approximately) verifable & thus factual answer, it was CORRECTLY placed in this forum. Angels on pins indeed. :rolleyes: ---
**Author:** ![jjimm](https://avatars.discourse-cdn.com/v4/letter/j/ba8739/32.png) [@jjimm](https://boards.straightdope.com/u/jjimm)\ **Post date:** [September 9, 2002, 10:18am UTC](https://boards.straightdope.com/t/can-anyone-verify-this-analogy/127624/6 "2002-09-09T10:18:08Z")
**Sublight** , [this site](http://ga.water.usgs.gov/edu/earthwherewater.html) gives the volume of the oceans at 317,000,000 miles[sup]3[/sup]. Since 1 mile[sup]3[/sup] = 4.1682 km[sup]3[/sup], the approximate volume of the oceans is ~ 1.3 x 10[sup]9[/sup]. That’s one extraordinary ass-sourced estimate you achieved! ---
**Author:** ![Kreekurmudgeon](https://avatars.discourse-cdn.com/v4/letter/k/9f8e36/32.png) [@Kreekurmudgeon](https://boards.straightdope.com/u/Kreekurmudgeon)\ **Post date:** [September 9, 2002, 1:08pm UTC](https://boards.straightdope.com/t/can-anyone-verify-this-analogy/127624/7 "2002-09-09T13:08:35Z")
Hereafter, when Sublight speaks, I listen. ---
**Author:** ![Go\_alien](https://avatars.discourse-cdn.com/v4/letter/g/9d8465/32.png) [@Go\_alien](https://boards.straightdope.com/u/Go_alien)\ **Post date:** [September 9, 2002, 1:18pm UTC](https://boards.straightdope.com/t/can-anyone-verify-this-analogy/127624/8 "2002-09-09T13:18:04Z")
Hearafter, when Sublight farts, I listen. 😃 ---
**Author:** ![jjimm](https://avatars.discourse-cdn.com/v4/letter/j/ba8739/32.png) [@jjimm](https://boards.straightdope.com/u/jjimm)\ **Post date:** [September 9, 2002, 1:41pm UTC](https://boards.straightdope.com/t/can-anyone-verify-this-analogy/127624/9 "2002-09-09T13:41:45Z")
Hereafter, when Sub lights his farts, I listen. 😃 ---
**Author:** ![zut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zut/32/2875_2.png) [@zut](https://boards.straightdope.com/u/zut)\ **Post date:** [September 9, 2002, 2:26pm UTC](https://boards.straightdope.com/t/can-anyone-verify-this-analogy/127624/10 "2002-09-09T14:26:26Z")
> [@](#): > > \*Originally posted by Sublight \* > 1.2 x 10[sup]25[/sup] of these glasses of water would have a volume of 4.3 x 10[sup]27[/sup]ml, or 4.3 x 10[sup]9[/sup]km[sup]3[/sup], which would make a solid sphere of water with a diameter of about 1000km. **Sublight** , I think you made an error here. You use the conversion 1 km[sup]3[/sup] = 10[sup]18[/sup]ml. Since 1 ml = 1 cc, this ought to be 1 km[sup]3[/sup] = 10\*\*[sup]15[/sup]\*\*ml. So, using **jjimm** ’s source and your previous calculation: 1 glass water = 360ml = 1.2 x 10[sup]25[/sup] molecules. Ocean = 1.3 x 10[sup]9[/sup] km[sup]3[/sup] = 1.3 x 10[sup]24[/sup] ml = 3.6 x 10[sup]21[/sup] glasses of water. Still more molecules in a glass of water than glasses of water in the ocean. 1 tsp water = 5ml = 6 x 10[sup]23[/sup]\*0.28 molecules = 1.7 x 10[sup]23[/sup] molecules. Ocean = 1.3 x 10[sup]24[/sup] ml = 2.6 x 10[sup]23[/sup] tsp. So, for **Aro** ’s last question: there are about as many molecules in a teaspoon as there are teaspoons in the ocean (teaspoon-and-a-quarter, actually). If I did the math right. ---
**Author:** ![Aro](https://avatars.discourse-cdn.com/v4/letter/a/b3f665/32.png) [@Aro](https://boards.straightdope.com/u/Aro)\ **Post date:** [September 9, 2002, 2:35pm UTC](https://boards.straightdope.com/t/can-anyone-verify-this-analogy/127624/11 "2002-09-09T14:35:21Z")
Cheers **Zut**. A teaspoon full it is, then. Makes my head _all funny_ to think in terms of there being so many microscopic millions/billions of '_wee things’_ like that, just in a spoonful. 😃 ---
**Author:** ![Sublight](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@Sublight](https://boards.straightdope.com/u/Sublight)\ **Post date:** [September 9, 2002, 10:37pm UTC](https://boards.straightdope.com/t/can-anyone-verify-this-analogy/127624/12 "2002-09-09T22:37:27Z")
Yep, I just woke up ten minutes ago and immediately realized my mistake. 1ml = 1cm[sup]3[/sup], not 1mm[sup]3[/sup]. That throws my answer off by a factor of 1000. So, actually, they’re not equal. There’s about 1000x more molecules in a glass than glasses in the ocean. **jjimm** , be careful when I light my farts, with my miscalculations I might end up flattening the whole building. “Hmmm… take the diameter, raise to the fourth power, times the coefficient… yeah, you’re safe.” FOOOMM!!! “Oh, wait, _third_ power! Sorry about that.” 😃 (we need a ‘smokey’ smiley!) Still, may I use that as a sig?