# How long can you tread water?

August 18, 2008 8:15 PM Subscribe

If everyone in the world got in the ocean at the same time, how much would sea levels rise?

I'm leaving aside various practical questions about how this would be arranged, of course. If everyone in the world got in the oceans, say, up to their necks, how much water would be displaced, and how would sea level be affected? What are the elements necessary to construct the formula to work this out?

I'm leaving aside various practical questions about how this would be arranged, of course. If everyone in the world got in the oceans, say, up to their necks, how much water would be displaced, and how would sea level be affected? What are the elements necessary to construct the formula to work this out?

The ICRP standard man is 70kg. Find the average density of humans, use that to convert 70kg to units of volume like liters. Then multiply that number by the total population of the earth. That will be how many liters of water would be displaced.

posted by pseudonick at 8:31 PM on August 18, 2008

posted by pseudonick at 8:31 PM on August 18, 2008

Best answer: Let's assume the average human takes up 70L of volume.

70 L * 6 billion = 420 000 000 m^3

420 000 000 (m^3) = 0.42 km^3

Various googled sources give the volume of the earth's oceans at between 1.3 and 1.6 billion km^3

So, none at all. Like, not even a little tiny bit.

posted by Space Coyote at 8:32 PM on August 18, 2008 [5 favorites]

70 L * 6 billion = 420 000 000 m^3

420 000 000 (m^3) = 0.42 km^3

Various googled sources give the volume of the earth's oceans at between 1.3 and 1.6 billion km^3

So, none at all. Like, not even a little tiny bit.

posted by Space Coyote at 8:32 PM on August 18, 2008 [5 favorites]

PS. it took my grade 7 math teacher a lot of time and exasperated effort to try to explain to me just how much bigger units cubed are than cubed units. It's pretty crazy how much manmeat you could pack into a couple of gravel pits if we really had to.

posted by Space Coyote at 8:37 PM on August 18, 2008

posted by Space Coyote at 8:37 PM on August 18, 2008

First, you have to know the volume of the average human being. Then you need the surface of the sea on earth.

Say we're approximately a box 0,5m wide by 1,5m high by 0,2m deep each, that gives you a volume of 0,15 cubic metres per person. There's 6 billions of us, so the total volume of humanity is 900 millions of cubic metres. Now, it is known that the oceans make for 2/3 of the earth surface, so if the radius of earth is 6400 km (6.4*10^6 m), and the earth is a sphere, the earth surface is 4*pi* r^2 = 5.14*10^14m^2, of which 2/3 (3.43*10^14m^2) are the ocean surface. Finally, you divide the volume of humanity (or of water displaced) by this surface and you get the height of the seawater rise.

The result is - if all my calculations are correct - in the order of the micron (10^-6 meters), and my really gross estimates might move it up or down an order of magnitude, tops.

Bottom line, all of humanity dipped in the oceans would not raise them more than a hair's thickness.

posted by _dario at 8:39 PM on August 18, 2008

Say we're approximately a box 0,5m wide by 1,5m high by 0,2m deep each, that gives you a volume of 0,15 cubic metres per person. There's 6 billions of us, so the total volume of humanity is 900 millions of cubic metres. Now, it is known that the oceans make for 2/3 of the earth surface, so if the radius of earth is 6400 km (6.4*10^6 m), and the earth is a sphere, the earth surface is 4*pi* r^2 = 5.14*10^14m^2, of which 2/3 (3.43*10^14m^2) are the ocean surface. Finally, you divide the volume of humanity (or of water displaced) by this surface and you get the height of the seawater rise.

The result is - if all my calculations are correct - in the order of the micron (10^-6 meters), and my really gross estimates might move it up or down an order of magnitude, tops.

Bottom line, all of humanity dipped in the oceans would not raise them more than a hair's thickness.

posted by _dario at 8:39 PM on August 18, 2008

Well, the amount of water displaced would be equal to the total volume of humanity.. going from Yahoo Answers we get a (rough) estimate of the total human volume as 12 Billion cubic feet.

Now, how much would the seas rise if you dumped that much volume into it? We should grab the oceans' total volume, which This seemingly-reasonable website gives at around 1.37 Billion cubic kilometers.

Now we convert the CuFeet to CuKm, and so we have about 0.34 CuKm. So roughly speaking, the total volume of humanity is about 2.5 * 10^(-8) % of the volume of the oceans, which in non-scientific notation is 0.000000025%. I'm reasonably certain that they'll climb that percentage of their total size? Someone less tired / foolish than I should check that step.

But a rough answer is "not much"

posted by Lemurrhea at 8:43 PM on August 18, 2008

Now, how much would the seas rise if you dumped that much volume into it? We should grab the oceans' total volume, which This seemingly-reasonable website gives at around 1.37 Billion cubic kilometers.

Now we convert the CuFeet to CuKm, and so we have about 0.34 CuKm. So roughly speaking, the total volume of humanity is about 2.5 * 10^(-8) % of the volume of the oceans, which in non-scientific notation is 0.000000025%. I'm reasonably certain that they'll climb that percentage of their total size? Someone less tired / foolish than I should check that step.

But a rough answer is "not much"

posted by Lemurrhea at 8:43 PM on August 18, 2008

Roughly, a person is, oh, I don't know, 50 kilograms (on average, taking into account that a bunch of people are children of various sizes).

Roughly, a person is the density of water, i.e. 1 gram per cubic centimeter.

Hence, a person is roughly 50,000 cubic centimeters.

Roughly, "up to your neck" is "completely submerged", so let's say 50,000 cubic centimeters of displacement per person.

Roughly, there are 6.7 billion people.

Hence, all people combined would displace about 335 trillion cubic centimeters, or a third of a cubic kilometer.

Roughly, the world is a sphere of radius 6400 kilometers. The volume of a sphere is 4 * pi * (radius ^ 3) / 3. Its volume is therefore about a trillion cubic kilometers.

Adding a third of a cubic kilometer to this volume while retaining sphericity would require that its radius increases by approximately, well, zero.

So, zero effect on sea levels.

Roughly.

posted by Flunkie at 8:54 PM on August 18, 2008

Roughly, a person is the density of water, i.e. 1 gram per cubic centimeter.

Hence, a person is roughly 50,000 cubic centimeters.

Roughly, "up to your neck" is "completely submerged", so let's say 50,000 cubic centimeters of displacement per person.

Roughly, there are 6.7 billion people.

Hence, all people combined would displace about 335 trillion cubic centimeters, or a third of a cubic kilometer.

Roughly, the world is a sphere of radius 6400 kilometers. The volume of a sphere is 4 * pi * (radius ^ 3) / 3. Its volume is therefore about a trillion cubic kilometers.

Adding a third of a cubic kilometer to this volume while retaining sphericity would require that its radius increases by approximately, well, zero.

So, zero effect on sea levels.

Roughly.

posted by Flunkie at 8:54 PM on August 18, 2008

To look at it a slightly different way, take the ocean area, 3.43*10^14m^2, and divide it by 6 billion people. You get 0.6*10^5 = 6*10^4 m^2 per person. In other words, build a tank with a diameter of 280 meters (about 300 yards) and plunk

posted by exphysicist345 at 9:09 PM on August 18, 2008 [5 favorites]

*one*person into it. The water level will rise the same amount as dumping everybody in the ocean. As you can see from this thought-experiment, it's negligibly small.posted by exphysicist345 at 9:09 PM on August 18, 2008 [5 favorites]

Here's another way to think about it. If you took all 6 billion people on the planet and stood them up tightly packed, they would just about fit in the five boroughs of New York City. Now look at New York City on a globe. It looks like a pinpoint. It is an insignificant speck that would have no noticeable effect on sea level. Even though we think of the earth as crowded, this analogy gives you an idea of how insignificant the human population really is.

posted by JackFlash at 9:54 PM on August 18, 2008 [3 favorites]

posted by JackFlash at 9:54 PM on August 18, 2008 [3 favorites]

Even more so, I recently read an article (it's too late to cite) that stated that the melting glaciers of greenland/arctic will take months if not years to make any sort of change at all in the pacific and indian oceans. the ocean does not spontaneously rise all at the same time.

posted by Mach5 at 10:55 PM on August 18, 2008

posted by Mach5 at 10:55 PM on August 18, 2008

I think most of the preceding calculations are incorrect. People float, so our displacement is only a function of our weight, not our volume.

70kg standard human, times 6e9 humans, divided by one kg per liter, gives us 4.2e11 liters total displacement; that's 4.2e8 cubic meters; the surface area of the oceans is very roughly 75% of the earth's surface or 3.8e14 square meters; so that much additional volume spread over the surface of the oceans is 1.1e-6 meter, that is, roughly one micron.

JackFlash: Alternatively, we could all stand on Zanzibar.

posted by hattifattener at 12:00 AM on August 19, 2008

70kg standard human, times 6e9 humans, divided by one kg per liter, gives us 4.2e11 liters total displacement; that's 4.2e8 cubic meters; the surface area of the oceans is very roughly 75% of the earth's surface or 3.8e14 square meters; so that much additional volume spread over the surface of the oceans is 1.1e-6 meter, that is, roughly one micron.

JackFlash: Alternatively, we could all stand on Zanzibar.

posted by hattifattener at 12:00 AM on August 19, 2008

First of all, people are basically as dense as water. The degree to which we are different from water is utterly insignificant with respect to this calculation, just as is the difference between the world's population and "6 billion", or between the average mass of a human and "70 kg", or between the percentage of the earth covered by water and "75%", or between that area and "3.8e14 square meters", or any number of other gross approximations that we are all making here, yourself included.I think most of the preceding calculations are incorrect. People float, so our displacement is only a function of our weight, not our volume.

Second, regardless of whether we normally bob like a cork or sink like lead or anything in between, the volume that we displace is exactly equal to our volume under the water line, and the poster explicitly said we were up to our necks in water. We therefore displace our volume, minus the volume of our heads; our mass is not relevant, except in terms of calculating our volume, minus the volume of our heads.

And again, in the grand scheme of things where "6 billion people" represents an acceptable level of accuracy, "minus the volume of our heads" can be safely ignored.

Finally, given all of these facts, your claim that the calculations preceding yours are "incorrect" because of this, together with the fact that you authoritatively say "one micron", strikes me as fundamentally absurd.

posted by Flunkie at 12:52 AM on August 19, 2008

Agree with Flunkie- we've already solved for mass and buoyancy because we already assumed that everyone would be up to their necks. So yes, it's just volume at that point.

And there's got to be a lawyer joke and an obese Americans joke in here somewhere.

posted by gjc at 7:09 AM on August 19, 2008

And there's got to be a lawyer joke and an obese Americans joke in here somewhere.

posted by gjc at 7:09 AM on August 19, 2008

*People float, so our displacement is only a function of our weight, not our volume.*

As I learned in Red Cross lifeguard training, people don't exactly "float;" they achieve neutral bouyancy when the entire body is submerged to about eye level, with just a little forehead and crown peeking out. That's not the same thing as floating, and is an important factor in why people sometimes drown. You are displacing almost your entire volume when neutrally balanced in water.

posted by Miko at 7:09 AM on August 19, 2008

there are some good answers here, but also some that get to the right answer through dodgy reasoning. in the hope that this will help the original poster understand here are some clarifications:

- floating bodies displace an amount of water whose weight is equal to the weight of the body supported (this is, roughly, what archimedes got all excited about in his bath). since water has a density of 1 kg per litre, and because typically people only just float, the volume of water displaced in litres is about the same as both the weight of people in kg and their volume in litres.

- to find the increase in depth you need to divide the total extra water by the

despite the various errors the general conclusion - that the increase would be negligible - sounds about right...

posted by not sure this is a good idea at 8:25 AM on August 19, 2008

- floating bodies displace an amount of water whose weight is equal to the weight of the body supported (this is, roughly, what archimedes got all excited about in his bath). since water has a density of 1 kg per litre, and because typically people only just float, the volume of water displaced in litres is about the same as both the weight of people in kg and their volume in litres.

- to find the increase in depth you need to divide the total extra water by the

*area*of the existing oceans. some people mentioned the*total volume*which is just wrong (you can see this because the increase would be the same whether the oceans are 6 feet or several miles deep - in both cases you are just adding a thin layer on top).despite the various errors the general conclusion - that the increase would be negligible - sounds about right...

posted by not sure this is a good idea at 8:25 AM on August 19, 2008

Response by poster: Lots if interesting responses. I suspected the answer would be not much, if any. Thanks, all.

posted by doift at 1:54 PM on August 20, 2008

posted by doift at 1:54 PM on August 20, 2008

This thread is closed to new comments.

how much water would be displacedI think the amount has to be equal to the volume of the displacing object, so you'd need to know the volume of all combined human beings to begin to look at this.

I'm no hydrophysicist so I'm going to stop there. But my gut instinct is to say that sea levels would not rise much, because a) the ocean is really really big and b) there are already a lot of things displacing the water in the oceans, namely thousands and thousands of enormous tanker ships equalling a not insignificant volume of human bodies, not to mention untold millions of small craft, inner tubes, oil platforms, shipwrecks, etc., -- and the localized effect from all that seems to be minimal.

posted by Miko at 8:31 PM on August 18, 2008