# How much, relative to sea level, does a kilogram/lb weigh at these 4 spots? What's the math? **URL:** \ **Category:** Factual Questions\ **Created:** [October 16, 2015, 7:41pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839 "2015-10-16T19:41:54Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [October 16, 2015, 7:41pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/1 "2015-10-16T19:41:54Z")
Make that 3 spots. Kind of offshoot from thread on ridiculous accuracy in cooking measurements– “Take a kilo/lb of _x_…” Say, pound cake, so named from baseline “lb of flour, lb of butter, lb of eggs, lb of sugar.” Would mean what when you are whipping one up at (all in feet; data primarily from graphic here (which unaccountably leaves off Dead Sea; Denver and Empire State Building are American units): [Highest and lowest points on Earth | Earth | EarthSky](http://earthsky.org/earth/highest-and-lowest-points-on-earth) [del]Sea level[/del] Denver 5280 La Riconada 16,700 (highest human habitation) Dead Sea -1400 (lowest) Or just give me the math and I’ll do it… I’ll also figure out for (and publish here all results for the TM clamoring in to know) Empire State Building 1450 Mt. Everest 29,000 Those long trains-oceanic flights 33,000 Kora Borehole -42,000 (deepest hole) ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [October 16, 2015, 7:52pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/2 "2015-10-16T19:52:51Z")
Gravity doesn’t vary uniformly just by height ASL, it’s [way](https://en.wikipedia.org/wiki/Gravity_anomaly), [way](https://en.wikipedia.org/wiki/Gravimetry) [more complicated](https://en.wikipedia.org/wiki/Gravity_of_Earth) than that. But that last link has the formula to do just altitude-based calculations. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [October 16, 2015, 7:54pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/3 "2015-10-16T19:54:47Z")
> [@Leo\_Bloom](#): > > … > …Say, pound cake, so named from baseline “lb of flour, lb of butter, lb of eggs, lb of sugar.” > > Would mean what … I tried to avoid it with “relative to,” but slipped up here if the sentence is read alone. On any place in the universe it would mean “lb of flour, lb of butter, lb of eggs, lb of sugar.” Of course, cooking at all these extreme environments would perhaps make ingredients rather different than expected and difficult to handle. Damn I wish I had made the hed something like “How to measure food on Mars?” If you’re a mod and reading this and in a good mood, perhaps you’ll change it? It certainly doesn’t merit a bugging pm. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [October 16, 2015, 7:59pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/4 "2015-10-16T19:59:15Z")
> [@MrDibble](#): > > Gravity doesn’t vary uniformly just by height ASL, … 😕 “ASL?” Most commonly used as “American Sign Language.” ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [October 16, 2015, 7:59pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/5 "2015-10-16T19:59:32Z")
g[sub]h[/sub] = g[sub]0/sub[sup]2[/sup] Where g[sub]h[/sub] is the gravitational acceleration at height h above sea level. r[sub]e[/sub] is the Earth’s mean radius. g[sub]0[/sub] is the standard gravitational acceleration. Finding those values in your quaint medieval measuring system I leave up to you ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [October 16, 2015, 8:00pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/6 "2015-10-16T20:00:41Z")
> [@Leo\_Bloom](#): > > 😕 “ASL?” > > Most commonly used as “American Sign Language.” Above (mean) Sea Level ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [October 16, 2015, 8:06pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/7 "2015-10-16T20:06:36Z")
> [@MrDibble](#): > > Above (mean) Sea Level :smack: ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [October 16, 2015, 8:09pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/8 "2015-10-16T20:09:44Z")
> [@MrDibble](#): > > … > Finding those values in your quaint medieval measuring system I leave up to you Yeah? Well no cake for you. ETA: What’s the lowest place on earth any human has ever been? ---
**Author:** ![Duckster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/duckster/32/1244_2.png) [@Duckster](https://boards.straightdope.com/u/Duckster)\ **Post date:** [October 16, 2015, 8:14pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/9 "2015-10-16T20:14:39Z")
> [@Leo\_Bloom](#): > > Yeah? Well no cake for you. > > ETA: What’s the lowest place on earth any human has ever been? For about 20 minutes, or so? ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [October 16, 2015, 8:17pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/10 "2015-10-16T20:17:28Z")
> [@Leo\_Bloom](#): > > What’s the lowest place on earth any human has ever been? Almost certainly [Challenger Deep](https://en.wikipedia.org/wiki/Challenger_Deep), almost 11 km below sea level. The deepest mines in the world only go about 4 km deep. > [@Duckster](#): > > For about 20 minutes, or so? James Cameron ruined that joke for us about three years ago. ---
**Author:** ![jtur88](https://avatars.discourse-cdn.com/v4/letter/j/e9c0ed/32.png) [@jtur88](https://boards.straightdope.com/u/jtur88)\ **Post date:** [October 16, 2015, 8:32pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/11 "2015-10-16T20:32:36Z")
> [@Leo\_Bloom](#): > > Yeah? Well no cake for you. > > ETA: What’s the lowest place on earth any human has ever been? I think that would depend on your definition of “lowest”. Closest to center of the earth, or furthest below sea level? As for the OP question, if your scale is a set of balances, the weight of the counter-weights would change in exactly the same way as the cake ingredients, so the premeasured flour would always perfectly balance the one-pound counterweight in the other pan, no matter where you took it – even to the moon… You might have a hard time getting your cake to bake up in La Riconada, without serious adjustments to the ingredient measures. For reasons unrelated to gravitational attraction to the batter. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [October 16, 2015, 9:02pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/12 "2015-10-16T21:02:09Z")
> [@jtur88](#): > > … for the OP question, if your scale is a set of balances, the weight of the counter-weights would change in exactly the same way as the cake ingredients, so the premeasured flour would always perfectly balance the one-pound counterweight in the other pan, no matter where you took it – even to the moon… Yes, I realized that, and added in the next post my awareness, showing one and all my skillz in Science, and am very proud of myself. > [@](#): > > …You might have a hard time getting your cake to bake up in La Riconada, without serious adjustments to the ingredient measures. For reasons unrelated to gravitational attraction to the batter. Absolutely. Let alone on Alpha Centauri. Or a black hole. Especially when sharing a stove when cooking with a cook constantly interrupting about anomalies and other gravimetric conundrums. Actually, since you’re here, there has to be a certain weight, “absolute” given certain conditions, within the realm of quantum measurement borders, right? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [October 16, 2015, 9:28pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/13 "2015-10-16T21:28:17Z")
Mass is mass, no matter where you go, and that’s what’s measured by a balance. Weight, however, depends on the local gravitational field. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [October 16, 2015, 9:34pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/14 "2015-10-16T21:34:40Z")
> [@Chronos](#): > > Mass is mass, no matter where you go, and that’s what’s measured by a balance. Weight, however, depends on the local gravitational field. See, even **Chronos** recognizes my mad skillz. (but did he think he had to weigh in (heh) because it sounded better coming from a bona-fide physicist, and not just a peon like me or **jtur**?) ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [October 16, 2015, 9:57pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/15 "2015-10-16T21:57:18Z")
I weighed in because of your last sentence, asking about an “absolute weight”. What you probably mean by that is the mass. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [October 16, 2015, 10:58pm UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/16 "2015-10-16T22:58:33Z")
> [@Chronos](#): > > Mass is mass, no matter where you go, and that’s what’s measured by a balance. Well, mass and buoyancy. Usually ignorable, but not always. ---
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [October 17, 2015, 12:06am UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/17 "2015-10-17T00:06:13Z")
> [@Dr.Strangelove](#): > > Well, mass and buoyancy. Usually ignorable, but not always. And also centrifugal motion. There is actually [a measurable difference in sensed acceleration at different latitudes](http://geophysics.ou.edu/solid_earth/notes/potential/igf.htm) for an object rotating with the Earth that is significant enough that we measure it on rocket motors and payloads to get a precise weight estimate. Stranger ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [October 17, 2015, 12:12am UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/18 "2015-10-17T00:12:18Z")
Doesn’t mass increase as we approach the speed of light? ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [October 17, 2015, 12:30am UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/19 "2015-10-17T00:30:13Z")
> [@Stranger\_On\_A\_Train](#): > > And also centrifugal motion. There is actually [a measurable difference in sensed acceleration at different latitudes](http://geophysics.ou.edu/solid_earth/notes/potential/igf.htm) for an object rotating with the Earth that is significant enough that we measure it on rocket motors and payloads to get a precise weight estimate. That’ll get cancelled on a balance scale, though, unless it’s a _really big_ balance. Though thinking about it, if you were weighing a 100 meter rocket (at the equator, for simplicity), mass at the top will weigh about 31 parts per million less than at the surface. A balance with a “short” counterweight could not sense this. ---
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [October 17, 2015, 1:07am UTC](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839/20 "2015-10-17T01:07:47Z")
You don’t measure a solid rocket motor or spacecraft with a balance scale; it is typically done with a crane and load cell. The purpose isn’t so much getting a precise weight at the location as it is assessing how much atmospheric water it may have absorbed and assuring that no propellants or other volatile components have leaked out. Stranger [Next page](https://boards.straightdope.com/t/how-much-relative-to-sea-level-does-a-kilogram-lb-weigh-at-these-4-spots-whats-the-math/734839.md?page=2)