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I've read somewhere that above 2500 meters (8,202 ft) 20% of climbers report having had altitude sickness. IIRC they also wrote that 40% of climbers report altitude sickness above 3500 meters (11,500 ft) though I'm unsure about the latter value. I wonder at what altitude the percentage approaches 50% and more. Preferrably in mid-latitude mountains (such as the Alps, the New Zealand Southern Alps, the Cascade range, northern Colorado or the Caucasus) because at the mid-latitudes the atmospheric pressure at an elevation should be about the same as at the pressure altitude on an aircraft's altimeter. Answer may include values from high altitude chambers.

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    I don't think there's a single number, as age, gender, physical condition, home elevation, rate of ascension and a lot of other factors come into play. This paper covers the Alps and Colorado as well as Nepal. Sep 13, 2023 at 19:02
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    It can be unclear what a person means by "altitude sickness". That is, what I commonly experience on Day 1 and think of as merely an annoying headache and a feeling of blahness, which clears up overnight or in at most a day, may be somebody else's definition of altitude sickness. Is this technically altitude sickness? Perhaps, but I don't think it is helpful to lump together minor, transitory symptoms with the sort of symptoms that demand a quick retreat to a lower elevation. Calling the latter "acute altitude sickness" is helpful, but (continued)
    – ab2
    Sep 13, 2023 at 20:42
  • (continued) without more info on symptoms, "altitude sickness" by itself can mean almost anything.
    – ab2
    Sep 13, 2023 at 20:46
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    It isn't useful to compare mountaineering with the pressure in an aircraft, where the passengers are inactive, and the crew are accustomed to the reduced pressure. Sep 13, 2023 at 21:28
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    I live near 6000 feet. The only time in my life I definitely have had mild altitude sickness was when I drove to a campground at around 8000 feet. That night I had had a wicked headache and mild nausea. Before and after I've been much higher, even under similar conditions (short drive to a campground - just was up over 11,000 feet). The difference in that one time? I'd spent about two weeks at sea level, then returned home for a week before going camping. So even for one person, how and when altitude symptoms start depends on many variables.
    – Jon Custer
    Sep 18, 2023 at 12:42

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It's not definable to the level of precision you seem to be imagining, but probably somewhere around 16,000' (~4,900 meters). It depends on what criteria you use. For some references, see the introductory section of this paper: Dallimore, J., & Rowbotham, E. C. (2009). Incidence of Acute Mountain Sickness in Adolescents. Wilderness & Environmental Medicine, 20(3), 221–224. doi:10.1580/07-weme-or-119r3.1 https://sci-hub.se/10.1580/07-WEME-OR-119R3.1

There is a background rate of something like 10%, which is just because people often feel bad while they're in the mountains because of factors like lack of sleep, caffeine withdrawal, and so on: https://pubmed.ncbi.nlm.nih.gov/22441083/

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