The highest and lowest elevations in the continental United States (the "Lower 48" more precisely) are both found in the state of California. Astoundingly, they are less than 88 miles (142 kilometers) apart with an elevation change approaching 15,000 feet.
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The California Highpoint is Mount Whitney at 14,494 feet (4,418 meters) above sea level, which crowns the mighty Sierra Nevada range. It continues to grow.
The lowest point in the United States, and anywhere in North America for that matter, is the Badwater Basin in Death Valley National Park just to the east. It is below sea level, in fact significantly so, at an elevation of -282 feet (-86 meters). The basin contains a small spring-fed pool where salts that have accumulated over the ages have poisoned it, thus the name "badwater." While the pool is marked as the lowpoint, the actual spot will be found a little further to the west. In other words, the real lowpoint is actually closer to Mt. Whitney than what I’ve drawn on the maps. Nonetheless, the lowpoint sign has been located at the badwater pool as a matter of convenience. It’s exceedingly dangerous to cross this basin and incidentally the lowpoint is never fixed in one spot for long, rather it shifts as weather conditions change.
Another interesting phenomenon is that while the two points are only about 88 miles (142 kilometers) apart, one would need to travel 135 miles (217 kilometers) by road between them because of the mountainous terrain that deflects a straight line.