Atmospheric pressure falls by half roughly every 5,500 m you climb.
Pressure decays near-exponentially with height. Everest base camp (~5,300 m) sits at about half sea-level pressure.
The scale height depends on temperature, so it is not one number: over cold polar air the halving distance is nearer 5 km, over the warm tropics closer to 6. Assume 5.5 everywhere and your altimeter is out by hundreds of metres at the extremes.
At 5,500 m the rule says 50.663 kPa and the exact answer is 50.507 kPa — within half a percent. It holds to within 5% up to 8552 m, then drifts.
Remarkably good through the altitudes anyone lives or flies a light aircraft at, and it drifts as you approach the top of the troposphere, where the atmosphere stops behaving the way the halving assumes.
The rule against the exact answer, computed across the range. Inside the shaded band the shortcut is close enough to use; outside it, reach for the calculator.
Estimate with the rule, then check it against the calculator that models it properly.
Open Altitude & Depth →Atmospheric pressure falls by half roughly every 5,500 m you climb. Pressure decays near-exponentially with height.