You live at the bottom of an ocean of air. At sea level it presses with about $100\ \mathrm{kPa}$ — the weight of everything overhead. Climb, and you leave some of that ocean below you, so the pressure falls. But air is squashable where water is not, so the fall is not a straight line: the real formula is an exponential decay, and this lesson tames it with two honest estimating rules.

Small climbs: near sea level the toll is about 12 kPa per kilometre. Big climbs: the pressure halves about every 5,500 m — half at 5,500 m, a quarter at 11,000 m, an eighth at 16,500 m, on and on. That is why jets pressurize their cabins and why Everest climbers carry bottled oxygen: near the summit, every breath collects about a third of the molecules a sea-level breath does. Estimate FIRST, always — a five-second guess catches almost every slip before the arithmetic starts.