Why Pressure Falls With Altitude
Atmospheric pressure at any point is simply the weight of the air column above it. As you ascend, there is less air above you, so the pressure drops. Near sea level, each cubic metre of air weighs about 1.2 kg, but at 10 km altitude, air density is only a third of that. The barometric formula quantifies this relationship, producing the characteristic exponential decay curve that governs everything from aircraft performance to mountain cooking.
The Barometric Formula
The barometric formula comes in two flavours. The isothermal version — P = P₀ exp(-Mgh/RT) — assumes constant temperature, which is a decent approximation for thin layers. The more realistic hypsometric version accounts for the temperature lapse rate (typically 6.5°C/km in the troposphere): P = P₀ × (1 - Lh/T₀)^(gM/RL). This simulation implements the hypsometric version and shows you the pressure, density, and boiling point at any altitude up to the stratosphere.
Practical Consequences
The pressure-altitude relationship has profound practical consequences. Aircraft altimeters work by measuring pressure and converting it to altitude via the barometric formula — which is why pilots must adjust for local pressure variations. Mountaineers above 8 km enter the 'death zone' where oxygen partial pressure is too low for sustained human survival. At 18 km (the Armstrong limit), pressure is so low that body fluids boil at 37°C without a pressure suit.
Pressure and Weather Systems
Variations in sea-level pressure drive the wind patterns we experience as weather. High-pressure systems (anticyclones, >1020 hPa) produce clear skies as air descends and warms. Low-pressure systems (cyclones, <1000 hPa) produce clouds and rain as air converges and rises. The tightest pressure gradients produce the strongest winds — a Category 5 hurricane can have a central pressure below 920 hPa, nearly 100 hPa below the surrounding environment.