How Much Does Earth's Atmosphere Weigh?
A classic physics Fermi problem combining pressure, area, and mass.
The Key Insight
Atmospheric pressure is the weight of air per unit area. So:
- Pressure = Weight / Area
- Weight = Pressure × Area
# Sea level atmospheric pressure
pressure = atm
# Earth's surface area
area = earth_surface_area5.10e+14 m^2 {area}
Calculation
# Total weight (force) of atmosphere
atmosphere_weight = pressure * area
# Convert to mass using g = 9.81 m/s²
atmosphere_mass = atmosphere_weight / g5.27e+18 Pa m s^2 {mass}
Result
The atmosphere weighs approximately 5.27e+18 Pa m s^2 {mass} (as a mass).
That's about 5 × 10^18 kg, or about 5 quintillion kilograms!
Sanity Check
# Mass per square meter at surface
mass_per_sqm = atmosphere_mass / area10332 (Pa s^2) / m
The mass per square meter is 10332 (Pa s^2) / m, which makes sense - roughly 10 tonnes pressing down on every square meter.