What is atmospheric pressure?
Air is matter, so it has mass and weight. The atmosphere is a thick blanket of air around the Earth. Its weight presses on everything below it.
Pressure = force ÷ area. The atmospheric pressure at a place is the force of the air column above each square metre. At sea level it is about 101 300 Pa (101.3 kPa). This value is called 1 atmosphere (1 atm).
Pressure in air acts in all directions: down, up and sideways. That is why we are not crushed: the air and fluids inside our body push outward with the same pressure.
Proving the air pushes
- Straw: sucking lowers the pressure in the straw; the outside air pushes the drink up.
- Card on a glass: fill a glass with water, cover with card, turn it over. The air pushes up on the card harder than the water pushes down.
- Can crush: heat a little water in an open can, then turn it upside down into cold water. Steam turns back to water, the inside pressure drops, and outside air crushes the can.
- Suction hook: pressing it squeezes out air; the outside air holds it to the wall.
- Magdeburg hemispheres (1654): two metal half-spheres with the air pumped out could not be pulled apart by teams of horses.
Measuring it: the barometer
In 1643 Evangelista Torricelli filled a glass tube about 1 m long with mercury and turned it upside down in a dish of mercury. The mercury fell until the column was about 760 mm tall, leaving a vacuum at the top. The air pushing on the dish holds up the column.
Pressure of a liquid column: p = ρ g h. For mercury: 13 600 × 9.8 × 0.76 ≈ 101 000 Pa. With water (ρ = 1000 kg/m³) the column would need to be about 10.3 m tall, which is why mercury is used.
An aneroid barometer has no liquid: a thin sealed metal box squeezes in or bulges out as pressure changes, and a needle shows it. An altimeter in an aircraft is an aneroid barometer marked in metres.
Pressure falls with height
As you go up, there is less air above you, so pressure falls. Air also gets thinner (less dense), so the fall is fast at first and slower higher up. Roughly, pressure halves every 5.5 km.
| Place | Height | Pressure |
|---|---|---|
| Sea level | 0 km | ≈ 101 kPa |
| Leh, Ladakh | 3.5 km | ≈ 66 kPa |
| Mount Everest top | 8.8 km | ≈ 33 kPa |
| Airliner cruise | 11 km | ≈ 23 kPa |
Effects: water boils below 100 °C on mountains (cooking takes longer; pressure cookers help), climbers get less oxygen per breath, ears "pop" in lifts and aircraft, and sealed packets swell.
Hydrostatic balance
Think of a thin layer of still air, thickness Δz, area A. Three forces act on it:
- pressure from below pushing up: p × A
- pressure from above pushing down: (p + Δp) × A
- its weight: ρ g A Δz
If the layer does not move up or down, these balance, giving Δp / Δz = − ρ g. Pressure decreases with height at a rate equal to the air density times g. This is hydrostatic balance. Near the ground ρ ≈ 1.2 kg/m³, so pressure falls about 12 Pa for every metre you rise (about 1 hPa per 8 m).
Weather maps use this: a column of cold, dense air loses pressure faster with height than a warm column.
Air pressure and wind
Pressure is not exactly the same everywhere at sea level. Warm air rises, leaving low pressure near the ground; cool air sinks, making high pressure. Air moves from high to low pressure: this is wind. The bigger the pressure difference over a distance (the pressure gradient), the stronger the wind.
Lines joining places of equal pressure are isobars. Close isobars mean strong wind. Low-pressure areas often bring clouds and rain; high-pressure areas bring clear, calm weather. Sea breezes and the monsoon are big examples of air flowing toward lower pressure. Weather pressure is often given in hectopascals: 1013 hPa = 101.3 kPa.
Try it: predict, then check
Card on a glass. Predict: will the water fall when you turn the glass over? Fill a glass to the brim, place a postcard on top, hold it, turn it over over a sink and let go of the card. Then explain it with "air pushes in all directions".
In the 3D: before you drag the slider to 5.5 km, guess the pressure. Then check: it should be close to half of 101 kPa.
Key formulas and definitions
- Pressure p = F / A (unit: pascal, 1 Pa = 1 N/m²)
- Liquid column: p = ρ g h
- 1 atm ≈ 101 300 Pa = 1013 hPa = 760 mm of mercury
- Hydrostatic balance: Δp / Δz = − ρ g
- Wind blows from high pressure to low pressure
Worked examples
1. Atmospheric pressure is 101 000 Pa. What force does the air exert on a table top of area 1.5 m²?
F = p × A = 101 000 × 1.5 = 151 500 N. The table does not break because air below the table pushes up almost equally.
2. Find the height of a mercury column that balances 101 000 Pa. (ρ = 13 600 kg/m³, g = 9.8 m/s²)
h = p / (ρ g) = 101 000 / (13 600 × 9.8) = 101 000 / 133 280 ≈ 0.758 m ≈ 758 mm.
3. How tall would a water barometer be at the same pressure? (ρ = 1000 kg/m³)
h = 101 000 / (1000 × 9.8) ≈ 10.3 m. Too tall for a lab, so mercury is used.
4. Near the ground, air density is 1.2 kg/m³. Using hydrostatic balance, by how much does pressure fall when you go up a 50 m tall building?
Δp = ρ g Δz = 1.2 × 9.8 × 50 ≈ 588 Pa. The pressure at the top is about 0.6 kPa lower.
5. A barometer reads 740 mm of mercury on one day and 770 mm a few days later. Which day was more likely rainy?
The 740 mm day: lower pressure is linked to rising air, clouds and rain. The 770 mm day was probably clear.
6. Place A has 1020 hPa and place B, 100 km away, has 1004 hPa. Which way does the wind tend to blow, and what is the pressure gradient?
From A (high) to B (low). Gradient = 16 hPa per 100 km = 0.16 hPa/km.
Common mistakes
- Thinking air has no weight. Air is light, but a 1 m² column of it is about 10 tonnes.
- Saying a straw "sucks" the drink up. You only lower the pressure inside; the outside air pushes the drink up.
- Thinking pressure acts only downward. Air pressure acts equally in all directions at a point.
- Thinking pressure falls by the same amount every kilometre. It falls quickly near the ground and more slowly higher up, because the air gets thinner.