Atmospheric pressure

Right now a column of air stretching all the way up through the atmosphere is pushing down on you with a force equivalent to the weight of a small car spread over your body — yet you don't feel crushed. This is atmospheric pressure: the push exerted by the weight of the air surrounding the Earth on every surface it touches, including your skin. It sounds dramatic, but it is completely ordinary — you have lived inside it your whole life. This article extends the pressure idea you already know from solids and liquids to the air itself, shows two simple activities that prove air pushes on things, gives a rough sense of just how large that push is, and explains why an invisible force strong enough to crush a tin can leaves you completely unharmed.

The core insight

Air has weight, so the atmosphere pushes on every surface with a large, usually unnoticed force called atmospheric pressure, balanced from the inside by the pressure of our own body fluids.

The core idea

Just like solids and liquids, air also exerts pressure — this is called atmospheric pressure. It arises because the entire column of air above any point, stretching many kilometres upward, has weight, and that weight presses down (and, because air is a fluid, also sideways and upward against undersides) on every surface it touches. The same basic definition of pressure that you use for solids and liquids still applies here:

Pressure=ForceArea\text{Pressure} = \dfrac{\text{Force}}{\text{Area}}

where: Force is the push exerted by the air (in newtons, N) and Area is the surface it acts on (in square metres, m²), giving pressure in pascals (Pa), where 1 Pa=1 N/m21\ \text{Pa} = 1\ \text{N/m}^2. Two classroom activities make this invisible push visible. In the folded-vs-unfolded paper activity, a flat sheet of paper is pressed against the mouth of a glass or plate that has been turned upside down, with a partial vacuum trapped inside. A large, unfolded sheet is far harder to pull off than a small, folded piece of the same paper — because the atmosphere pushes on the larger outer area with a much bigger total force, holding it firmly in place even though the pressure itself is the same in both cases. In the rubber sucker activity, pressing a suction cup onto a smooth surface squeezes most of the air out from underneath it, leaving a region of much lower pressure inside. The full atmospheric pressure pushing on the sucker from outside is now far greater than the low pressure trapped inside, and this pressure difference is what clamps the sucker to the surface. How large is this push? The force exerted by the column of air above a small area of about 15 cm times 15 cm is roughly equal to the weight of a 225 kg mass, about 2250 N — atmospheric pressure is invisible but genuinely large. So why aren't we crushed? Our bodies also contain air and fluids that push outward from the inside, and this internal pressure is, on average, equal to the atmospheric pressure pushing in from outside. The two pushes balance, so we feel nothing — until that balance is disturbed, such as when a plane cabin loses pressure or your ears "pop" going up a hill.

Figure
A sealed jar with a folded sheet of paper on top held down by downward air-pressure arrows, next to a suction cup on a wall held on by an inward air-pressure arrow against a low-pressure pocket underneath
Two proofs that air pushes on surfaces paper on inverted glass air pushes down on paper bigger sheet, bigger total force, harder to pull off rubber sucker on a wall low P outside air pushes in high outside pressure vs low inside pressure holds it stuck
Derivation AEstimating atmospheric pressure from its everyday force

The goal is to take the everyday fact that the air above a 15 cm by 15 cm patch weighs roughly as much as a 225 kg mass, worth about 2250 N of force, and turn it into a numerical value for atmospheric pressure in pascals, using nothing beyond the basic definition of pressure and unit conversion of the area from centimetres to metres, so that the size of atmospheric pressure stops being an abstract claim and becomes a checkable number.

Step 1. Write down the known values. The force pressing down on the patch is F≈2250 NF \approx 2250\ \text{N}, and the patch has side length 15 cm=0.15 m15\ \text{cm} = 0.15\ \text{m}, so its area is A=0.15 m×0.15 m=0.0225 m2A = 0.15\ \text{m} \times 0.15\ \text{m} = 0.0225\ \text{m}^2.

Step 2. Apply the pressure formula. Since Pressure=F/A\text{Pressure} = F/A, substituting the values gives Pressure=2250 N0.0225 m2\text{Pressure} = \dfrac{2250\ \text{N}}{0.0225\ \text{m}^2}.

Step 3. Carry out the division. 2250÷0.0225=100,0002250 \div 0.0225 = 100{,}000, so Pressure≈100,000 N/m2=100,000 Pa\text{Pressure} \approx 100{,}000\ \text{N/m}^2 = 100{,}000\ \text{Pa}.

Step 4. Interpret the number. One lakh pascals acting on every square metre of your body is an enormous total force, yet you feel nothing, because the pressure of the fluids and air inside your body pushes outward with almost exactly the same 100,000 Pa, cancelling the inward push and leaving no net force on your skin.

Worked example

The atmosphere pushes down on an area of 15 cm times 15 cm with a force roughly equal to the weight of a 225 kg mass, taken as 2250 N. In the folded-paper activity, a student presses a large unfolded sheet of area 0.08 m² against the mouth of an inverted glass, and separately presses a small folded piece of area 0.02 m² against an identical glass, with the atmosphere pushing at roughly 100,000 Pa in both cases. Find the atmospheric pressure from the first setup, then find and compare the total force holding each piece of paper.

Step 1. Find the pressure from the 15 cm by 15 cm patch, as in the derivation above: Pressure=2250 N/0.0225 m2=100,000 Pa\text{Pressure} = 2250\ \text{N} / 0.0225\ \text{m}^2 = 100{,}000\ \text{Pa}. This is the value used for the paper pieces too, since the atmospheric pressure at a given place is the same everywhere nearby, regardless of the shape of the surface it acts on.

Step 2. Rearrange the pressure formula to find force: Force=Pressure×Area\text{Force} = \text{Pressure} \times \text{Area}.

Step 3. Force on the large sheet: F1=100,000 Pa×0.08 m2=8000 NF_1 = 100{,}000\ \text{Pa} \times 0.08\ \text{m}^2 = 8000\ \text{N}. Force on the small folded piece: F2=100,000 Pa×0.02 m2=2000 NF_2 = 100{,}000\ \text{Pa} \times 0.02\ \text{m}^2 = 2000\ \text{N}.

Step 4. Compare. The large sheet is held down by 8000 N, four times the 2000 N holding the small folded piece — because it has four times the area for the same atmospheric pressure to act on, which is why the large sheet is so much harder to peel off the glass.

Competitive stretch

If a much larger inverted tray had an opening of area 0.5 m², the same 100,000 Pa atmospheric pressure would hold a sheet covering it with a force of 100,000×0.5=50,000 N100{,}000 \times 0.5 = 50{,}000\ \text{N} — about the weight of a loaded truck, all supplied by ordinary air pressure and a partial vacuum, with no glue involved.

Common traps

  • Thinking atmospheric pressure is negligible because it is invisible — the worked example shows it is about 100,000 Pa, a genuinely large value.
  • Believing the rubber sucker "sucks" using some special force — it works purely because removing air from underneath lowers the pressure there, letting the unchanged outside atmospheric pressure hold it in place.
  • Assuming we should feel crushed by atmospheric pressure — we don't, because the pressure inside our bodies balances the pressure of the atmosphere outside.
  • Confusing "larger area held" with "larger pressure" — the atmospheric pressure is the same in both paper pieces; only the total force (pressure times area) changes with area.

Ask the tutor: Curious why airplane cabins are pressurised or why your ears pop going up a hill — ask the AI tutor to connect those everyday experiences to atmospheric pressure.

If atmospheric pressure is really 100,000 Pa, why don't I feel it pressing on me all the time

You are built to live inside this pressure, so your body's internal fluids and the air in your lungs and sinuses push outward with almost exactly the same 100,000 Pa. The two pushes cancel, leaving no net force on your skin, which is why you feel nothing even though a huge force is technically acting on you. You only notice atmospheric pressure changing, such as your ears popping when a lift or plane changes altitude quickly, because the balance is briefly disturbed.

Does a rubber sucker create its own pulling force, like a magnet

No. A sucker has no pulling force of its own. Pressing it onto a surface squeezes out most of the air trapped underneath, so the pressure inside the small gap becomes much lower than the atmospheric pressure outside. The ordinary, unchanged atmosphere pushing in from outside is now stronger than the low pressure pushing out from inside, and that pressure difference is what holds the sucker firmly against the surface — the "pull" you feel is really the atmosphere pushing.

Why does the folded paper come off more easily than the flat sheet, if the pressure is the same on both

Pressure being equal does not mean force is equal. Force equals pressure times area, so with the same 100,000 Pa acting on both pieces, the larger unfolded sheet, with more area exposed to the atmosphere, is held by a much bigger total force than the smaller folded piece. It is the area, not the pressure, that changes between the two cases, which is why comparing forces rather than pressures explains the difference you observe.

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