Pressure · System
Atmospheric pressure
A little water is boiled in an empty can, which is then sealed and cooled. The can crushes itself flat, and nothing goes anywhere near it.
Start here
Nothing touched the can.
A little water is boiled in a thin metal can until steam has driven the air out. The can is sealed and stood in cold water. It folds in on itself with a bang, in about a second.
What crushed it?
The air outside. It was pressing that hard the whole time — about 100 000 N on every square metre of that can, from every side. Nothing changed outside; what changed was inside. Steam filled the can and pushed back just as hard, and when the steam cooled it turned back into a few drops of water and stopped pushing. With the push from inside gone, the outside push had nothing to work against. Nothing sucked the can in.
You are at the bottom of an ocean of air about a hundred kilometres deep, and it has weight. All of it presses down on you, and — as with any fluid — it presses in every direction at once, roughly 100 000 Pa at sea level. Climb, and some of that air is now below you instead of above you, so there is less weight pressing and the pressure falls. Air is squashable, unlike water, so most of its mass is packed into the lowest few kilometres, which is why the pressure drops fastest near the ground.
At the bench · take three things up a mountain
Same objects. Less air above them.
Change a control to begin
A foil bag sealed at sea level, a pan of water on a stove, and a barometer. Choose a height, and choose which one to watch.
Commit first. A foil bag of crisps is sealed at sea level and carried up to 5500 m. What happens to it?
Height above sea level
What to watch
Height
—
Air pressure
—
Air left above you
—
The case
—
The relationship · a stack, not a triangle
Air pressure = weight of the air above ÷ the area it presses on
P = W ÷ A
Every layer adds its weight to what is below it.
Climb, and the layers you pass are no longer pressing on you.
Worked example · one step at a time
A window is 2 m². At sea level the air presses on it with 101 000 Pa. What force is that?
Step 0 of 5
Convert
101 000 Pa stays 101 000 Pa · 2 m² stays 2 m²
The pressure is already in pascals and the area already in square metres, so there is nothing to convert.
Formula
force = pressure × area
The same relationship as always, rearranged for the force.
Insert
force = 101 000 Pa × 2 m²
Pascals are newtons per square metre, so this will give newtons.
Fine-tune
101 000 × 2 = 202 000
Two square metres carry twice the force of one.
Answer
force = 202 000 N
Two hundred thousand newtons on one window — and the same again from inside, which is why it stays put.
Worked example · one step at a time
A skylight is 0.8 m². At a mountain station the air presses with 80 kPa. What force is that?
Step 0 of 5
Convert
80 kPa × 1000 = 80 000 Pa
A kilopascal is a thousand pascals, and only pascals times square metres give newtons.
Formula
force = pressure × area
Rearranged for the force.
Insert
force = 80 000 Pa × 0.8 m²
The converted pressure goes in. The 80 never does.
Fine-tune
80 000 × 0.8 = 64 000
Newtons per square metre times square metres leaves newtons.
Answer
force = 64 000 N
Insert 80 instead of 80 000 and the answer comes out 64 N — a thousand times too small.
Your turn · the same five steps
Your height: Sea level, where the air presses with 101 000 Pa. What force is that on one palm, 0.01 m²?
Write all five lines before you check. The pressure is the one your own bench is showing.
The five lines, marked
Convert
101 kPa × 1000 = 101 000 Pa
A kilopascal is a thousand pascals, and only pascals times square metres give newtons.
Formula
force = pressure × area
The same relationship as always, rearranged for the force.
Insert
force = 101 000 Pa × 0.01 m²
The converted pressure goes in. The 101 never does.
Fine-tune
101 000 × 0.01 = 1010
Newtons per square metre times square metres leaves newtons.
Answer
force = 1010 N
And the same force is pushing back on the other side of your hand, which is why you feel nothing.
The five lines give 1010 N on a palm at Sea level. At sea level the same palm carries about 1010 N.
A car windscreen is 1.5 m². The air outside presses on it with 98 kPa. What force is that?
This one needs the Convert line to do some work.
The five lines, marked
Convert
98 kPa × 1000 = 98 000 Pa
A kilopascal is a thousand pascals, and only pascals times square metres give newtons.
Formula
force = pressure × area
Rearranged for the force.
Insert
force = 98 000 Pa × 1.5 m²
The converted pressure goes in. The 98 never does.
Fine-tune
98 000 × 1.5 = 147 000
Newtons per square metre times square metres leaves newtons.
Answer
force = 147 000 N
Insert 98 instead of 98 000 and the answer comes out 147 N.
The five lines give 147 000 N — and the same again from inside the car, which is why the glass survives.
Key fact
Atmospheric pressure is the weight of the air above you, spread over the area it presses on — about 100 000 Pa at sea level. It falls as you climb, because less air is left above you. Nothing sucks: air pushes.
Think again
“A vacuum sucks things in.”
A vacuum is nothing, and nothing cannot pull. Every case that looks like sucking is the air on the other side pushing. Drinking through a straw: you lower the pressure in your mouth, and the atmosphere pressing on the surface of the drink pushes it up the straw. A sink plunger: you squeeze the air out, and the outside air holds it against the surface. The can at the top of this lesson: the steam stopped pushing outwards and the air outside had a free run. Rewriting these the right way round is the whole skill — what is pushing, and from where?
“If air really pressed that hard, we would feel it.”
You are pressed by roughly 100 000 Pa right now — about 1000 N on each palm — and you feel nothing, for two reasons. It pushes equally in every direction, so it does not squash you in any one direction; and the fluids and gases inside your body push out just as hard, so the two match. You only notice when the balance changes, which is exactly what your ears do on a plane or a mountain road: for a few seconds the pressure inside the eardrum no longer matches the pressure outside, and you can feel the difference until it evens out.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Calculate
Atmospheric pressure is 100 000 Pa. What force does the air push on a shop window of 1.5 m² with?
Rung 2 · The one that catches people
A foil bag of crisps sealed at sea level puffs up tight on an aircraft at cruising height. Which statement is right?
Rung 3 · Explain
Explain why atmospheric pressure at the top of a mountain is lower than at sea level. Use the weight of the air in your answer.
Rung 4 · Take it somewhere new
Explain how a drink comes up a straw, without using the word suck. Then say what would happen if you tried it on the Moon, and why.
Key note
The atmosphere has weight, and atmospheric pressure is that weight divided by the area it presses on — about 100 000 Pa at sea level, in every direction at once. It decreases with height, because the higher you go the less air there is above you. Air pushes; nothing sucks. What looks like suction is always the atmosphere pushing on one side of something while the push on the other side has been reduced.
Going further
Atmospheric pressure does not only change with height — it changes with the weather, and that is what a weather map is showing. A “low” is a region where the air above is lighter and the pressure at the ground is a few thousand pascals below normal; a “high” is the opposite. Air flows from high pressure towards low, which is what wind is, and the tighter the lines on the map are packed the stronger the wind.
The first instrument to measure any of this was a tube of mercury stood upside down in a dish by Torricelli in 1643: the atmosphere pushing on the dish held a column of mercury about 760 mm high, and when the weather changed the height changed with it. Blood pressure is still quoted in millimetres of mercury for that reason.
Aircraft take the same physics seriously. At 11 km the air outside a cabin is at about 23 kPa, far too little to keep anyone conscious, so cabins are pumped up to roughly the pressure you would meet at 2000 to 2400 m — enough to be comfortable, low enough that the hull is not fighting a full 100 kPa difference. The cost of that difference is why a fuselage is a pressure vessel and why a cabin door is enormous work to open in flight. Climbers face the raw version: at the summit of Everest each breath contains about a third of the oxygen molecules it would at sea level, which is why bodies acclimatise for weeks and why almost everyone still carries gas. And in the kitchen it shows up gently — at altitude water boils below 100 °C, so an egg genuinely takes longer to cook and rice may never soften properly.
Before this lesson
Connects to
At GCSE this becomes
- Atmospheric pressure from the weight of the air column, why the decrease with height is not a straight line, and pressure differences in gases.
Where to next
Ask Mr Badmus AI
Got a case that looks like sucking and needs rewriting?
The heights and pressures are standard-atmosphere values rounded to the nearest kilopascal: real pressure at any height varies with the weather by several kilopascals, and with temperature. The boiling points are approximate for pure water. “Air left above you” is the share of the whole atmosphere’s weight still overhead, worked out from the pressure itself. The bag is drawn swelling in proportion to the pressure drop and is clipped once it would leave the panel; a real bag stops stretching and then splits.
Lesson content © MrBadmusAI.