TL;DR:
Pressure is force per area:
P = F/A, in pascals (1 Pa = 1 N/m²).In a fluid at rest, pressure grows with depth:
P = ρgh, plus the air pressure on top.A tire gauge reads gauge pressure, the amount above the atmosphere. Absolute pressure is gauge plus about 101 kPa.
You can push a thumbtack into a corkboard with your thumb, but you could not push the flat head into the board the same way. Your thumb pushes with the same force on both ends, so the force is not the difference. The area is.
Force spread over area
Pressure is the force pressing at right angles on a surface, divided by the area it is spread over: P = F / A. The SI unit is the pascal, where 1 Pa = 1 N/m². A pascal is tiny, so you will see kilopascals (kPa) often, and the pound-force per square inch (psi) in everyday life in the US.
The same force on a small area means high pressure. The same force on a big area means low pressure. Snowshoes work this way, and so does a sharp knife.
Worked example: why the tack goes in point first
Say your thumb pushes with 10 N. The flat head has an area of 1 cm², and the tip has an area of 0.1 mm². Convert to square metres first, since pascals need m².
Head:
1 cm² = 1 × 10⁻⁴ m². Pressure:10 / 10⁻⁴ = 1 × 10⁵ Pa, which is 100 kPa.Tip:
0.1 mm² = 0.1 × 10⁻⁶ m² = 1 × 10⁻⁷ m². Pressure:10 / 10⁻⁷ = 1 × 10⁸ Pa, which is 100,000 kPa.Ratio:
10⁸ ÷ 10⁵ = 1000, the same as the area ratio10⁻⁴ ÷ 10⁻⁷ = 1000.
The tip presses a thousand times harder per unit area, and that is enough to push the wood fibres apart. Your thumb, spread over the big head, stays at a comfortable pressure. Check units: N / m² = Pa. Since 10 N is a modest push, a pressure around 10⁵ Pa on a thumb is normal.
Sharp points: High pressure is what lets points and blades cut. Keep tacks, needles and knives away from your eyes and fingers, and put them away after you use them.
Pressure rises with depth
Imagine a column of water above a point. The pressure there has to hold up the weight of that column. The column's weight is ρ × A × h × g, where ρ is density, h is the depth and A is the area. Divide by A and the area cancels: P = ρgh.
For water, ρ = 1000 kg/m³ and g = 9.8 m/s². At a depth of 10 m the extra pressure is 1000 × 9.8 × 10 = 98,000 Pa, which is 98 kPa. Air pressure on the surface is about 101 kPa, so the total at 10 m is roughly 98 + 101 = 199 kPa, close to double the surface value.
Notice that only depth matters, not the shape of the container or the width of the water. A narrow tube and a wide lake give the same pressure at the same depth. Fluids also pass pressure on in all directions, so the pressure pushes sideways and upward equally.
What a tire gauge actually reads
A tire pressure gauge reads gauge pressure: how much more than the surrounding air. A reading of zero on a flat tire does not mean empty. There is still air inside at atmospheric pressure.
Say a tire reads 220 kPa. This is about 32 psi, since 220 ÷ 6.895 ≈ 31.9. The absolute pressure inside is 220 + 101 = 321 kPa. Gas pressure comes from molecules hitting the inside wall, so more air in the same volume means more collisions and a higher pressure. Driving warms the tire and raises it further.
Follow the label: Use the pressure on your vehicle's door label or in its manual, not the maximum on the tire sidewall. Never overinflate, and check pressure when the tires are cold. If you are unsure, ask a tire shop.
How to check your answer
Convert first. Square centimetres to square metres means multiplying by
10⁻⁴. Square millimetres to square metres means10⁻⁶.Units.
kg/m³ × m/s² × m = N/m².Ratio check. If the area drops by a factor of 1000, the pressure must rise by the same factor.
Gauge or absolute? Ask which one the question wants before you add or subtract the atmosphere.
Mistakes that cost marks
Mixing units: newtons with square centimetres.
Using the weight of an object as the force but the wrong area (only the contact area counts).
Thinking pressure depends on the width of the liquid, when only depth matters.
Leaving out atmospheric pressure when asked for absolute pressure.
Confusing force with pressure.
Where you will use it next
The depth formula leads straight into buoyancy: water pushes up on the bottom of an object harder than down on the top, because the bottom is deeper. Pressure and temperature meet again in heat vs temperature.
Frequently asked questions
Why do your ears feel pressure when you dive to the bottom of a pool?
The water above you adds pressure of ρgh, and your eardrum feels the difference between the water outside and the air inside until it equalises.
Is 1 atmosphere the same as 101 kPa?
Standard atmospheric pressure is about 101.3 kPa, and 101 kPa is a handy round figure.
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