Pressure (P = F/A) · pressure with depth (P = hρg) · Archimedes' principle · buoyant force (Fₐ = ρVg) · density & flotation
Drop a stone in water and it sinks; set a steel ship of ten thousand tonnes on the sea and it floats. The difference is not weight but density, and the reason is upthrust — the push a fluid gives back. Archimedes' principle pins it down: that push equals the weight of the fluid you shove aside, Fₐ = ρVg. The same idea lifts hot-air balloons, hides nine-tenths of an iceberg, and lets a submarine choose its depth.
This page covers pressure (P = F/A), how pressure grows with depth (P = hρg), thrust and upthrust, Archimedes' principle, the buoyant force (Fₐ = ρVg), density and relative density, and the rule for flotation. By the end you'll be able to:
Every ship, submarine, balloon, dam and syringe runs on pressure and buoyancy — and "Force & Pressure" plus "Gravitation" are among the most-tested chapters everywhere. We go beyond the syllabus, but we never skip it:
Searched as: Archimedes' principle, why ships float, buoyant force formula, upthrust, pressure in fluids, P = hρg, relative density, why a stone sinks, does an iceberg float.
Pick a material (or set the density by hand), choose the fluid, and drop the object in. Watch it settle to the depth where the upthrust balances its weight — or sink when it is too dense. Try iron in water, then switch the fluid to mercury and watch it rise. 🟢 real buoyancy engine
Pick a material and a fluid to see whether it floats, and how deep it sits.
In plain terms: a fluid presses harder the deeper you go, so it pushes up on anything inside it. That upward push — the upthrust — equals the weight of the fluid the object shoves aside.
Pressure is force spread over area, P = F/A, measured in pascals. Inside a fluid the pressure grows with depth, P = hρg, because you are carrying the weight of everything above you. Since the bottom of a submerged object sits deeper than its top, the fluid pushes up on the bottom harder than it pushes down on the top — and that difference is the upthrust, or buoyant force. It always points straight up, against gravity.
Archimedes' principle pins the size of that push exactly: the upthrust equals the weight of the fluid the object displaces — pushes out of the way. Lower a stone into a brim-full bucket and the water that spills over weighs precisely as much as the upthrust the stone feels. In symbols, Fₐ = ρVg: the fluid's density, times the submerged volume, times gravity. An object then floats if it is less dense than the fluid and sinks if it is denser — weight itself never decides it, density does.
The tank above drops your object into the fluid and lets it settle. The Tank tab shows the weight arrow (down) and the upthrust arrow (up); when the object floats, it sinks just far enough that the two arrows match. The Submerged vs density tab plots how deep it rides against how dense it is — a straight climb until the densities are equal, then it sinks and rests on the bottom. Try iron in water (it sinks), then switch the fluid to mercury and watch the same iron rise and float. 🟡 the maths of the picture
Exams want the method, not just the idea. Here is one fully worked, the way you'd set it out in an answer.
A metal block of volume 0.002 m³ is fully submerged in water (ρ = 1000 kg/m³). Its weight in air is 50 N. Find the upthrust on it and its apparent weight in the water. (g = 9.8 m/s²)
The water pushes up with 19.6 N, so on an underwater scale the block reads 30.4 N — lighter, but it still sinks, because its weight (50 N) beats the upthrust. That is exactly what the tank shows for a dense object.
Exams reward the method, not just the answer. Work it out one step at a time — read the thought, predict the line, then reveal it. Switch to practice to type your own numbers and check them.
The physics is visible in the tank; the maths usually hides. These little labs make it visible too — drag a slider and watch the upthrust, the float depth and the pressure change.
Some wrong ideas about floating and sinking are so common they deserve their own warning label. Tap a card to bust the myth.
A steel ship floats because its hollow, air-filled hull has an average density below water's, so it pushes aside enough water to match its huge weight. A submarine goes further: it floods ballast tanks to grow denser and dive, then blows them clear with air to rise — steering by buoyancy alone.
Air is a fluid too, so it gives upthrust. A hot-air balloon heats the air inside until it is thinner — less dense — than the cool air around it, and the surrounding air's upthrust lifts the whole craft. A helium balloon does the same trick with a gas that is light to begin with.
A hydrometer floats deeper in a thin liquid and higher in a dense one, so its float depth reads off density — used to test milk, batteries and beer. The Plimsoll line painted on a ship's hull shows how low it may safely sit, since salt, fresh, warm and cold water each float it differently.
Once humans understood upthrust, they built ships, submarines, balloons, hydrometers — and machines that lift with a squeeze of fluid.
Water's density is the dividing line: 1000 kg/m³. Drag from cork to gold and watch each material ride higher or drop to the bottom as its density climbs past water's. Everything lighter than water floats; everything denser sinks — no matter its size or shape.
Float or sink is never about how heavy a thing is — only whether it is packed tighter than the water it sits in.
Physics you can hold. Each project below demonstrates the law you just met — and the measuring is what turns a demo into a science-fair winner. Pick one, build it from things at home, and graph something.
Build: drop a whole orange in water — it floats. Now peel it and drop it in again — it sinks.
Measure: weigh both, and work out the volume each time; the peel's trapped air lowers the average density below water's.
Build: a fresh egg sinks in tap water. Stir in salt spoon by spoon until it rises and hovers.
Measure: the grams of salt needed to lift it — you have raised the water's density past the egg's.
Build: shape a square of aluminium foil into a boat and float it, then add coins one at a time.
Measure: the number of coins it holds before sinking, against the hull's area — more displaced water carries more weight.
Build: hang a stone from a rubber band or spring scale, note the reading, then lower it into water.
Measure: the drop in the reading — that fall is the upthrust, and it equals the weight of water the stone displaces.
Build: weight a straw with a little modelling clay at one end so it floats upright, and mark the waterline.
Measure: how the line shifts in salt water, sugar water and oil — a home-made density meter.
Build: seal a sauce sachet (or a capped dropper) in a full plastic bottle so it just floats, then squeeze.
Measure: the squeeze pressure that makes it dive — compressing its air shrinks its volume, so its density rises past water's.
Floating and sinking hide more than they show. Here are the questions that come up most — each answer reads on its own, lifted clean off the page.
Archimedes' principle says that when an object is placed in a fluid, the fluid pushes it up with a force equal to the weight of the fluid the object pushes aside. Lower a stone into a full bucket and water spills over; the weight of that spilled water is exactly the upthrust the stone feels. This one rule explains why things feel lighter in water and decides whether an object floats or sinks.
| Feature | Mass | Weight | Density |
|---|---|---|---|
| What it is | Amount of matter | Pull of gravity on it | Mass per volume |
| Unit | kilogram (kg) | newton (N) | kg/m³ |
| Changes with place? | No | Yes (weaker on the Moon) | No |
| Decides floating? | No | No | Yes |
Floating depends on density — mass per volume — not on weight alone. A solid steel nail is denser than water, so it sinks. A ship is a hollow steel shell full of air, so its average density is far below water's; it pushes aside a huge volume of water, and the upthrust grows until it matches the ship's full weight. Flood the hull and its average density rises above water's, which is how ships sink.
Use Fₐ = ρVg. Take the fluid's density ρ (about 1000 kg/m³ for water), multiply by the submerged volume V in cubic metres, and by g (about 9.8 m/s²); the answer is the upthrust in newtons. For a fully submerged object use its whole volume; for a floating one use only the part below the surface, because that is all the fluid it has pushed aside. A 2-litre block fully under water gets about 20 N of upthrust.
Pressure at any depth comes from the weight of all the fluid stacked above that point, so the deeper you go the more fluid presses down and the higher the pressure. The rule is P = hρg, where h is the depth, ρ the fluid's density and g gravity. It is why a dam is built thick at its base, why your ears hurt at the bottom of a pool, and why deep-sea submarines need very strong hulls.
It does not lose any real weight, but it feels lighter because the water pushes up on it. The reading you get is the apparent weight — the true weight minus the upthrust. A rock weighing 50 N in air might read only 30 N on a scale under water, because the water supplies 20 N of upthrust. Lift it clear of the water and the full 50 N returns.
Ice has a density of about 917 kg/m³ and sea water about 1025 kg/m³, so ice floats — but only just. A floating object sits with the fraction of itself submerged equal to the ratio of the two densities, which for ice in sea water is about 0.90. That means roughly nine-tenths of an iceberg lies below the surface and only about a tenth shows — the origin of "the tip of the iceberg".
Relative density (also called specific gravity) is an object's density divided by the density of water: RD = ρ_object / ρ_water. It has no units. If the value is less than 1 the object floats in water; if more than 1 it sinks. Gold has a relative density of about 19, cork about 0.24. Because water is 1000 kg/m³, an object's density in kg/m³ is simply its relative density times 1000.
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A thing floats or sinks not by how heavy it is, but by how tightly it is packed against the sea that holds it.