{"id":346,"date":"2026-06-28T19:43:45","date_gmt":"2026-06-28T19:43:45","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=346"},"modified":"2026-06-28T19:43:46","modified_gmt":"2026-06-28T19:43:46","slug":"archimedes-principle","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/archimedes-principle\/","title":{"rendered":"Archimedes’ Principle and Buoyancy"},"content":{"rendered":"\n
Definition<\/div>

\n\nArchimedes’ principle states that any object placed in a fluid is pushed upward by a buoyant force equal to the weight of the fluid the object displaces. The force is found with F_b = \u03c1Vg, where \u03c1 is the fluid’s density, V the displaced volume, and g gravity. An object floats when this upward force balances its weight.\n\n<\/p><\/div>\n

Drop a steel spanner into a sink and it plunges straight to the bottom. Yet a steel ship the length of three football pitches sits calmly on the ocean, carrying thousands of cars. Same metal, opposite fate. The rule that explains both \u2014 and the floating ice in your drink, and the lift under a hot-air balloon \u2014 is one of the oldest in physics.<\/p>\n

It came from a puzzle about a king’s crown more than two thousand years ago, and it still decides how submarines dive, how life jackets save lives, and how much of every iceberg hides beneath the waves. Once you can picture the fluid being pushed out of the way<\/em>, the whole thing clicks.<\/p>\n

What Is Archimedes’ Principle?<\/h2>\n

Picture lowering a sealed box into a bathtub. The water has to go somewhere, so it rises \u2014 the box has displaced<\/strong> a certain volume of water. Archimedes’ principle says the fluid pushes back: it shoves the box upward with a force exactly equal to the weight of the water that was moved aside.<\/p>\n

That upward push is the buoyant force<\/strong> (also called upthrust). It does not care what the object is made of, only how much fluid the object displaces and how heavy that fluid is. This idea is often written simply as the Archimedes principle<\/strong>, and it applies to every fluid \u2014 water, oil, even the air around you.<\/p>\n

So whether an object floats or sinks is a contest between two forces: gravity pulling it down by its weight, and buoyancy pushing it up by the weight of displaced fluid. Win the contest and it rises; lose and it sinks; tie and it hovers in place.<\/p>\n

The man behind it, Archimedes of Syracuse (c. 287\u2013212 BC), reportedly hit on the idea in his bath and shouted “Eureka!” The famous story has him testing a king’s gold crown for cheating. Whether he literally used a bathtub is debated by historians \u2014 a careful hydrostatic balance is the more likely method \u2014 but the physics he uncovered is rock-solid.<\/p>\n

The Buoyant Force Formula<\/h2>\n

The size of the upthrust comes straight from the weight of displaced fluid. Since weight is mass times gravity, and the displaced mass is the fluid’s density times the displaced volume, the buoyant force is:<\/p>\n

F_b = \u03c1Vg<\/div>\n

Every symbol has a job, and each one carries an SI unit. Get the units right and the answer lands in newtons every time.<\/p>\n

\n\n\n\n\n
Symbol<\/th>\nQuantity<\/th>\nSI unit<\/th>\n<\/tr>\n<\/thead>\n
F_b<\/strong><\/td>Buoyant force (upthrust)<\/td>newton (N)<\/td><\/tr>\n
\u03c1<\/strong> (rho)<\/td>Density of the fluid<\/em><\/td>kg\/m\u00b3<\/td><\/tr>\n
V<\/strong><\/td>Volume of fluid displaced<\/td>m\u00b3<\/td><\/tr>\n
g<\/strong><\/td>Gravitational field strength<\/td>\u2248 9.81 m\/s\u00b2<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

One trap worth flagging now: \u03c1 is the density of the fluid<\/strong>, never the object. Swap in the object’s density by mistake and the physics falls apart.<\/p>\n

Apparent weight and the float fraction<\/h3>\n

When an object hangs submerged on a scale, the scale reads less than its true weight, because buoyancy lifts part of the load. That reduced reading is the apparent weight<\/strong>:<\/p>\n

W_app = W \u2212 F_b<\/div>\n

For something that floats, there is a neat shortcut for how deep it rides. The fraction of its volume sitting below the surface equals the ratio of the two densities:<\/p>\n

V_sub \/ V = \u03c1_obj \/ \u03c1_fluid<\/div>\n

This single ratio is why a denser object floats lower, and why ice \u2014 slightly less dense than water \u2014 barely pokes above the surface. You can run the numbers for any object and fluid with our Buoyancy Calculator<\/a>.<\/p>\n

How Buoyancy Works<\/h2>\n

Where does the upward push actually come from? Pressure. In any fluid, pressure grows with depth, because deeper layers carry the weight of everything above them. The relationship is P = \u03c1gh \u2014 go deeper, and h grows, so the pressure climbs.<\/p>\n

Now think about a submerged block. The fluid presses on every face, but the bottom face sits deeper than the top face. So the upward push on the bottom beats the downward push on the top. That difference is<\/em> the buoyant force.<\/p>\n

Put numbers on it. If the top face is at depth d<\/em> and the block has height h<\/em> and face area A<\/em>, the bottom sits at depth d + h<\/em>. The net upward force is the bottom force minus the top force:<\/p>\n

F_b = \u03c1g(d + h)A \u2212 \u03c1g(d)A = \u03c1g(hA) = \u03c1gV. The depth d<\/em> cancels, leaving exactly \u03c1Vg \u2014 the displaced volume V = hA times \u03c1g. NASA’s Glenn Research Center walks through this same pressure-difference derivation in its Archimedes’ principle activity<\/a>.<\/p>\n\n\n<\/marker>\n<\/marker>\n<\/marker>\n<\/marker>\n<\/defs>\n\n\n\nfluid surface<\/text>\n\nobject<\/text>\n\n\nsmaller pressure (top)<\/text>\n\n\nlarger pressure (bottom)<\/text>\n\nF_b (buoyant force)<\/text>\n\nW (weight)<\/text>\n<\/svg>\n

Fluid pressure is greater on the deeper bottom face than on the top, and that imbalance produces the net upward buoyant force.<\/p>\n

Try it yourself. In the lab below, change the object’s density, its volume, and the fluid. Watch the weight, buoyant force, apparent weight and submerged percentage update live as the block settles to float or sink.<\/p>\n

<\/span>Buoyancy Lab<\/span><\/div>