How this instrument works
Buoyant force is what a fluid does to anything taking up room inside it. Pressure in still liquid climbs with depth as ρ·g·h, so an object's underside sits in stronger pressure than its top face; total that mismatch over every surface and what remains is one upward push worth ρ·g·V. Nothing about an object's own material survives that sum — only how much fluid got displaced.
Archimedes set this out around 250 BCE in On Floating Bodies, earliest surviving work of hydrostatics, and framed it as a statement about weight rather than pressure: any body immersed in fluid is buoyed up by force matching the weight of fluid displaced. His argument needed no calculus, only equilibrium reasoning about a bowl-shaped ocean. Twenty-two centuries later, load lines painted on hulls — Samuel Plimsoll's mark, written into British law in 1876 — turned that same statement into an enforceable limit on cargo.
This formula assumes still fluid of uniform density wrapped completely around your object. It drifts where density varies: a balloon climbing through thinning air steadily loses lift, and ocean layers of differing salinity can drop a trimmed submarine onto what crews call a liquid bottom. It fails outright where fluid cannot reach underneath — a flat slab suction-sealed against smooth seabed has no upward pressure acting on it at all, and stays exactly where it is.
- Set Fluid density to whatever your object sits in: 1000 kg/m³ fresh water, 1025 seawater, 1.204 air at 20 °C. That menu also accepts g/cm³ and lb/ft³.
- Enter Volume displaced — fluid pushed aside, which for a partly floating object means only its underwater portion. Millilitres, litres, cubic feet and gallons all convert.
- Read Buoyant force in newtons, or switch that field to kgf if you would rather see upthrust expressed as a mass of displaced fluid.
- Weigh that result against your object's own weight: more upthrust and it rises, less and it sinks, matched and it hovers at depth.
Worked example — pushing a litre bottle under
Hold a sealed, empty one-litre bottle beneath a sink of fresh water. Fluid density reads 1000 kg/m³ and Volume displaced is one litre, which converts to 0.001 m³. So F = 1000 × 9.80665 × 0.001 = 9.80665 N — near enough 9.81 newtons, or 1.00 kgf if you flip that output unit.
One kilogram of upthrust, precisely, which explains how hard a bottle fights back: your arm holds down a kilo. Empty plastic weighs perhaps 0.3 N, so almost all of it is net lift. Notice too that plastic never entered any part of that arithmetic. Swap fresh water for seawater at 1025 kg/m³ and an identical litre yields 10.05 N — a 2.5% gain, which is why hulls ride higher leaving a river estuary for open ocean.
Questions
What unit does buoyant force come in?
Newtons, because buoyancy is a force: 1 N = 1 kg·m/s². This instrument also offers kgf, where 1 kgf = 9.80665 N exactly, turning your reading straight into 'mass of fluid displaced' — convenient, since Archimedes' rule gets quoted as weight. For US engineering work choose lbf, roughly 4.448 N apiece, or kN once figures run past a few thousand.
Should I enter an object's whole volume or just its submerged part?
Only whatever sits under the surface. Volume displaced means fluid actually pushed aside, so for a floating hull you enter underwater volume, not total hull volume. Getting this wrong is far and away the commonest mistake with Archimedes' rule, and it inflates answers badly. Fully submerged bodies are simpler: displaced volume then equals their own volume, so a sunken crate and its water-filled outline agree.
Why is an object's density missing from this formula?
Because upthrust originates in a fluid, never in whatever is floating there. Pressure at each depth depends only on fluid density and gravity, so lead and balsa cubes of matched size feel identical push in identical water. Density of your object decides what follows: set buoyant force beside weight, and their difference tells you whether something rises, sinks, or hangs motionless.
How much does air buoyancy affect a weighing?
Air lifts too, and calibration labs correct for it. Sea-level air runs about 1.2 kg/m³, so a stainless steel kilogram occupying roughly 125 cm³ displaces 0.15 g of air and reads that much light on a balance — about 150 parts per million. Weigh a litre of water and that shortfall grows near 1.2 g. Below milligram precision, ignore it; above, an air buoyancy correction becomes routine practice.
When does Archimedes' principle break down?
Where fluid cannot surround your object, or where density refuses to stay uniform. A slab sealed flat against smooth rock feels no upward pressure and will not lift. In stratified water, a submarine trimmed for one layer settles through into a denser one. Acceleration matters as well, since upthrust scales with effective gravity: fluid in free fall supplies none whatsoever, which is exactly why bubbles refuse to rise aboard a space station.
How does buoyant force connect to density ratios?
Divide object density by fluid density and you get a floating fraction without touching forces. Come out below 1 and it floats, with submerged proportion equal to that ratio — an iceberg near 917 kg/m³ adrift in 1025 kg/m³ seawater rides 89% below waterline. Buoyant force answers a different question: how many newtons a mooring line, crane, or diver's arm must actually supply.