Archimedes' principle says the upward force on any object in a fluid equals the weight of the fluid that object displaces. That single sentence answers every buoyancy question, and this buoyancy calculator applies it in both directions: it works out the force on an object held fully under, and it finds the equilibrium position of an object left free to float, including how much of it ends up below the surface.
Arb Digital builds free calculators that report the quantity people actually need rather than the one that is easiest to compute. For buoyancy that means the submerged fraction and the apparent weight, not just the force in newtons. A diver wants to know how much lead to carry. A boat builder wants to know the waterline. A lab technician weighing a dense sample in air wants to know how large the air-buoyancy correction is. All three come from the same principle applied carefully.
What This Buoyancy Calculator Does
Enter the object's mass and its total external volume, then choose the fluid. In free mode the tool compares the object's average density with the fluid's and decides what actually happens. If the object is less dense it floats, and the calculator returns the fraction submerged, the volume of fluid displaced at equilibrium and a buoyant force exactly equal to the object's weight — because that is what equilibrium means. If it is denser it sinks, and the calculator returns the full-volume buoyant force and the apparent weight that remains once buoyancy has been subtracted.
In held mode the object is assumed to be entirely under the surface regardless of its density. The buoyant force is then the weight of its whole volume of fluid, and the apparent weight can come out negative — which is the physical statement that you would have to push down to keep it there. The magnitude of that negative number is the force required to hold it under, and it is the figure that governs how much ballast a buoy or a submerged pipeline needs.
The bar shows the submerged fraction visually, which makes the difference between a marginal float and a comfortable one obvious at a glance. An object at 95 percent submerged is technically floating and practically a hazard.
How to Use It
- Use the displaced volume, not the material volume. A sealed hollow object displaces its full external volume. This is the single most important input on the page and the one people most often get wrong.
- Pick the fluid, or type a density. The presets cover common cases; anything else can be entered directly, and the density calculator will work out a density from a mass and a volume you measured.
- Choose the condition. Free mode answers "what will it do?" Held mode answers "what force is involved if I keep it under?"
- Read the submerged fraction as a design margin. Freeboard — the part above the surface — is what absorbs waves, spray and added load.
- Check the apparent weight before lifting. Underwater, an object weighs its dry weight minus the buoyant force, which is why heavy salvage is often manageable until the moment it breaks the surface.
The Formula: How Buoyancy Is Calculated
The buoyant force is FB = ρfluid × Vdisplaced × g, with g = 9.80665 m/s². For a fully submerged object the displaced volume is the object's whole volume. Taking the defaults — a 50 kg object of 0.06 m³ held under fresh water at 998 kg/m³ — the force is 998 × 0.06 × 9.80665 = 587.3 N. The object's own weight is 50 × 9.80665 = 490.3 N, so the apparent weight is 490.3 − 587.3 = −97.0 N. Negative means it is trying to rise, and 97 N of downward force is what holds it under.
Left free, that object floats, because its average density is 50 ÷ 0.06 = 833.3 kg/m³, below the fluid's 998. The submerged fraction is simply the ratio of the two densities: 833.3 ÷ 998 = 0.835, so 83.5 percent of its volume sits below the surface. The displaced volume is 0.835 × 0.06 = 0.0501 m³, and the buoyant force on that displaced volume is 998 × 0.0501 × 9.80665 = 490.3 N — identical to the object's weight, as equilibrium requires. That identity is a genuine check on the arithmetic rather than a restatement of it.
The density-ratio result explains the familiar iceberg figure. Ice is roughly 917 kg/m³ and seawater roughly 1025, so the ratio is about 0.895 and roughly ten percent of an iceberg's volume stands above the water. The OpenStax University Physics section on Archimedes' principle and buoyancy derives the same relation from the pressure difference between the top and bottom surfaces of the object.
Why Buoyancy Exists at All
The upward force is not a separate law of nature bolted onto fluid statics. It is a direct consequence of pressure increasing with depth. The bottom face of a submerged object is deeper than the top face, so it experiences a higher pressure, and the net of those two pressure forces is upward. Integrate that pressure difference over any shape and the result is exactly the weight of the displaced fluid — which is why the principle holds for irregular objects as well as for neat cubes.
This also explains a case that confuses people: an object resting flat on the bottom of a tank with no fluid underneath it experiences no buoyant force at all. A suction-cupped tile on a pool floor, or a barge settled onto silt at low tide, has no upward pressure acting on its underside, and lifting it requires overcoming both its full weight and the pressure of the water above. Breaking that seal is the hard part of refloating a grounded vessel.
The pressure that drives all this comes from the depth of fluid above, and our hydrostatic pressure calculator handles that side of the problem directly if you need the pressure itself rather than the resulting force.
The Cases Where Average Density Is What Matters
Nothing in the equation refers to what an object is made of. Steel has a density of about 7,850 kg/m³ and a solid steel block sinks in water instantly. Form the same steel into a hull enclosing a large volume of air and the average density of the whole hull-plus-air assembly drops below 1,000 and it floats. The material never changed; the displaced volume did.
Submarines exploit this deliberately. Filling ballast tanks with seawater raises average density above the surrounding water and the boat descends; blowing the tanks with compressed air reverses it. A fish does the same thing more elegantly with a swim bladder, adjusting gas volume to hold neutral buoyancy at a chosen depth. Neutral buoyancy — average density exactly equal to the fluid — is the unstable middle case where the object neither rises nor sinks, and this calculator reports it when the two densities match.
Divers manage the same balance with weight belts and buoyancy compensators, complicated by the fact that a neoprene suit compresses with depth. Its volume falls, so its buoyancy falls, so a diver neutrally buoyant at the surface becomes negatively buoyant deeper down. The equation still holds; it is the volume input that has changed.
Air Buoyancy: The Correction Almost Everyone Ignores
Buoyancy applies in gases too, and air at sea level has a density of about 1.225 kg/m³. That sounds negligible, and for most purposes it is, but it becomes measurable in precision weighing. An object of one litre volume displaces 1.225 grams of air, and a balance that compares it against dense metal reference masses reads slightly low as a result.
For a low-density sample such as a plastic or a powder, the buoyancy correction can reach a tenth of a percent of the reading — far larger than the resolution of a good analytical balance. Metrology laboratories correct for it explicitly. If you have ever wondered why a certified mass standard comes with a stated volume as well as a stated mass, this is why: without the volume, the air-buoyancy correction cannot be computed.
Set the fluid to air in this calculator and you can see the size of the effect for your own object. It is also the reason a helium balloon rises: the average density of the envelope and its gas is below 1.225, so the same rule that floats a boat lifts a balloon. For material densities and mass-from-volume work, the material weight calculator and the density converter cover the neighbouring cases, and the OpenStax section on fluids, density and pressure sets out the definitions this all rests on.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Entering the material volume instead of the displaced volume — a hollow object displaces its full external volume. Using only the volume of solid material makes every floating object appear to sink.
- Assuming heavy things sink — buoyancy depends on average density, never on total weight. A loaded ship weighs far more than a coin and floats where the coin does not.
- Using fresh-water density for seawater — seawater is around 2.7 percent denser, which shifts a waterline noticeably and is why a vessel floats higher at sea than in a river.
- Forgetting that a suit or foam compresses with depth — buoyancy falls as volume falls, so an object neutrally buoyant near the surface can become negatively buoyant deeper.
- Ignoring buoyancy in precision weighing — air displacement changes a balance reading measurably for low-density samples, which is why certified masses carry a stated volume.
Related Free Tools From Arb Digital
Buoyancy problems start with density and pressure. Get the density from the density calculator, the pressure at depth from the hydrostatic pressure calculator, and the flow case from the Bernoulli equation calculator. For the mass of a known volume of material use the material weight calculator, for pool and tank volumes the pool volume calculator, and for unit work the density converter. Everything else is listed in the free online tools hub.
Frequently Asked Questions
It states that the upward buoyant force on an object in a fluid equals the weight of the fluid the object displaces. It follows directly from pressure increasing with depth, so the upward force on the object's lower surface exceeds the downward force on its upper surface.
Compare its average density with the fluid's. Less dense floats, denser sinks, equal densities give neutral buoyancy. Average density means total mass divided by total displaced volume, including any sealed air inside.
Because a floating object is in equilibrium. It sinks only until the displaced fluid weighs exactly as much as it does, at which point the forces balance and it settles. That is why the tool reports the two figures as identical for a float.
That buoyancy exceeds weight, so the object is trying to rise. The magnitude is the downward force needed to hold it fully submerged, which is the figure that determines how much ballast a buoy or a submerged pipe requires.
Yes. Air has a density of about 1.225 kg/m³ at sea level, which is why balloons filled with a lighter gas rise. The same effect makes a measurable correction in precision weighing of low-density samples.
Because buoyancy depends on the volume the hull displaces, not on the density of the steel. The hull encloses a large air space, so the average density of the whole vessel is well below that of water even though the material is not.
Only if fluid can reach underneath it. An object sealed flat against the bottom has no upward pressure on its lower face, so there is no buoyant force, and lifting it means overcoming the full weight of the water above as well.
This tool is provided for educational and study use. It applies ideal static buoyancy and is not naval architecture, diving or lifting-operation guidance.
