Buoyancy Experiment Calculator
Use this calculator for three classic buoyancy experiments. In Force mode, enter a fluid density and submerged volume to get the upward buoyant force from Archimedes' principle. In Float/Sink mode, enter an object's mass and density to check whether it floats and see how deep it sits. In the Two-Liquid Density mode, place a ball at the interface of two fluids and solve for the unknown upper-liquid density - exactly the experiment used to measure dish-soap density at home. Switch between metric and imperial units, and choose Earth, Moon, or Mars gravity.
What is buoyancy and why does it matter?
Buoyancy is the upward force a fluid exerts on any object placed in it. It arises because pressure in a fluid increases with depth: the bottom of an object experiences higher pressure than the top, and the net upward push is exactly equal to the weight of the fluid the object displaces. This is Archimedes' principle, formulated around 250 BCE. Whether something floats or sinks depends entirely on whether that upward push exceeds, equals, or falls short of the object's own weight. Ships are made of steel that is far denser than water, yet they float because their hollow hull displaces a large volume of water relative to the total weight of the vessel. Submarines alter their buoyancy by filling or emptying ballast tanks with water to dive or surface. Even a helium balloon floats because the balloon-plus-gas system is less dense than the surrounding air.
The three modes explained
This calculator covers three classic buoyancy scenarios. In Force mode you supply the fluid density and the submerged volume, and the tool returns the buoyant force in Newtons (or pound-force) and the mass of displaced fluid. In Float/Sink mode you supply the object's mass and average density along with the fluid density: if the object density is lower than the fluid it floats, and the calculator shows what fraction of the object sits below the surface. If its density is higher it sinks, and the net downward force is displayed. In the Two-Liquid Density experiment, a ball sits at the interface between a known dense lower liquid (such as salt water) and an unknown lighter liquid above. By measuring the diameter of the ball and how much of it pokes into the upper layer, the calculator solves for the unknown density using the spherical-cap equilibrium formula. This is the experiment used in school labs to measure the density of everyday liquids like dish soap, juice, or cooking oil.
The mathematics behind the calculations
The fundamental equation is F_B = rho times V times g, where rho is the fluid density in kg/m^3, V is the displaced volume in m^3, and g is gravitational acceleration (9.807 m/s^2 on Earth). For the float/sink check, the submerged fraction at equilibrium equals the ratio of the object density to the fluid density: f = rho_object / rho_fluid. If this ratio is below 1 the object floats with that fraction underwater. For the two-liquid experiment the ball floats at the interface when rho_ball times V_ball times g equals rho1 times V_bottom times g plus rho2 times V_cap times g, where V_cap is the spherical cap volume V_cap = pi times h^2 times (3r - h) / 3, h is the cap height in the upper liquid, and r is the ball radius. Rearranging gives rho2 directly. All internal computation uses SI units; the display converts to the chosen unit system.
Running the two-liquid density experiment at home
To identify an unknown liquid at home, fill a tall clear glass about halfway with a denser reference liquid such as salt water (dissolving about 30 g of table salt in 100 mL of water gives roughly 1200 kg/m^3). Gently pour the unknown liquid on top - it should float if it is lighter. Place a small ball (a marble, a round grape, or a small bouncy ball) at the interface. Measure the ball's diameter with a ruler, weigh it on a kitchen scale, and measure the height of the cap that sits above the interface. Enter those values into the Two-Liquid Density mode and the calculator will return the density of the upper liquid. Compare the result against the reference table to identify it. Common results: dish soap typically falls between 1020 and 1060 kg/m^3; olive oil around 910 kg/m^3; honey around 1400 kg/m^3.
Common fluid and material densities
| Substance | Density (kg/m³) | Floats in water? |
|---|---|---|
| Air | 1.2 | Yes |
| Gasoline | 700 | Yes |
| Cooking oil | 910 | Yes |
| Ethanol (alcohol) | 789 | Yes |
| Ice | 917 | Yes |
| Wood (oak) | 600-900 | Yes (just) |
| Fresh water | 998 | Neutral / reference |
| Sea water | 1025 | - |
| Milk | 1030 | - |
| Salt water (30%) | 1228 | - |
| Concrete | 2000-2400 | No |
| Steel | 7750-8050 | No |
| Mercury | 13 534 | No |
Reference densities at approximately 20 degrees C (68 degrees F).
Frequently asked questions
What is the formula for buoyant force?
The buoyant force in Newtons equals the fluid density (kg/m^3) multiplied by the submerged volume (m^3) multiplied by gravitational acceleration (m/s^2): F_B = rho x V x g. In practical terms, a 1-litre (0.001 m^3) object fully submerged in fresh water (998 kg/m^3) on Earth experiences a buoyant force of 998 x 0.001 x 9.807 = 9.78 N, which is about 1 kilogram-force.
Why does an object float when its density is lower than the fluid?
When the object density is lower than the fluid density, the maximum buoyant force (when fully submerged) exceeds the object's weight. The object rises until a fraction of it is above the surface and the submerged volume is just small enough that the buoyant force equals the weight. At equilibrium the submerged fraction equals the ratio of the object density to the fluid density - that is why an iceberg (density about 917 kg/m^3) sits about 917/1025, or roughly 89 percent, below the sea surface.
Does buoyancy change on the Moon or Mars?
Yes. The buoyant force scales with gravitational acceleration, so it is weaker on the Moon (g = 1.62 m/s^2) and on Mars (g = 3.72 m/s^2) than on Earth (g = 9.807 m/s^2). Crucially, the weight of the object also scales by the same factor, so the float-or-sink outcome does not change - an object that floats on Earth also floats on the Moon. However, the absolute forces are smaller, which matters for engineering calculations.
How accurate is the two-liquid density experiment?
Accuracy depends mainly on how precisely you measure the cap height and the ball diameter. A 1 mm error in cap height on a 4 cm ball can shift the result by 20 to 50 kg/m^3, which is about 2 to 5 percent. Use a caliper rather than a ruler if you need better accuracy, and repeat the measurement several times. Temperature also matters: fluid densities vary by roughly 0.1 to 0.3 kg/m^3 per degree C, so work at room temperature and let the liquids settle before measuring.
What is the difference between buoyancy and upthrust?
They mean exactly the same thing. Upthrust is the older British English term; buoyancy is more common in American usage and in international physics literature. Both refer to the net upward force exerted on an object by a surrounding fluid.
Can I use this calculator for gases, not just liquids?
Yes. Air is a fluid, and Archimedes' principle applies to gases too. Enter the gas density (air at sea level is about 1.2 kg/m^3) and the volume of the object. This is how you calculate the lift force of a balloon or the buoyant correction in precision weighing. Use the custom fluid entry to enter any gas density.