Buoyant Force Calculator
Enter the volume of fluid displaced by an object and select the surrounding fluid to calculate the buoyant (upthrust) force acting on it. Uses Archimedes' principle: B = rho x V x g. Choose from nine common preset fluids or enter a custom density, switch between metric and imperial volume units, and adjust gravity for other planets. The "Show your work" panel walks through every step of the calculation.
Formula
Worked example
A 1-litre water bottle (V = 0.001 m3) is fully submerged in fresh water (rho = 1000 kg/m3) under Earth gravity (g = 9.81 m/s2). Displaced mass = 1000 x 0.001 = 1 kg. Buoyant force = 1 x 9.81 = 9.81 N. Because a full 1-litre bottle of water weighs about 9.81 N, it is neutrally buoyant when full and rises when partially empty.
Archimedes' principle and the buoyancy formula
Buoyancy is the upward force a fluid exerts on any object that displaces it. Archimedes of Syracuse (circa 250 BC) established that this force equals the weight of fluid displaced: B = rho x V x g, where rho is the fluid density in kg/m3, V is the submerged volume in m3, and g is gravitational acceleration in m/s2. The result is in Newtons. Notice that the buoyant force depends entirely on the surrounding fluid and the displaced volume, not on what the object is made of. A solid iron sphere and a hollow iron sphere of the same outer dimensions experience identical buoyancy.
Floating, sinking, and neutral buoyancy
An object floats when its weight is less than or equal to the maximum buoyant force the fluid can exert (when the object is fully submerged). It sinks when its average density exceeds the fluid density. It is neutrally buoyant when its average density exactly matches the fluid density, which is how submarines trim to hover at depth and how fish use their swim bladders. Ships float because their average density (steel hull plus large air-filled interior) is far less than sea water, even though the steel alone is about eight times denser than water.
How to use this calculator
Select the fluid from the preset list or choose Custom density to enter any value you need. Enter the displaced volume in cubic metres (metric mode) or cubic feet (imperial mode). If you need to work in litres, convert first: 1 L = 0.001 m3. Adjust the gravity field to model other planets: Mars (3.72 m/s2), Moon (1.62 m/s2), or Jupiter (24.79 m/s2). The results update as you type and the step-by-step panel shows the full working.
Partial submersion and real-world applications
When an object is only partly submerged, V in the formula is only the submerged portion of its volume. A ship floating with half its hull below the waterline displaces water equal to half its hull volume. In engineering, buoyancy calculations are used when designing ships and submarines, sizing life jackets and floatation devices, anchoring underwater pipelines, and assessing whether buried tanks will float during flooding. The buoyant force must be compared to the object's actual weight (mass x g) to decide whether extra ballast, anchoring, or structural support is needed.
Common fluid densities
| Fluid | Density (kg/m3) | Notes |
|---|---|---|
| Fresh water | 1000 | Standard reference; varies 999-1000 between 4-20 C |
| Sea water | 1025 | Varies 1020-1029 with salinity |
| Milk (whole) | 1030 | Varies slightly with fat content |
| Ethanol | 789 | Pure ethyl alcohol at 20 C |
| Glycerin | 1261 | Used in medical and cosmetic applications |
| Gasoline | 720 | Typical; varies 710-770 by blend |
| Diesel fuel | 850 | Typical; varies 820-900 by grade |
| Air (sea level) | 1.225 | Decreases with altitude and temperature increase |
| Mercury | 13534 | Liquid metal; extremely dense |
Reference densities at approximately 20 degrees Celsius and standard atmospheric pressure.
Frequently asked questions
What is the buoyant force formula?
The buoyant force is calculated as B = rho x V x g, where rho is the fluid density (kg/m3), V is the volume of fluid displaced by the submerged object (m3), and g is gravitational acceleration (m/s2, typically 9.81 on Earth). The result is the upward force in Newtons.
Does buoyancy depend on the shape or material of the object?
No. Buoyancy depends only on the volume of fluid displaced and the fluid's density, not on the object's shape, material, or weight. A solid gold cube and a hollow wooden cube of identical outer dimensions experience the same buoyant force in the same fluid.
How do I calculate buoyant force on a partially submerged object?
Use only the submerged portion of the object's volume as V in the formula. For example, if a rectangular block with volume 0.01 m3 is 60% submerged in water, the displaced volume is 0.006 m3 and B = 1000 x 0.006 x 9.81 = 58.86 N.
What units does buoyant force use?
Buoyant force is measured in Newtons (N) in the SI system. One Newton is the force needed to accelerate 1 kg at 1 m/s2. For practical reference, 9.81 N is approximately the weight of a 1-kilogram mass under standard Earth gravity.
Why does an object float or sink?
An object floats if its average density is less than the fluid's density, because the maximum buoyant force (when fully submerged) exceeds its weight. It sinks if its average density is greater than the fluid's. It is neutrally buoyant when both densities match exactly.
How does buoyancy change on the Moon or Mars?
Buoyant force is directly proportional to gravitational acceleration. On the Moon (g = 1.62 m/s2), buoyancy is about 16.5% of its Earth value; on Mars (g = 3.72 m/s2), about 38%. However, object weight scales the same way, so the condition for floating or sinking is unchanged. An object that floats on Earth will still float on the Moon in the same fluid.