Buoyancy Calculator
Buoyant force F = ρ V g on an object in water, seawater or any fluid, whether it floats, sinks or is neutral, how much of it sits under the surface when floating, and its apparent weight when submerged.
Result…
How it's calculated
F_b = ρ_fluid × V_displaced × g Weight W = m g = ρ_object × V × g Floats if ρ_object < ρ_fluid; share under = ρ_object ÷ ρ_fluid Apparent weight = W − F_b
Archimedes' principle says a fluid pushes up on an object with a force equal to the weight of fluid it displaces: ρ_fluid × V × g. If the object's average density is less than the fluid's, it floats with just enough of its volume under the surface to displace its own weight, a share equal to ρ_object ÷ ρ_fluid. If it is denser it sinks, and feels lighter by the buoyant force. The presets use about 1000 kg/m³ for fresh water and about 1025 kg/m³ for surface seawater, as given by The Physics Factbook; enter your own value for any other fluid or temperature. Unit factors are exact: 1 lb = 0.45359237 kg, 1 ft = 0.3048 m, 1 US gal = 3.785411784 L, 1 UK gal = 4.54609 L.
Your numbers, step by step
About the Buoyancy calculator
This buoyancy calculator applies Archimedes' principle: the upward force on an object equals the weight of the fluid it pushes aside, F = ρ_fluid × V × g. Enter the object's volume and either its mass or its density, choose fresh water, seawater or your own fluid density, and it tells you whether the object floats, sinks or is neutrally buoyant. For a floating object you get the share of it under the surface and the force needed to hold it fully under; for a sinking one, its apparent weight in the fluid. Volume works in litres, m³, cm³, ft³, in³ and US or UK gallons, density in kg/m³, g/cm³ or lb/ft³, and force in N, kN, lbf or kgf. It suits physics homework, boats, floats, diving weights and lifting things underwater, with every step shown.
How to use it
- Choose the “Fluid”, or pick another fluid and enter its “Fluid density”.
- Enter the “Object volume” and its unit: the whole volume it would displace when fully under.
- Under “I know its”, choose mass or density and enter the “Object mass” or “Object density”.
- Keep standard gravity or change “Gravitational acceleration”, pick a “Force unit”, and read the buoyant force, the result and the share under the surface or the apparent weight.
Worked example
A 40 kg block of volume 0.05 m³ is put in seawater at 1025 kg/m³. Its density is 40 ÷ 0.05 = 800 kg/m³, less than the water's, so it floats with 800 ÷ 1025 = 78.0% of its volume (0.039 m³) under the surface. Its weight is 40 × 9.80665 = 392.3 N. Fully under, the water would push up with 1025 × 0.05 × 9.80665 = 502.6 N, so holding it down takes 110.3 N.
Updated
Questions people ask
How do I calculate buoyant force?
Multiply the fluid's density by the volume of fluid displaced and by g: F = ρ V g. With density in kg/m³, volume in m³ and g = 9.80665 m/s², the answer is in newtons. One litre of fresh water fully displaced gives about 9.8 N.
How can I tell if an object will float or sink?
Compare its average density with the fluid's. Less dense floats, denser sinks, and equal density is neutrally buoyant. A steel ship floats because its average density, including the air inside the hull, is less than the water's.
How much of a floating object is under water?
The share under the surface is the object's density divided by the fluid's. A block of 600 kg/m³ in fresh water at 1000 kg/m³ floats with 60% of its volume under the surface.
What density should I use for seawater?
The preset uses about 1025 kg/m³, a usual estimate for surface seawater given by The Physics Factbook, which notes a range of roughly 1020 to 1030 kg/m³. A common mistake is to use the freshwater value of 1000 kg/m³ at sea, which slightly understates the lift.
What does the buoyancy calculator not cover?
It treats a solid or sealed object in still fluid. It ignores surface tension, water flowing in, fluid moving past the object and changes in density with depth and temperature. For lifting, diving or boat loading, follow the equipment's ratings and a qualified professional's advice. For density on its own, use the density calculator.