Buoyancy Calculator
Find the buoyant force on a submerged object using Archimedes' principle, Fb = ρ·V·g. Enter the displaced volume (liters, m³, gallons, or cubic feet) and pick a fluid — the tool returns the upward force in newtons and pounds-force and can check whether an object floats or sinks.
Example: with Submerged volume 10 · Volume unit liters · Fluid Fresh water (1000 kg/m³) · Object mass (optional, kg) 0 → Buoyant force: 98.07 N (22.0 lbf).
- Mass it can support10 kg of mass
- Float or sinkEnter object mass to check float vs sink
Computed by the calculator below using its default values. Change any input to see your own numbers.
Archimedes' principle: the upward buoyant force equals the weight of the fluid the object pushes aside. Displace more water and you float higher.
Archimedes' principle in practice
Any object placed in a fluid pushes aside a volume of that fluid, and the fluid pushes back up with a force equal to the weight of what was displaced. That is Archimedes' principle, and in equation form it is Fb = ρ·V·g: fluid density times displaced volume times gravity. Because it depends only on the fluid and the submerged volume, a steel hull and a beach ball of the same submerged size feel the same buoyant force.
Whether something floats is a contest between that buoyant force and the object's weight. If the object weighs less than the fluid it can displace, it rises until only part of it is submerged and the forces balance; if it weighs more, it sinks. This is why the same ship floats lower in fresh water than in denser seawater, and why a life jacket that adds volume without much weight keeps a swimmer up.
How it’s calculated
Buoyant force Fb = ρ·V·g, with fluid density ρ in kg/m³, displaced volume V in m³, and g = 9.80665 m/s². Volume converts to m³ (L ÷1000, mL ÷1e6, US gal ×0.00378541, ft³ ×0.02831685, in³ ×1.6387e-5). Supported mass = ρ·V (kg); lbf = N × 0.224809. Float check compares object mass with supported mass.
Assumes the object is fully submerged and the fluid density is uniform. Fluid densities are nominal room-temperature values and shift with temperature and, for seawater, salinity.
Buoyant force per liter displaced
| Fluid | Density (kg/m³) | Force per liter | Mass supported |
|---|---|---|---|
| Oil | 900 | 8.83 N | 0.90 kg |
| Fresh water | 1000 | 9.81 N | 1.00 kg |
| Seawater | 1025 | 10.05 N | 1.03 kg |
| Glycerin | 1260 | 12.36 N | 1.26 kg |
| Mercury | 13534 | 132.7 N | 13.5 kg |
Computed with Fb = ρ·V·g for V = 1 L; rounded.
Common mistakes
- Using the object's total volume when only part is submerged — buoyancy depends on displaced volume only.
- Mixing volume units; a value in liters left as cubic meters overstates force a thousandfold.
- Comparing buoyant force (newtons) directly with mass (kilograms) instead of converting one to match.
- Assuming any hollow object floats — it sinks if its total weight beats the fluid it can displace.
Frequently asked questions
What is the buoyancy formula?
Fb = ρ × V × g, the fluid density times the displaced volume times gravity (9.81 m/s²). It equals the weight of the fluid the object pushes aside.
What makes an object float or sink?
Compare its weight with the buoyant force it can generate when fully submerged. If it weighs less than the fluid it displaces, it floats; if more, it sinks.
Why do things float better in seawater?
Seawater is about 2.5% denser than fresh water, so the same displaced volume produces more buoyant force. Ships ride slightly higher in the ocean than in a freshwater lake.
Does buoyant force depend on depth?
For an incompressible fluid, no — it depends on displaced volume and fluid density, which stay essentially constant with depth. Pressure rises with depth, but the net upward buoyant force does not.