Buoyancy Force Calculator
Calculate the buoyancy force acting on any object submerged in a fluid using Archimedes' principle. Enter the fluid density, gravitational acceleration, and submerged volume to instantly find the upward buoyant force.
Earth surface = 9.81 m/s². Moon ≈ 1.62 m/s². Mars ≈ 3.72 m/s².
Enter all values above to calculate the buoyancy force.
Common Fluid Densities
| Fluid | Density (kg/m³) |
|---|---|
| Fresh water | 1,000 |
| Seawater | 1,025 |
| Glycerol | 1,261 |
| Vegetable oil | 920 |
| Mineral oil | 850 |
| Mercury | 13,600 |
| Air (sea level) | 1.225 |
Quick answer
Buoyancy force equals the weight of the fluid displaced by a submerged object, calculated as F = ρ × g × V, where ρ is fluid density in kg/m³, g is gravitational acceleration (9.81 m/s² on Earth), and V is the submerged volume in m³. A 0.5 m³ object fully submerged in water experiences a buoyancy force of 4,905 N. If the buoyancy force exceeds the object's weight, the object floats; if it is less, the object sinks. This principle, discovered by Archimedes around 250 BC, explains why ships float and hot-air balloons rise.
Formula & method
F_b = ρ × g × V
- F_b — Buoyancy force (Newtons, N)
- ρ — Fluid density (kg/m³)
- g — Gravitational acceleration (m/s², default 9.81)
- V — Volume of fluid displaced / submerged volume (m³)
Archimedes' principle — the buoyant force equals the weight of the displaced fluid.
Examples
- Input
- ρ = 1000 kg/m³, g = 9.81 m/s², V = 0.5 m³
- Result
- F_b = 4,905 N
- Why
- F_b = 1000 × 9.81 × 0.5 = 4,905 N. The water exerts an upward force of 4,905 N on the block. If the block weighs less than 4,905 N it will float; otherwise it sinks.
- Input
- ρ = 1025 kg/m³, g = 9.81 m/s², V = 0.1 m³
- Result
- F_b = 1,005.53 N
- Why
- F_b = 1025 × 9.81 × 0.1 = 1,005.525 N ≈ 1,005.53 N. Seawater is slightly denser than fresh water, so the buoyancy force is about 2.5% higher than it would be in fresh water for the same volume.
- Input
- ρ = 850 kg/m³, g = 9.81 m/s², V = 2 m³
- Result
- F_b = 16,677 N
- Why
- F_b = 850 × 9.81 × 2 = 16,677 N. Vegetable or mineral oil has a lower density than water, producing a smaller buoyancy force per cubic meter. The 2 m³ container still experiences a substantial upward push of about 16.7 kN.
- Input
- ρ = 13600 kg/m³, g = 9.81 m/s², V = 0.02 m³
- Result
- F_b = 2,668.32 N
- Why
- F_b = 13600 × 9.81 × 0.02 = 2,668.32 N. Mercury is about 13.6 times denser than water, so even a small 0.02 m³ sphere experiences a very large buoyancy force — over 2.6 kN — which is why nearly all solid materials float on mercury.
Frequently asked questions
What is Archimedes' principle?
Archimedes' principle states that the buoyant force on an object submerged in a fluid equals the weight of the fluid that the object displaces. This means F_b = ρ × g × V, where ρ is the fluid density, g is gravitational acceleration, and V is the displaced volume.
Does buoyancy depend on the weight of the object?
No. Buoyancy force depends only on the density of the fluid, gravitational acceleration, and the volume of fluid displaced — not on the object's own weight or material. However, whether the object floats or sinks is determined by comparing its weight to the buoyancy force.
Why does a ship made of steel float?
A steel ship floats because its hollow hull displaces a large volume of water. The buoyancy force generated by that displaced water exceeds the total weight of the ship. If the steel were formed into a solid block, it would displace much less water and sink because its weight would exceed the buoyancy force.
What is the buoyancy force in seawater vs fresh water?
Seawater has a typical density of about 1,025 kg/m³ compared to fresh water at 1,000 kg/m³. For the same submerged volume, seawater produces about 2.5% more buoyancy force. This is why objects float slightly higher in the ocean than in a freshwater lake.
How do I convert buoyancy force from Newtons to other units?
To convert Newtons to kilogram-force (kgf), divide by 9.81 (1 kgf ≈ 9.81 N). To convert to pound-force (lbf), divide by 4.448 (1 lbf ≈ 4.448 N). For example, 4,905 N ÷ 9.81 ≈ 500 kgf, and 4,905 N ÷ 4.448 ≈ 1,102.9 lbf.
What happens at neutral buoyancy?
An object achieves neutral buoyancy when the buoyancy force exactly equals its weight. At this point the object neither floats nor sinks — it remains suspended at any depth. Submarines use ballast tanks to control their average density and achieve neutral buoyancy at a desired depth.
Sources & references
- https://www.britannica.com/science/Archimedes-principle
- https://physics.nist.gov/cuu/Units/index.html
- https://www.engineeringtoolbox.com/fluid-density-temperature-pressure-d_309.html
External references open in a new tab. We are independent and not affiliated with these organizations.
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