🌊 Buoyancy Calculator
Calculate buoyant force using Archimedes' principle: Fb = ρ × V × g. Solve for force, fluid density, displaced volume, or gravity. Includes float/sink analysis and a comprehensive fluid density reference table.
What Is Buoyancy?
Buoyancy is the upward force exerted by a fluid on an object placed in it. It arises because pressure increases with depth — the pressure on the bottom of the object is greater than on the top, creating a net upward force. This phenomenon was first explained by the ancient Greek mathematician Archimedes around 250 BCE.
Archimedes' Principle
Archimedes' principle states that the buoyant force on an object equals the weight of the fluid it displaces:
Fb = ρ · V · g
where Fb = buoyant force (N), ρ = fluid density (kg/m³), V = displaced volume (m³), g = gravitational acceleration (m/s²)
The displaced volume V is the volume of the object that is submerged in the fluid. For a fully submerged object, V equals the object's total volume. For a partially submerged object (floating), V is only the volume below the fluid surface.
This principle explains a wide range of everyday phenomena:
- Why ships float: A ship is hollow and filled with air, so its average density is less than water. It displaces water equal to its weight.
- Why ice floats: Ice has a density of about 917 kg/m³ — less than water (1000 kg/m³). About 92% of an iceberg is submerged.
- Why balloons rise: Helium is less dense than air. A helium balloon displaces more air weight than its own weight.
- Why steel sinks: Solid steel has a density of about 7850 kg/m³ — much greater than water. A steel ship floats because it's hollow.
Float, Sink, or Neutral Buoyancy?
Whether an object floats or sinks depends on the comparison between its density and the fluid density:
- Floats: ρobject < ρfluid — the buoyant force exceeds the object's weight.
- Sinks: ρobject > ρfluid — the object's weight exceeds the buoyant force.
- Neutral buoyancy: ρobject = ρfluid — the object hovers at a constant depth.
For a floating object, the fraction submerged is given by:
fraction submerged = ρobject / ρfluid
For example, ice (917 kg/m³) floating in water (1000 kg/m³) has a fraction submerged of 917/1000 = 0.917, meaning about 92% of the ice is below the surface.
Why Use This Calculator?
- Solve for any variable: Calculate Fb, ρ, V, or g depending on what's unknown.
- Fluid presets: Quickly load common fluid densities (water, seawater, mercury, oil, etc.).
- Float/sink analysis: Get an instant determination of whether the object floats or sinks.
- Step-by-step solution: See exactly how the calculation is performed.
- Free & private: No registration, no data storage — all calculations are done in your browser.
❓ Buoyancy Calculator FAQ
What is the formula for buoyant force?
The formula is Fb = ρ × V × g, where ρ is fluid density, V is displaced volume, and g is gravitational acceleration.
What is Archimedes' principle?
Archimedes' principle states that the buoyant force on an object equals the weight of the fluid it displaces. This principle applies to both fully and partially submerged objects.
Why do some objects float and others sink?
An object floats if its average density is less than the fluid's density. It sinks if its density is greater. For example, ice (917 kg/m³) floats on water (1000 kg/m³), while steel (7850 kg/m³) sinks.
How do ships float despite being made of steel?
A ship is hollow and filled with air, so its average density (including the air inside) is less than water. The ship displaces water equal to its own weight, allowing it to float.
What is the density of seawater?
Seawater has a density of approximately 1025 kg/m³, about 2.5% higher than freshwater. This is why it's easier to float in the ocean than in a lake.
What is neutral buoyancy?
Neutral buoyancy occurs when an object's density equals the fluid density. The object neither floats nor sinks — it hovers at a constant depth. Submarines use this principle to maintain depth.
How does the shape of an object affect buoyancy?
Shape affects buoyancy only in that it determines how much volume is submerged. A hollow shape (like a ship's hull) displaces more water than a solid shape of the same weight, increasing the buoyant force.
What is the standard value for gravity in buoyancy calculations?
Standard gravity is 9.80665 m/s². For most calculations, 9.81 m/s² is sufficiently accurate.
How accurate is this calculator?
This calculator uses the exact Archimedes' principle formula Fb = ρVg. Accuracy depends on the precision of the input values. You can adjust the decimal precision in the output.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required.