Buoyancy is the upward force a fluid exerts on any object placed in it. It is one of the oldest and most useful principles in physics, first described by Archimedes of Syracuse around 250 BCE: a body immersed in a fluid experiences an upward force equal to the weight of the fluid it displaces. This calculator applies that principle directly, letting you compute the buoyant force, work backwards to find the fluid density, or determine the submerged volume required to produce a known upthrust — all in one tool.
Practical uses range from everyday questions (“will this foam float?”) to engineering design (ship hull sizing, submarine ballast, life-jacket certification, hot-air balloon lift) and scientific measurement (using buoyancy to infer the density of irregular solids). The net-force mode extends the tool to answer the real-world question engineers always ask: given both the buoyant force and the object weight, which direction does the net force act?
How it works
The governing equation is Archimedes’ principle:
F_b = ρ × V × g
| Symbol | Meaning | SI unit |
|---|---|---|
| F_b | Buoyant force (upthrust) | N (newtons) |
| ρ | Fluid density | kg/m³ |
| V | Volume of fluid displaced (= submerged volume of object) | m³ |
| g | Standard gravitational acceleration = 9.80665 m/s² | m/s² |
The formula rearranges cleanly in all three directions:
- Solve for force: F_b = ρ · V · g
- Solve for density: ρ = F_b ÷ (V · g)
- Solve for volume: V = F_b ÷ (ρ · g)
The standard gravity value 9.80665 m/s² is the internationally defined constant from ISO 80000-3, used in all engineering and scientific standards — not the local gravitational field, which varies by ±0.5% with latitude and altitude.
Worked example
A hollow steel buoy has a submerged volume of 0.2 m³ and floats in sea water (density 1025 kg/m³). What is the buoyant force, and if the buoy plus fittings weigh 180 kg, does the assembly float?
- F_b = ρ × V × g = 1025 × 0.2 × 9.80665 ≈ 2010.4 N
- Object weight W = m × g = 180 × 9.80665 ≈ 1765.2 N
- Net force = F_b − W = 2010.4 − 1765.2 = +245.2 N upward → the buoy floats and still has 245 N of positive buoyancy available for attachments.
A second example: an aluminium cylinder (mass 2.7 kg, volume 0.001 m³) is submerged in fresh water (998.2 kg/m³).
- F_b = 998.2 × 0.001 × 9.80665 ≈ 9.79 N
- Weight = 2.7 × 9.80665 ≈ 26.48 N
- Net force = 9.79 − 26.48 = −16.69 N (downward) → the cylinder sinks.
Formula note
The calculator uses the full standard gravity (g = 9.80665 m/s²) rather than the rounded approximation of 9.81 or 10. For most engineering problems the difference is under 0.05 %, but using the ISO standard value keeps results consistent with published data tables (which themselves use 9.80665). If your context uses a local gravity value (e.g. high-altitude experiments), multiply the reported buoyant force by your local g ÷ 9.80665 to correct it.
For partially submerged objects (boats, floating buoys) set V to the displaced volume — the volume of fluid pushed aside — not the total object volume. For a fully submerged object (submarine, diver) the displaced volume equals the object’s own volume.