Buoyancy Calculator — Archimedes' Principle Explained
Archimedes supposedly leaped from his bath shouting "Eureka!" after realising that a submerged object displaces fluid equal to its own volume. That insight became the principle that explains why steel ships float, submarines dive, and hot-air balloons rise. The free buoyancy calculator on PublicSoftTools makes the calculation instant.
Archimedes' Principle
The buoyant force on a submerged object equals the weight of the fluid it displaces:
F_b = ρ × V × g
Where ρ is the fluid density in kg/m³, V is the displaced volume in m³, and g = 9.81 m/s² is gravitational acceleration. The result F_b is in Newtons.
Buoyancy by Fluid Type
| Fluid | Density | Buoyancy per 1 L displaced |
|---|---|---|
| Freshwater | 1,000 kg/m³ | 9.81 N |
| Seawater | 1,025 kg/m³ | 10.06 N |
| Mercury | 13,600 kg/m³ | 133.4 N |
| Vegetable oil | ~900 kg/m³ | 8.83 N |
| Air (sea level) | 1.225 kg/m³ | 0.012 N |
Float or Sink?
An object floats when buoyant force ≥ object weight (F_b ≥ mg). It sinks when weight exceeds buoyancy. The condition simplifies to:
- Floats if average object density < fluid density
- Sinks if average object density > fluid density
- Neutral buoyancy if average object density = fluid density
This is why a steel ship floats: a hollow hull filled with air has an average density much less than water's 1,000 kg/m³. A solid steel block with density ~7,800 kg/m³ sinks immediately.
How to Use the Calculator
- Open the buoyancy calculator.
- Select the fluid from the presets (water, seawater, mercury, oil, air) or enter a custom density.
- Enter the displaced volume V in m³. (1 liter = 0.001 m³; 1 cm³ = 1×10⁻⁶ m³)
- Optionally enter the object mass to enable the float/sink check.
- Read the buoyant force, object weight, net force, and float/sink status.
Real-World Applications
Submarines and ballast tanks
Submarines achieve neutral buoyancy by pumping water into or out of ballast tanks, adjusting their average density. To dive, they flood the tanks (increase average density); to surface, they blow compressed air into the tanks (decrease average density). Neutral buoyancy allows hovering at any depth without engine power.
Hot-air balloons
A balloon floats in air when its total weight (envelope + gas + basket + passengers) is less than the weight of displaced air. Hot air at ~100°C has density ~0.946 kg/m³ vs. cool air at ~1.225 kg/m³. For a 2,800 m³ balloon, the buoyancy difference is: (1.225 − 0.946) × 2800 × 9.81 ≈ 7,658 N — enough to lift about 780 kg.
Common Questions
Does buoyancy depend on depth?
Not directly. F_b = ρVg depends only on fluid density, displaced volume, and gravity — not on depth. However, fluid density can vary slightly with depth (especially in the ocean due to salinity and temperature), which causes small depth-dependent changes.
Why does it feel easier to float in saltwater than freshwater?
Seawater is denser (~1025 kg/m³ vs. 1000 kg/m³) so it exerts about 2.5% more buoyant force for the same displaced volume. For an average adult, this 2.5% difference is enough to shift from barely floating to comfortably floating.
Calculate Buoyant Force
Enter fluid density, displaced volume, and optionally object mass to check buoyancy instantly.
Open Buoyancy Calculator