Buoyancy Calculator: Buoyant Force, Float or Sink, and Fraction Submerged
Solve buoyant force from Archimedes' principle F = ρ·V·g, get a float or sink verdict from densities, and find the fraction submerged, with a sourced fluid density table.
Enter fluid density and displaced volume to see the buoyant force.
Buoyant force F_b
Enter values
- Mass of displaced fluid m_disp ρ_fluid · V
- Gravity g used
- Formula used
- Fraction submerged percent, then the raw ratio
- Fraction above surface
- Solved density
- Displaced volume V_disp
Apparent weight W_app
Enter values
- True weight W_true ρ_object · V · g
- Buoyant force F_b ρ_fluid · V · g
- Gravity g used
| Fluid | Density (kg/m³) | Condition | Source |
|---|---|---|---|
| Fresh water | 1000 | 4 °C (maximum density) | Engineering ToolBox, Water - Density |
| Fresh water | 998.2 | 20 °C | Engineering ToolBox, Water - Density |
| Fresh water | 997 | 25 °C | Engineering ToolBox, Water - Density |
| Seawater | 1025 | S = 35 PSU, surface, about 15 °C (nominal) | Engineering ToolBox, Seawater - Properties |
| Mercury | 13546 | 20 °C (13545.85, CRC/NIST high-accuracy) | CRC Handbook / NIST |
| Ethanol | 789 | 20 °C | Engineering ToolBox, Liquids - Densities |
| Glycerin | 1260 | 20 °C | Engineering ToolBox, Liquids - Densities |
| Olive oil | 918 | 20 °C | Engineering ToolBox, Liquids - Densities |
F_b = ρ_fluid · V · g; f = ρ_object / ρ_fluid; W_app = (ρ_object - ρ_fluid) · V · g
How?
How this is calculated
Buoyant force follows Archimedes' principle: the upward force on a body equals the weight of the fluid it displaces, F_b = ρ_fluid · V · g. Enter the fluid density and the displaced volume and the tool solves the force; leave any one of the four fields blank and it solves that field from the other three.
A body floats when its average density is below the fluid's, sinks when it is above, and hovers at neutral buoyancy when the two are equal. For a floating body in equilibrium its weight equals the buoyant force, so the fraction submerged is f = ρ_object / ρ_fluid. A denser-than-fluid body sinks and displaces its full volume: the reported fraction is capped at 100% rather than shown above it.
Apparent weight is the reduced weight a fully submerged body registers, W_app = W_true - F_b = (ρ_object - ρ_fluid) · V · g. A floating body is not fully submerged, so buoyancy supports it completely and the apparent weight is reported as zero, never as a negative number.
Formula: F_b = ρ_fluid · V · g; f = ρ_object / ρ_fluid; W_app = (ρ_object - ρ_fluid) · V · g
How buoyancy works, and why the iceberg sits 90% underwater
Archimedes' principle turns "will it float" into one comparison: average density against the fluid's. Ice has a density near 917 kg/m³ and seawater near 1025 kg/m³, so ice floats with 917 / 1025 = 0.895 of its volume submerged. That is the familiar "about 90% of an iceberg is underwater." In fresh water (1000 kg/m³) the same ice sits with 91.7% below the surface.
Conventions used
Several choices change the numbers, so this tool names each one.
- Gravity g = 9.81 m/s² by default. The rounded 9.8 and the defined standard gravity 9.80665 m/s² (3rd CGPM, 1901) are one click away on the preset select, and the field stays editable for other bodies. The value used is stated beside every force result.
- Water default 1000 kg/m³ is fresh water at 4 °C, its maximum density. The temperature-dependent values (998.2 at 20 °C, 997.0 at 25 °C) are in the reference table so the choice is explicit and correctable.
- Fraction submerged is capped at 100%. A body denser than the fluid sinks and displaces its full volume; the tool reports "fully submerged" rather than a fraction above 100%.
- Apparent weight is defined only for a fully submerged body. A floating body reports zero apparent weight with a note, not a negative number.
- Fluid density is the density that enters the force, and volume is the displaced volume. Entering object density where fluid density belongs is the common error; the field labels guard against it.
Sources
- University Physics Volume 1, 14.4 Archimedes' Principle and Buoyancy. OpenStax. Retrieved .
- 14.6: Archimedes' Principle and Buoyancy (University Physics I, OpenStax). Physics LibreTexts. Retrieved .
- SI Brochure: standard gravity g_n = 9.80665 m/s^2 (3rd CGPM, 1901). BIPM. Retrieved .
- Water - Density, Specific Weight and Thermal Expansion Coefficients. Engineering ToolBox. Retrieved .
- Liquids - Densities. Engineering ToolBox. Retrieved .