Any object in a fluid is pushed up by a force equal to the weight of fluid it displaces. Archimedes is said to have realised this in his bath while checking whether a crown was pure gold.
How to use the Archimedes’ Principle Calculator
- Object mass m
- Object given by
- Object density
- Object volume
- Fluid
- Fluid density
- Gravitational acceleration g
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the object’s mass and either its density or volume, choose the fluid and the gravitational acceleration.
Inputs explained
| Field | What to enter |
|---|---|
| Object mass m | Units: kg, g, mg, t, lb, oz |
| Object given by | Choose one: Density, Volume |
| Object density | Units: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³ |
| Object volume | Units: L, mL, m³, US gal, ft³ |
| Fluid | Choose one: Fresh water (20 °C), Seawater, Air (sea level, 15 °C), Ethanol … |
| Fluid density | Units: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³ |
| Gravitational acceleration g | Units: m/s², ft/s², g, cm/s² |
What each result means
- Buoyant force (fully submerged) = [rf]×[V]×[Gravitational acceleration g]
- Apparent weight = [Object mass m]×[Gravitational acceleration g] – [rf]×[V]×[Gravitational acceleration g]
- Apparent mass = [Object mass m] – [rf]×[V]
- Displaced volume (fully submerged) = [V]
- Submerged fraction when floating = min(1, [Object mass m]÷[V]÷[rf])×100
Example values
How the main result changes when Object mass m changes and everything else stays at the example values above:
| Object mass m (kg) | Buoyant force (fully submerged) (N) |
|---|---|
| 1 | 3.6256 |
| 1.5 | 5.4383 |
| 2 | 7.2511 |
| 2.5 | 9.0639 |
| 3 | 10.8767 |
| 4 | 14.5022 |
Formula
F_B = ρ_f·V·g, W_apparent = m·g − F_B, floating fraction = ρ_object/ρ_f
Worked example
Inputs — Object mass m: 2 kg; Object given by: Density; Object density: 2,700 kg/m³; Fluid: Fresh water (20 °C); Gravitational acceleration g: 9.80665 m/s².
Results — Buoyant force (fully submerged) = 7.25111 N; Apparent weight = 12.36219 N; Apparent mass = 1.26059 kg; Displaced volume (fully submerged) = 0.74074 L; In this fluid it = Sinks; Submerged fraction when floating = 100 %.
Key terms
- Buoyancy
- Upward force from fluid pressure differences.
Frequently asked questions
Why do ships float?
Their hull displaces water weighing as much as the ship.
Does depth change the buoyant force?
Not for an incompressible fluid.
What is apparent weight?
Weight minus buoyancy – what a scale shows underwater.
How did Archimedes test the crown?
By comparing its displaced volume with that of pure gold of the same mass.