# Archimedes’ Principle Calculator

URL: https://speedycalculator.com/calculators/physics/archimedes-principle/
Last updated: 2026-10-30

> The Archimedes' principle calculator finds the buoyant force on an object immersed in a fluid, its apparent weight and mass, and whether it floats – from its mass, its density or volume and the fluid density.

## Inputs

- Object mass m (kg, g, mg, t, lb, oz)
- Object given by
- Object density (kg/m³, g/cm³, g/mL, lb/ft³, lb/in³)
- Object volume (L, mL, m³, US gal, ft³)
- Fluid
- Fluid density (kg/m³, g/cm³, g/mL, lb/ft³, lb/in³)
- Gravitational acceleration g (m/s², ft/s², g, cm/s²)

## Results

- Buoyant force (fully submerged)
- Apparent weight
- Apparent mass
- Displaced volume (fully submerged)
- In this fluid it
- Submerged fraction when floating

## Formula

```
F_B = ρ_f·V·g,  W_apparent = m·g − F_B,  floating fraction = ρ_object/ρ_f
```

## Explanation

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

FieldWhat to enterObject mass mUnits: kg, g, mg, t, lb, ozObject given byChoose one: Density, VolumeObject densityUnits: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³Object volumeUnits: L, mL, m³, US gal, ft³FluidChoose one: Fresh water (20 °C), Seawater, Air (sea level, 15 °C), Ethanol …Fluid densityUnits: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³Gravitational acceleration gUnits: 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)13.62561.55.438327.25112.59.0639310.8767414.5022

## 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.

## FAQ

**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.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)