# Buoyancy Calculator

> Calculate the buoyant force on a submerged volume with Archimedes’ principle, and compare it with an object’s weight to see whether it floats or sinks.

Category: Science & engineering · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/buoyancy-calculator

Archimedes’ principle: a fluid pushes up on a submerged object with a force equal to the weight of the fluid it displaces, F = ρ g V. Add the object’s mass to see whether it floats.

Also called: Buoyant force calculator, Archimedes’ principle calculator, Upthrust calculator.

## Inputs
- Fluid density (default 1000)
- Density unit (options: kg/m³, g/cm³, lb/ft³; default kgm3)
- Submerged volume (default 2)
- Volume unit (options: cubic metres (m³), litres (L), millilitres (mL), cubic feet (ft³), cubic inches (in³), US gallons; default l)
- Object mass (optional) (default 1.5; optional)
- Mass unit (options: kilograms (kg), grams (g), tonnes (t), pounds (lb), ounces (oz); default kg)
- Gravitational acceleration (g) (unit m/s²; default 9.80665)

## Results
- Buoyant force
- Buoyant force
- Mass of fluid displaced
- Object weight
- Net upward force when fully submerged
- Float or sink

## Formula

```
F_b = ρ_fluid × g × V;  W = m g;  net = F_b − W;  fraction submerged when floating = W ÷ F_b(full volume)
```

Where:
- F_b: buoyant force in N
- ρ_fluid: fluid density in kg/m³
- V: volume of fluid displaced in m³
- m: object mass in kg

## Worked example
1. V = 2 L = 0.002 m³; displaced water = 1,000 × 0.002 = 2 kg.
2. F_b = 2 kg × 9.80665 = 19.6133 N.
3. Weight = 1.5 × 9.80665 = 14.71 N, less than F_b, so it floats with 1.5 ÷ 2 = 75% of its volume under water.

**Result:** A 2-litre object fully under water feels 19.6 N of upthrust; at 1.5 kg it floats, riding 75% submerged.

## What the result means

An object floats if its average density is below the fluid’s. Ships float despite steel hulls because the hull encloses air, lowering the average density. The net force tells you how much ballast (if negative) or buoyancy aid (if positive) is needed for neutral buoyancy.

## Assumptions and limits
- Fluid of uniform density at rest.
- For the float check, the volume entered is the object’s whole volume.
- Ignores surface tension, which matters only for very small objects.

## Questions

### Why do objects float higher in seawater?

Seawater is denser than fresh water, so less volume needs to be submerged to displace the object’s weight.

### Does depth change the buoyant force?

Not for an incompressible object in a uniform liquid. Compressible things such as divers’ wetsuits lose volume, and buoyancy, as they go deeper.

## Sources
- [BIPM: The International System of Units (SI)](https://www.bipm.org/)

## Related calculators
- [Density Calculator](https://calculators.geekmidst.com/calculators/density-calculator)
- [Hydrostatic Pressure Calculator](https://calculators.geekmidst.com/calculators/hydrostatic-pressure-calculator)
- [Weight Calculator](https://calculators.geekmidst.com/calculators/weight-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/buoyancy-calculator