# Buoyancy / Archimedes' Principle Calculator

Calculate buoyant force using Archimedes' principle F_b = ρVg. Determine if an object floats or sinks. Enter fluid density, volume, and mass.

## What this calculates

Archimedes' principle states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces: F_b = ρ_fluid × V × g. This calculator computes the buoyant force, compares it to the object's weight, and determines whether the object will float, sink, or be neutrally buoyant.

## Inputs

- **Fluid Density (ρ_fluid)** (kg/m³) — min 0 — Fresh water: 1000, Seawater: 1025, Oil: ~900
- **Displaced Volume (V)** (m³) — min 0
- **Object Mass** (kg) — min 0
- **Object Density (optional)** (kg/m³) — min 0 — If given with mass, volume is calculated

## Outputs

- **Buoyant Force** (N) — F_b = ρ_fluid × V × g
- **Object Weight** (N) — W = mg
- **Net Vertical Force** (N) — Positive = floats upward, Negative = sinks
- **Float or Sink?** — formatted as text — Whether the object floats or sinks

## Frequently Asked Questions

**Q: What is Archimedes' principle?**

A: Archimedes' principle states that any object partially or fully submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced. Legend has it that Archimedes discovered this while taking a bath, observing that the water level rose as he got in, and exclaimed 'Eureka!' It applies to all fluids, including gases.

**Q: Why do some objects float and others sink?**

A: An object floats if its average density is less than the fluid's density, because the buoyant force exceeds its weight. If its density is greater than the fluid, it sinks. A steel ship floats because its hollow hull gives it an overall density less than water, even though steel itself is denser than water.

**Q: Why is it easier to float in the Dead Sea?**

A: The Dead Sea has extremely high salinity, giving it a density of about 1,240 kg/m³ compared to regular seawater at 1,025 kg/m³. The higher fluid density produces a larger buoyant force for the same displaced volume, making it much easier to float. Humans are less dense than Dead Sea water, so they float effortlessly.

**Q: How does buoyancy work for hot air balloons?**

A: Hot air is less dense than the surrounding cooler air. The balloon displaces a volume of cool air, and the buoyant force equals the weight of that displaced cool air. Since the hot air inside weighs less than the cool air it displaces, the net upward force lifts the balloon. This is Archimedes' principle applied to gases.

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Source: https://vastcalc.com/calculators/physics/buoyancy
Category: Physics
Last updated: 2026-04-21