What is Archimedes' Principle?

Archimedes' Principle states that any object fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces: F_b = ρ × V × g.

What units does this calculator use?

Fluid density is in kg/m³, displaced volume is in m³ (converted internally from cm³ or liters if selected), gravity in m/s², and the result is in Newtons (N). One Newton equals the force needed to accelerate 1 kg at 1 m/s².

How do I know if an object floats or sinks?

Compare the buoyant force to the object's weight (mass × g). If F_b ≥ weight, the object floats or is neutrally buoyant. If F_b < weight, it sinks.

What is the density of seawater vs fresh water?

Fresh water is approximately 1000 kg/m³. Seawater averages about 1025 kg/m³ due to dissolved salts, making its buoyant force roughly 2.5% greater.

Can I use this for gases like air?

Yes. Air at sea level is about 1.225 kg/m³. The same formula applies — this is how weather balloons and blimps are designed.

What if only part of the object is submerged?

Enter only the submerged (displaced) volume, not the total object volume. A floating object displaces a volume equal to the portion below the fluid surface.

Buoyant Force Calculator (Archimedes' Principle)

Name: Buoyant Force Calculator (Archimedes' Principle)
Availability: InStock
Author: Nham Vu

Enter fluid density, displaced volume, and gravity to instantly compute the buoyant force via Archimedes' Principle.

Input Parameters

Fluid

Density of the surrounding fluid in kg/m³

Displaced Volume

Volume of fluid displaced by the submerged portion

Gravitational Acceleration

Object Weight (optional — for float/sink check)

Weight of the object in Newtons (mass × g)

Result

Fill in the inputs and click Calculate.

Common Fluid Densities

Fluid	kg/m³
Fresh water (20 °C)	998
Seawater	1 025
Ethanol	789
Crude oil	870
Mercury	13 600
Air (sea level)	1.225
Hydrogen gas (0 °C)	0.0899

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Summary

Enter fluid density, displaced volume, and gravity to instantly compute the buoyant force via Archimedes' Principle.

How it works

Select a preset fluid (water, seawater, oil, air) or enter a custom fluid density in kg/m³.
Enter the volume of fluid displaced by the object in m³, cm³, or liters.
Adjust the gravitational acceleration (default 9.81 m/s² for Earth) or pick a planet preset.
Click Calculate to see the buoyant force in Newtons, along with the equivalent weight it supports.
Use the result to determine whether the object floats, sinks, or is neutrally buoyant compared to its weight.

Use cases

Determine whether a ship hull design will float given its displaced water volume.
Estimate the upthrust on a submarine at a given depth using seawater density.
Verify buoyancy in physics homework or lab problems.
Calculate the lifting force on a weather balloon in air.
Check if a material sample will sink or float in a specific liquid.
Explore how gravity differences on other planets affect buoyancy.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu