# What is the buoyancy force?

Finds the buoyant force by Archimedes’ principle, F = ρ × V × g, for water, seawater and other fluids, and with the object’s mass, whether it floats or sinks and its apparent weight.

- Page: https://www.acalculator.org/physics/buoyancy-calculator
- JSON spec: https://www.acalculator.org/physics/buoyancy-calculator.json
- Version: 94714e036e1f

## Default answer

Example with the default inputs (Fluid Fresh water, 4 °C (1,000 kg/m³), Volume under the surface (V) 0.353146667214886 ft³, Gravity (g), m/s² 9.80665): The buoyant force is 98.0665 N (22.0462 lbf).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| fl | Fluid | The fluid the object is in, with its density from OpenStax Tables 14.1 and 14.2, or your own. |
| rho | Fluid density (ρ) | The density of the fluid. |
| V | Volume under the surface (V) | The volume of the object that is under the surface: the volume of fluid it pushes aside. |
| m | Object mass (optional) | The mass of the object. With it, V is the whole object held under the surface, and the page says whether it floats. |
| g | Gravity (g), m/s² | The acceleration of gravity: 9.80665 m/s² is standard gravity on Earth. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| force | Buoyant force (F_B), N | F_B = ρ × V × g, in newtons. |
| forceLbf | Buoyant force, lbf | The buoyant force in pounds-force. |
| fluidMass | Mass of fluid pushed aside, kg | ρ × V: the fluid whose weight is the buoyant force. |
| rho | Fluid density (ρ), kg/m³ | The fluid density used. |
| weight | Object weight (W), N | The object’s weight, m × g. |
| apparent | Apparent weight under the surface, N | W − F_B: what a scale reads under the surface. Below 0, the fluid pushes it up. |
| objectDensity | Object density, kg/m³ | m ÷ V, the object’s average density. |
| verdict | Floats or sinks | Compares the object’s density with the fluid’s. |
| submerged | Share under the surface when floating, % | 100 × ρ_object ÷ ρ_fluid, for an object that floats. |

## Method

F_B = ρ × V × g, the weight of the fluid pushed aside. With the mass m: W = m × g, apparent weight W − F_B, object density m ÷ V; it floats when m ÷ V < ρ, with 100 × (m ÷ V) ÷ ρ percent under the surface.

## Assumptions

- The fluid is at rest and has the same density throughout.
- With a mass, V is the object’s whole volume, held fully under the surface.
- Typed values are read as the exact decimals you typed; each result is rounded once to show.

## Worked examples

1. fl = water4, V = 0.01, g = 9.80665 gives force = 98.0665, fluidMass = 10, forceLbf = 22.0462. Source: OpenStax, University Physics Volume 1, §14.4 Archimedes’ Principle and Buoyancy (F_B = w_fl; fraction submerged = ρ_obj ÷ ρ_fl; Example 14.4: floating 97.0% submerged in fresh water means 970 kg/m³), https://openstax.org/books/university-physics-volume-1/pages/14-4-archimedes-principle-and-buoyancy (retrieved 2026-10-19); OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (Table 14.1: densities of common substances; Table 14.2: densities of water and seawater), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure (retrieved 2026-10-19); NIST Special Publication 811, Appendix B.8 (standard gravity 9.80665 m/s², 1 lbf = 4.4482216152605 N, 1 ft³ = 0.028316846592 m³, 1 lb = 0.45359237 kg), https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-19).
2. fl = water4, V = 0.028317, g = 9.80665 gives force = 277.693, forceLbf = 62.428. Source: OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (Table 14.1: densities of common substances; Table 14.2: densities of water and seawater), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure (retrieved 2026-10-19); NIST Special Publication 811, Appendix B.8 (standard gravity 9.80665 m/s², 1 lbf = 4.4482216152605 N, 1 ft³ = 0.028316846592 m³, 1 lb = 0.45359237 kg), https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-19).
3. fl = sea, V = 1, g = 9.8 gives force = 10,094, fluidMass = 1,030. Source: OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (Table 14.1: densities of common substances; Table 14.2: densities of water and seawater), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure (retrieved 2026-10-19).
4. fl = water4, V = 0.1, m = 97, g = 9.8 gives objectDensity = 970, submerged = 97, verdict = Floats: it is less dense than the fluid, apparent = −29.4. Source: OpenStax, University Physics Volume 1, §14.4 Archimedes’ Principle and Buoyancy (F_B = w_fl; fraction submerged = ρ_obj ÷ ρ_fl; Example 14.4: floating 97.0% submerged in fresh water means 970 kg/m³), https://openstax.org/books/university-physics-volume-1/pages/14-4-archimedes-principle-and-buoyancy (retrieved 2026-10-19).
5. fl = water4, V = 0.002, m = 5, g = 9.80665 gives weight = 49.0333, force = 19.6133, apparent = 29.42, verdict = Sinks: it is denser than the fluid. Source: OpenStax, University Physics Volume 1, §14.4 Archimedes’ Principle and Buoyancy (F_B = w_fl; fraction submerged = ρ_obj ÷ ρ_fl; Example 14.4: floating 97.0% submerged in fresh water means 970 kg/m³), https://openstax.org/books/university-physics-volume-1/pages/14-4-archimedes-principle-and-buoyancy (retrieved 2026-10-19).
6. fl = air, V = 1, g = 9.80665 gives force = 12.6506. Source: OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (Table 14.1: densities of common substances; Table 14.2: densities of water and seawater), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure (retrieved 2026-10-19).

## FAQ

### How do you calculate buoyant force?

Multiply the fluid density by the volume under the surface and by g: F = ρ × V × g. Ten litres (0.01 m³) under fresh water: F = 1,000 × 0.01 × 9.80665 = 98.07 N, the weight of 10 kg of water.

### What is Archimedes’ principle?

The buoyant force on an object equals the weight of the fluid it pushes aside (OpenStax University Physics §14.4). It does not depend on what the object is made of, only on the volume under the surface and the fluid.

### How do I know if an object will float or sink?

Compare densities. An object denser than the fluid sinks; a less dense one floats. A 5 kg object of 2 litres has 2,500 kg/m³, so it sinks in water (1,000 kg/m³); held under, it still weighs 49.03 − 19.61 = 29.42 N.

### How much of a floating object is under water?

The share under the surface is ρ_object ÷ ρ_fluid. An object of 970 kg/m³ floats in fresh water with 970 ÷ 1,000 = 97% under, as in OpenStax Example 14.4.

### What is the buoyant force of 1 cubic foot of water?

One cubic foot is 0.028316846592 m³, so in fresh water at 4 °C the force is 1,000 × 0.028316846592 × 9.80665 = 277.69 N, or 62.43 lbf: the weight of a cubic foot of water.

### Why do things float more easily in seawater?

Seawater is denser, 1,030 kg/m³ against 1,000 kg/m³ for fresh water (OpenStax Table 14.2), so the same volume under the surface gives 3% more lift.

## Sources

- OpenStax, University Physics Volume 1, §14.4 Archimedes’ Principle and Buoyancy: F_B = w_fl; a floating object has ρ_obj ÷ ρ_fl of its volume submerged; Example 14.4 (floating 97.0% submerged in fresh water means 970 kg/m³), retrieved 2026-10-19. https://openstax.org/books/university-physics-volume-1/pages/14-4-archimedes-principle-and-buoyancy
- OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure: Table 14.1 (densities of common substances, liquids at 0 °C, air at 0 °C and 101.3 kPa) and Table 14.2 (densities of water and seawater), retrieved 2026-10-19. https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure
- NIST Special Publication 811, Appendix B.8: standard gravity 9.80665 m/s², 1 lbf = 4.4482216152605 N, 1 lb = 0.45359237 kg, 1 ft³ = 0.028316846592 m³, 1 gal = 0.003785411784 m³, 1 in³ = 0.000016387064 m³, retrieved 2026-10-19. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8