Quick answer
The buoyant force is F_b = ρ g V, the weight of displaced fluid. A 0.5 m³ object submerged in fresh water feels 4,903.3 N of upthrust, equal to the weight of 500 kg of water.
Choose the fluid and enter the displaced volume. The calculator returns the buoyant force and the mass of the fluid displaced.
Related tools: Force Calculator: Force from mass and acceleration (Newton's second law). Reynolds Number Calculator: Reynolds number and flow regime in a pipe. Flow Rate Calculator: Volumetric flow rate from area and velocity, or volume and time.
How to use the Buoyant Force Calculator
- Choose fluid: Fresh water (about 1,000 kg/m³), Seawater (about 1,025 kg/m³) and Custom density.
- Optionally, enter custom density (kg/m³) (above 0).
- Enter volume displaced (m³) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Fluid | Choose one: Fresh water (about 1,000 kg/m³); Seawater (about 1,025 kg/m³); Custom density | Starts at Fresh water (about 1,000 kg/m³) |
| Custom density (optional) | A number, in kg/m³ | > 0 |
| Volume displaced | A number, in m³ | > 0 |
Formula and method
Formula
F_b = ρ g V
IEEE-754 double precision; shown to the decimals indicated.
Fresh water is taken as 1,000 kg/m³ and seawater as 1,025 kg/m³ (typical values).
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Fluid = Fresh water (about 1,000 kg/m³); Volume displaced = 0.5.
| Result | Value |
|---|---|
| Buoyant force | 4,903.325 N |
| Mass of fluid displaced | 500 kg |
Example 2
Inputs: Fluid = Seawater (about 1,025 kg/m³); Volume displaced = 2.
| Result | Value |
|---|---|
| Buoyant force | 20,103.6325 N |
| Mass of fluid displaced | 2,050 kg |
Example 3
Inputs: Fluid = Custom density; Volume displaced = 0.1; Custom density = 800.
| Result | Value |
|---|---|
| Buoyant force | 784.532 N |
| Mass of fluid displaced | 80 kg |
The first line is the headline result (buoyant force). Below it the buoyant Force Calculator lists mass of fluid displaced, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Floating or sinking
An object floats if its average density is below the fluid's. Compare the buoyant force with the object's weight: a 500 kg object in this volume would be neutrally buoyant, a lighter one floats.
Fluid density
Fresh water is about 1,000 kg/m³ and seawater about 1,025 kg/m³, so the same volume gets 2.5% more upthrust in the sea. Density varies with temperature and salinity.
How the result changes with volume displaced
Holding every other input at the first worked example, this table changes only volume displaced. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Volume displaced | Buoyant force | Mass of fluid displaced |
|---|---|---|
| 0.25 | 2,451.6625 N | 250 kg |
| 0.5 | 4,903.325 N | 500 kg |
| 1 | 9,806.65 N | 1,000 kg |
| 2 | 19,613.3 N | 2,000 kg |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Custom density: left empty shows "Enter the fluid density." beside that field and no result.
- Volume displaced: entering "0" shows "Volume displaced must be greater than 0." beside that field and no result.
Choosing between the Buoyant Force Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Force Calculator](/science/force-calculator/) | mass and acceleration | Force |
| [Reynolds Number Calculator](/science/reynolds-number-calculator/) | fluid density, flow velocity and pipe diameter | Reynolds number |
| [Flow Rate Calculator](/science/flow-rate-calculator/) | use | Flow rate |
| [Specific Gravity Calculator](/science/specific-gravity/) | density | Specific gravity |
| [Water Viscosity Calculator](/science/water-viscosity/) | temperature | Dynamic viscosity |
Background: fluid flow
Volumetric flow rate is Q = A × v (cross-sectional area times average velocity). Bernoulli's equation, P + ½ρv² + ρgh = constant, holds along a streamline for steady, incompressible, frictionless flow, so real pipes need friction corrections. The Reynolds number Re = ρvL/μ compares inertia with viscosity.
Laminar flow in a pipe is usually quoted below Re of about 2,100 to 2,300 and fully turbulent above about 4,000, with an uncertain transition between; treat the thresholds as approximate.
Assumptions and limitations
- Density varies with temperature and salinity
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for custom density and volume displaced to confirm this.
Frequently asked questions
Why do ships float?
They displace a large volume of water.
What is Archimedes' principle?
Upthrust equals the weight of the displaced fluid.
What is the upthrust in seawater?
About 5,026 N for 0.5 m³.
What does the Buoyant Force Calculator calculate?
Upward buoyant force on a submerged object (Archimedes' principle). It returns Buoyant force and Mass of fluid displaced.
What formula does the Buoyant Force Calculator use?
F_b = ρ g V. Fresh water is taken as 1,000 kg/m³ and seawater as 1,025 kg/m³ (typical values).
What do I need to enter in the buoyant Force Calculator?
You enter Fluid and Volume displaced (m³). Optional: Custom density (kg/m³).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Density varies with temperature and salinity.
What does the “Fluid” option change?
It sets how the buoyant Force is worked out. The choices are Fresh water (about 1,000 kg/m³), Seawater (about 1,025 kg/m³) and Custom density.
What is an example of a buoyant Force result?
With fluid Fresh water (about 1,000 kg/m³) and volume displaced 0.5, the buoyant force is 4,903.325 N.
Where does the method come from?
The method follows: Archimedes' principle; typical seawater density from UNESCO/EOS-80 practice; CODATA 2018 / SI exact constants: g₀ = 9.80665 m/s², c = 299,792,458 m/s, h = 6.62607015×10⁻³⁴ J·s, e = 1.602176634×10⁻¹⁹ C, G = 6.67430×10⁻¹¹ m³/(kg·s²).
Related calculators
- Force Calculator — Force from mass and acceleration (Newton's second law).
- Reynolds Number Calculator — Reynolds number and flow regime in a pipe.
- Flow Rate Calculator — Volumetric flow rate from area and velocity, or volume and time.
- Specific Gravity Calculator — Specific gravity from density, relative to water at 1,000 kg/m³.
- Water Viscosity Calculator — Dynamic viscosity of liquid water at a temperature.
- Water Velocity Calculator — Water velocity in a pipe from flow and inside diameter.
Sources
- Archimedes' principle; typical seawater density from UNESCO/EOS-80 practice; CODATA 2018 / SI exact constants: g₀ = 9.80665 m/s², c = 299,792,458 m/s, h = 6.62607015×10⁻³⁴ J·s, e = 1.602176634×10⁻¹⁹ C, G = 6.67430×10⁻¹¹ m³/(kg·s²)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.