EngineeringFormulaFluid Mechanics
Buoyant Force Calculator
Calculate buoyant force, displaced fluid volume, or fluid density from Archimedes' principle using F_B = rho g V_displaced.
Buoyant force is the upward force a fluid exerts on an immersed object. By Archimedes' principle, the buoyant-force magnitude equals the weight of the fluid displaced by the object: F_B = rho g V_displaced. This calculator lets you solve for buoyant force itself, the displaced fluid volume, or the surrounding fluid density while keeping the key idea explicit: the important volume is the fluid displaced, not automatically the object's total geometric volume.
rho · Mass density of the surrounding fluid, treated as constant over the displaced volume.
g · Local gravitational acceleration magnitude.
V_d · Volume of fluid displaced by the immersed portion of the object. This equals the submerged object volume, not always the total object volume.
Enter displaced fluid volume, not automatically total object volume. Buoyant force here is reported as an upward magnitude from Archimedes' principle.
Solution
Enter the required values to calculate buoyant force.
F_B = rho g V_d
Formula Sheet
- F_BBuoyant Force
- rhoFluid Density
- gGravity
- V_dDisplaced Fluid Volume
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| F_B | Buoyant Force | Upward buoyant-force magnitude exerted by the fluid on the immersed object. | N, kN, lbf |
| rho | Fluid Density | Mass density of the surrounding fluid, treated as constant over the displaced volume. | kg/m³, g/cm³, lb/ft³ |
| g | Gravity | Local gravitational acceleration magnitude. | m/s², ft/s², g |
| V_d | Displaced Fluid Volume | Volume of fluid displaced by the immersed portion of the object. This equals the submerged object volume, not always the total object volume. | m³, L, ft³, US gal |
How to Use This Calculator
- 01Choose whether you want to solve for buoyant force, fluid density, or displaced volume.
- 02Enter the known values using the engineering units that match your problem. Gravity must be positive, and density should be positive for real fluids.
- 03Use displaced volume, not necessarily total object volume. For a fully submerged rigid object, displaced volume equals submerged object volume. For a floating or partially submerged object, use only the submerged/displaced portion.
- 04Select Calculate to see the result, active formula, and a substitution line in coherent SI units. Then compare buoyant force with object weight: F_B greater than weight means upward net force, F_B less than weight means downward net force, and F_B equal to weight means neutral or floating equilibrium.
How the Formula Works
Pressure in a fluid increases with depth, so the fluid pushes upward more strongly on the bottom of an immersed object than it pushes downward on the top. That difference creates the buoyant force. Archimedes' principle summarizes the result compactly: the buoyant-force magnitude equals the weight of the fluid displaced.
For constant fluid density, that becomes F_B = rho g V_displaced. The formula depends on the fluid density, gravity, and displaced volume only. It does not directly depend on the object's mass or weight. Those matter only when you compare the buoyant force against the object's weight to decide whether it rises, sinks, or remains neutrally suspended.
A useful next check is apparent weight: W_apparent = W_object - F_B. A positive apparent weight means the object still loads the support or sinks; zero means neutral support; a negative value means extra downward restraint or ballast would be needed to keep it submerged.
Worked Example 01
Buoyant force on a fully submerged object in fresh water
Known
- Fluid Density (rho): 1000 kg/m³
- Gravity (g): 9.81 m/s²
- Displaced Volume (V_d): 0.02 m³
Formula
F_B = rho g V_d
Substitution
F_B = 1000 x 9.81 x 0.02
Result
F_B = 196.2 N
A submerged body displacing 0.02 cubic meters of fresh water experiences an upward buoyant force of 196.2 N.
Worked Example 02
Displaced volume required in seawater
Known
- Buoyant Force (F_B): 154.5 N
- Fluid Density (rho): 1030 kg/m³
- Gravity (g): 9.81 m/s²
Formula
V_d = F_B / (rho g)
Substitution
V_d = 154.5 / (1030 x 9.81)
Result
V_d ≈ 0.01529 m³
In seawater, less displaced volume is needed than in fresh water for the same buoyant force because the fluid density is higher.
Worked Example 03
Fluid density from measured buoyant force
Known
- Buoyant Force (F_B): 88.29 N
- Gravity (g): 9.81 m/s²
- Displaced Volume (V_d): 0.009 m³
Formula
rho = F_B / (g V_d)
Substitution
rho = 88.29 / (9.81 x 0.009)
Result
rho ≈ 1000 kg/m³
That measured buoyant force and displaced volume correspond closely to fresh water density.
Applications
- 01Estimating lift on submerged components, floats, and marine hardware
- 02Checking displaced volume needed to obtain a target buoyant force in water or another fluid
- 03Back-calculating approximate fluid density from a measured buoyant force and displaced volume
- 04Screening whether a submerged object needs ballast, restraint, or more displacement volume
Typical Fluid Densities for Buoyancy Estimates
| Fluid | Density (kg/m³) | Buoyancy note |
|---|---|---|
| Fresh water | about 1000 | Baseline: 1 L displaced gives about 9.81 N of lift |
| Sea water | about 1025-1030 | Slightly more lift than fresh water for the same displacement |
| Olive oil | about 920 | Less lift than water; many plastics float differently here |
| Glycerin | about 1260 | More lift than water because density is higher |
| Air (standard conditions) | about 1.2 | Buoyancy exists but is small unless volume is large |
Assumptions
- 01The fluid density is treated as uniform over the displaced volume.
- 02The calculator returns buoyant-force magnitude only, not a signed vertical force balance.
- 03The displaced volume entered corresponds to the immersed portion of the object.
Where This Model Stops
- 01Does not determine by itself whether an object floats or sinks, because that also requires the object's weight or average density.
- 02Does not model layered fluids, compressibility, or fluid density changes with depth.
- 03Does not calculate apparent weight directly, though apparent weight can be found separately as object weight minus buoyant force.
References
- [1]University Physics Volume 1, Section 14.4: Archimedes' Principle and Buoyancy
OpenStax
Defines buoyant force, states Archimedes' principle, and explains floating, sinking, and fraction submerged.
- [2]Chapter 14 Summary
OpenStax
Summarizes buoyant-force conditions for floating, sinking, and neutral suspension.
Frequently Asked Questions
Is displaced volume the same as object volume?
Only when the object is fully submerged. For a floating or partially submerged object, the displaced volume equals only the submerged portion of the object, because that is the amount of fluid actually displaced.
Does an object that sinks still experience buoyant force?
Yes. Buoyant force is present on any immersed object in any fluid. A sinking object simply has a weight greater than the buoyant force, so the net force is downward.
How do I tell whether an object floats?
Compare buoyant force with the object's weight, or compare the object's average density with the fluid density. If buoyant force exceeds weight, it rises; if it is smaller, it sinks; if they are equal, it can remain suspended or float in equilibrium.
How is this different from the Hydrostatic Pressure Calculator?
Hydrostatic pressure calculates pressure at a depth using p = rho g h. Buoyant force uses the pressure difference over the object and collapses that effect into F_B = rho g V_displaced, so the key input is displaced volume rather than depth alone.