Buoyancy Force Calculator
Archimedes' principle states that the upward buoyant force on a submerged object equals the weight of the fluid it displaces. The formula Fb = rho_fluid x g x V gives the buoyant force in Newtons, where rho_fluid is the density of the surrounding fluid (kg/m^3), g is the standard gravitational acceleration (9.80665 m/s^2), and V is the volume of fluid displaced by the object (m^3). This principle underlies all floating and submerged body analysis, including ship design, submarine ballast, balloon lift, and geological isostasy. Enter the fluid density and displaced volume to find the buoyant force.
Archimedes' principle formula
Fb = rho_fluid × g × V
Fb is buoyant force in Newtons (N), rho_fluid is fluid density (kg/m^3), g = 9.80665 m/s^2, V is volume of fluid displaced (m^3). The mass of displaced fluid = rho_fluid x V. The weight of displaced fluid = Fb.
Worked example
- A 1 L (0.001 m^3) block fully submerged in fresh water (1,000 kg/m^3).
- Fb = 1,000 x 9.80665 x 0.001 = 9.81 N.
- This equals the weight of 1 kg of water (mass displaced = 1 kg, weight = 9.81 N).
- If the block itself weighs less than 9.81 N, it will float; if more, it will sink.
Frequently asked questions
What is Archimedes' principle?
Archimedes' principle states that the buoyant force on a submerged object equals the weight of the fluid displaced by the object: Fb = rho_fluid x g x V, where rho_fluid is the fluid density, g is gravitational acceleration, and V is the volume of fluid displaced.
Does a floating object have a net upward force?
No. A floating object is in equilibrium: the buoyant force exactly equals the weight of the object. The submerged volume adjusts until Fb = mg. For an object that sinks, Fb is less than its weight.
What is the density of seawater vs freshwater?
Fresh water has a density of approximately 1,000 kg/m^3 at 4 degrees C. Seawater averages about 1,025 kg/m^3. Objects float more easily in seawater because the buoyant force per unit volume is higher.
What is the standard value of g used?
The standard acceleration due to gravity is g = 9.80665 m/s^2, as defined by NIST. The buoyant force Fb = rho g V uses this value unless a local gravitational acceleration is needed for precision work.
How is buoyancy used in ship design?
Ships are designed so that the volume of water displaced by the hull produces a buoyant force equal to the total weight of the ship and cargo. The draft (depth of hull below waterline) is calculated from Archimedes' principle for safe loading.
Official sources
- NIST: Standard Acceleration of Gravity (NIST CODATA).
- OpenStax University Physics: 14.4 Archimedes' Principle and Buoyancy.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.