Buoyancy Force Calculator

Understanding Buoyancy Force Calculator

Archimedes' principle: the buoyant force on a submerged object equals the weight of the displaced fluid.

How to use this calculator

1. Enter the fluid density, \(\rho_f\), in \(\text{kg/m}^3\).
2. Enter the gravitational acceleration, \(g\), in \(\text{m/s}^2\).
3. Enter the displaced volume, \(V_{displaced}\), in \(\text{m}^3\).
4. Click calculate to get the buoyant force, \(F_b\), in newtons.

The formula explained

The formula \(F_b = \rho_f g V_{displaced}\) computes the upward buoyant force on an object using Archimedes' principle. It shows that the force depends on the fluid density, gravity, and how much fluid the object displaces.

• \(F_b\) = buoyant force, in newtons
• \(\rho_f\) = density of the fluid, in \(\text{kg/m}^3\)
• \(g\) = acceleration due to gravity, in \(\text{m/s}^2\)
• \(V_{displaced}\) = volume of fluid displaced by the object, in \(\text{m}^3\)

Step by step method

1. Identify the fluid density, gravity, and displaced volume.
2. Multiply the fluid density by gravity.
3. Multiply that result by the displaced volume to get \(F_b\).

Worked example

Problem. An object displaces \(0.020\,\text{m}^3\) of water. If the water density is \(1000\,\text{kg/m}^3\) and \(g = 9.8\,\text{m/s}^2\), what is the buoyant force?

1. Use the formula \(F_b = \rho_f g V_{displaced}\).
2. Substitute the values, \(F_b = 1000 \times 9.8 \times 0.020\).
3. Compute the result, \(F_b = 196\,\text{N}\).

Tips and common mistakes

• Make sure the volume is the displaced volume, not the object's full volume unless it is completely submerged.
• Keep units consistent, because \(\rho_f\) must be in \(\text{kg/m}^3\), \(g\) in \(\text{m/s}^2\), and volume in \(\text{m}^3\).

Frequently asked questions