# Buoyant Force Calculator

Created by Krishna Nelaturu
Reviewed by Aleksandra Zając, MD
Last updated: Jun 05, 2023

This buoyant force calculator can help you determine the force of buoyancy acting on an object submerged or floating in a fluid. Buoyancy plays a vital role in numerous fluid applications, so we shall briefly discuss the basics here. Specifically, let's look at:

• What is buoyant force;
• Buoyant force formula; and
• How do you calculate the buoyant force in water - or any other fluid.

## What is buoyant force

When you get into a bathtub, have you noticed how your body feels lighter the more you immerse yourself in water? The water is applying an upthrust on your body. But where does this upthrust originate?

The particles in a fluid like water can freely move relative to each other. Subject to gravity, all particles are pulled to the bottom, resulting in a fluid pressure that increases as we go deeper into the fluid. Any object placed in a fluid will experience this fluid pressure resulting in an upthrust or buoyant force, and we call this phenomenon buoyancy.

If the buoyant force is larger than the object's weight, then the object floats. Otherwise, the object sinks. In either case, it will displace some fluid. Archimedes' principle states that the buoyant force is equal to the weight of the displaced fluid. Let's use this relation to find an equation for the buoyant force.

## Buoyant force formula

Using Archimedes' principle, we get the formula for buoyancy force:

\begin{align*} B &= W_f \cdot g\\ &= \rho_f \cdot V_{disp} \cdot g \end{align*}

Where:

• $B$ - The buoyant force;
• $W_f$ - Weight of the displaced fluid;
• $g$ - Acceleration due to gravity, $(g \approx 9.81 \text{m/s}^2)$;
• $\rho_f$ - Density of the fluid; and
• $V_{disp}$ - Volume of the fluid displaced.

To manually find the buoyancy force, we must first measure the object's weight when immersed in the fluid using a spring balance or similar weighing apparatus. Then we must subtract this weight from the object's weight when measured typically (without the fluid).

$\small B = Weight_{\rm{outside fluid}} - Weight_{\rm{inside fluid}}$

## How to use this buoyant force calculator

Our versatile buoyancy force calculator is simple to use:

1. Select the type of fluid to provide the fluid's density value automatically. Alternatively, you can enter any custom density value for the fluid.

2. Enter the volume of the displaced fluid. The calculator will instantly calculate the buoyant force for you. Alternatively, you can enter the mass of the fluid displaced to achieve the same result.

Our calculator assumes a value of g = 9.807 m/s2 for the acceleration due to gravity. You can adjust this value by clicking on the advanced mode button.

For similar calculations related to buoyancy, use the following tools:

## FAQ

### How do you calculate buoyant force in water?

Follow these steps to calculate the buoyant force on an object in water:

1. Measure the mass of the fluid displaced due to the object. Alternatively, measure the volume of the fluid displaced and multiply it with the fluid density to get its mass.

2. Multiply the mass of the displaced fluid with acceleration due to gravity to get the buoyant force.

### How can I tell whether an object will sink or float in water?

An object will sink if its density is higher than the density of water. Otherwise, it will float.

Krishna Nelaturu
Fluid type (optional)
Sea water
Fluid density (ρ)
lb/cu in
Volume (V)
cu ft
Buoyant force (B)
lbf
Mass of displaced fluid
lb
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