How to Calculate Force of Buoyancy

This powerful calculator helps you determine the upward buoyant force on an object submerged in a fluid, a core concept in physics and engineering. By understanding how to calculate the force of buoyancy, you can predict whether an object will float, sink, or remain suspended. Our tool simplifies Archimedes’ principle, making it accessible for students, engineers, and enthusiasts alike.

Chart comparing buoyant force in different fluids for the given volume.

What is the Force of Buoyancy?

The force of buoyancy, also known as the buoyant force, is the upward force exerted on an object that is partially or fully submerged in a fluid (a liquid or a gas). This phenomenon is described by Archimedes’ principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. Understanding how to calculate the force of buoyancy is crucial in fields like naval architecture, aerospace engineering, geology, and even scuba diving. It determines whether a ship floats, a balloon rises, or a submarine can control its depth.

A common misunderstanding is that buoyancy is a property of the object itself. In reality, it’s a result of the pressure difference in the fluid. As depth increases, fluid pressure increases. Therefore, the pressure on the bottom of a submerged object is greater than the pressure on the top, resulting in a net upward force.

Force of Buoyancy Formula and Explanation

The formula to calculate the force of buoyancy is simple yet powerful. It directly relates the fluid’s properties and the object’s submerged volume to the resulting upward force.

F_b = ρ × V × g

Where:

Variable	Meaning	Metric Unit	Imperial Unit
Fb	Force of Buoyancy	Newtons (N)	Pound-force (lbf)
ρ (rho)	Density of the fluid	kilograms per cubic meter (kg/m³)	pounds per cubic foot (lb/ft³)
V	Volume of the submerged part of the object	cubic meters (m³)	cubic feet (ft³)
g	Acceleration due to gravity	meters per second squared (m/s²)	feet per second squared (ft/s²)

Variables used in the buoyant force formula.

Practical Examples

Example 1: A Wooden Block in Water (Metric)

Let’s find the buoyant force on a wooden block with a submerged volume of 0.05 m³ in fresh water.

• Fluid Density (ρ): The density of fresh water is approximately 1000 kg/m³.
• Submerged Volume (V): 0.05 m³
• Gravity (g): 9.81 m/s²

Calculation:
F_b = 1000 kg/m³ × 0.05 m³ × 9.81 m/s²
F_b = 490.5 Newtons

The upward buoyant force on the block is 490.5 N. If the block’s own weight is less than this, it will float.

Example 2: An Aluminum Cube in Seawater (Imperial)

Now, let’s calculate the force on an aluminum cube with a submerged volume of 2 ft³ in seawater.

• Fluid Density (ρ): The density of seawater is about 64 lb/ft³.
• Submerged Volume (V): 2 ft³
• Gravity (g): 32.2 ft/s²

Calculation:
F_b = 64 lb/ft³ × 2 ft³ × 1 (This calculation is simpler in Imperial as lb/ft³ is often a measure of specific weight, ρ*g)
F_b = 128 lbf

The buoyant force is 128 pound-force. Note that density in Imperial is often given as lb/ft³, which can sometimes be specific weight (density x gravity). Our calculator handles these conversions automatically for clarity.

How to Use This Buoyancy Force Calculator

Using our calculator is straightforward. Follow these steps to accurately determine the buoyant force:

1. Select Unit System: Start by choosing between Metric and Imperial units. This will adjust the labels and expected input ranges for all fields.
2. Enter Fluid Density: Input the density of the fluid in which the object is submerged. For example, fresh water is ~1000 kg/m³ or ~62.4 lb/ft³. Our fluid density chart can help you find common values.
3. Enter Submerged Volume: Provide the volume of the part of the object that is below the fluid’s surface. This is the volume of fluid being displaced.
4. Adjust Gravity (Optional): The calculator defaults to Earth’s gravity (9.81 m/s² or 32.2 ft/s²). You can change this value to calculate buoyancy on other planets or for specific scenarios.
5. Interpret the Results: The calculator instantly shows the final buoyant force. The intermediate values show the inputs you provided, and the chart visualizes how the force would change in different common fluids like seawater or oil.

Reference Table of Common Fluid Densities at standard temperature.

Fluid	Density (kg/m³)	Density (lb/ft³)
Fresh Water	1000	62.4
Seawater	1025	64.0
Gasoline	720	45.0
Ethyl Alcohol	789	49.3
Mercury	13600	849.0
Air (at sea level)	1.225	0.0765

Key Factors That Affect Buoyancy

Several key factors influence the magnitude of the buoyant force. Understanding them is key to mastering how to calculate the force of buoyancy.

• Fluid Density: The denser the fluid, the greater the buoyant force. This is why it’s easier to float in salty ocean water than in a freshwater pool. You can learn more with our specific gravity calculator.
• Submerged Volume: The more volume an object displaces, the greater the upward force. A large but hollow object can float easily because it displaces a large volume of fluid without having much weight.
• Acceleration due to Gravity: Buoyant force is directly proportional to gravity. On the Moon, where gravity is weaker, the buoyant force would be significantly less for the same object and fluid.
• Object’s Weight/Density: While not part of the buoyant force formula itself, an object’s own weight is what buoyancy counteracts. An object floats if its average density is less than the fluid’s density. It sinks if it’s denser. Learn more about this with a density calculator.
• Fluid Pressure: The underlying cause of buoyancy is the increase in pressure with fluid depth. This principle is a cornerstone of fluid dynamics.
• Temperature: Temperature can affect a fluid’s density. Generally, as a liquid gets warmer, it expands and becomes less dense, which would slightly decrease the buoyant force.

Frequently Asked Questions (FAQ)

1. What is Archimedes’ Principle?

Archimedes’ principle states that any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

2. Why does a heavy steel ship float?

A ship floats because its hull is shaped to displace a large volume of water. While the steel itself is very dense, the ship’s *average* density (including all the air inside the hull) is less than the density of water. The buoyant force on the displaced water is large enough to support the ship’s total weight.

3. What’s the difference between buoyant force and an object’s weight?

Buoyant force is the upward push from the fluid. Weight is the downward pull of gravity on the object. If the buoyant force is greater than the weight, the object rises. If weight is greater, it sinks. If they are equal, it has neutral buoyancy.

4. Does the shape of an object affect its buoyancy?

For a fully submerged object, shape does not affect the buoyant force; only the displaced volume matters. For a floating object, however, the shape is critical because it determines how much volume is submerged for a given weight, as you can explore with a volume calculator.

5. How do you calculate force of buoyancy in Newtons?

To get the force in Newtons (N), you must use metric units: fluid density in kg/m³, submerged volume in m³, and gravity in m/s². The product of these values gives the force directly in Newtons.

6. What happens if an object is denser than the fluid?

If an object’s average density is greater than the fluid’s density, its weight will be greater than the maximum possible buoyant force (achieved when fully submerged). Therefore, the object will sink.

7. How do submarines use buoyancy?

Submarines control their buoyancy by using ballast tanks. To dive, they flood the tanks with water, increasing their overall weight and density. To surface, they pump the water out and replace it with compressed air, making them less dense and more buoyant.

8. Does air have buoyancy?

Yes. Any object in the air is buoyed by a force equal to the weight of the air it displaces. This is how hot air and helium balloons work. Because hot air and helium are less dense than the surrounding cooler air, the buoyant force is greater than the balloon’s weight, causing it to rise.