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What is Archimedes’ Principle, Formula, and Calculations?


Archimedes’ Principle is a fundamental concept in fluid mechanics that explains the buoyancy of objects submerged in a fluid. It was discovered by the ancient Greek mathematician and physicist Archimedes, who made significant contributions to various scientific fields.

In this article, we will delve into the intricacies of Archimedes’ Principle, understanding its underlying formula and calculations. Whether you’re a student, a science enthusiast, or just curious about the world around you, this article will provide you with the expertise, authority, and trust you seek regarding the topic “What is Archimedes’ Principle, formula, and calculations.”

What is Archimedes’ Principle?

Archimedes’ Principle, also known as the Law of Buoyancy, states that an object immersed in a fluid experiences an upward force equal to the weight of the fluid it displaces. In simpler terms, it explains why objects float or sink in liquids, like a ship floating on water or a submerged toy sinking in a pool.

This principle is the reason why massive steel ships can stay afloat on the surface of the ocean. Understanding the concept of buoyancy is crucial for various applications, from designing boats to understanding natural phenomena.

The Formula and Calculations

To calculate the buoyant force acting on an object immersed in a fluid, we use the formula:

Buoyant Force (FB) = Density of the Fluid (ρ) x Volume of the Displaced Fluid (V) x Acceleration due to Gravity (g)


  • Density of the Fluid (ρ) is the mass of the fluid per unit volume.
  • Volume of the Displaced Fluid (V) is the volume of the fluid that the object displaces when submerged.
  • Acceleration due to Gravity (g) is the acceleration experienced by objects due to the gravitational force on Earth.

Now, let’s explore the steps to calculate the buoyant force with a practical example:

Example Calculation:

Q: Imagine a cube-shaped wooden block with dimensions 10 cm x 10 cm x 10 cm is submerged in water. The density of water is 1000 kg/m³. Calculate the buoyant force acting on the wooden block.


First Step: Convert dimensions to meters:

  • Length (L) = 10 cm = 0.10 m
  • Width (W) = 10 cm = 0.10 m
  • Height (H) = 10 cm = 0.10 m

Second Step: Calculate the volume of the wooden block:

  • Volume (V) = L x W x H = 0.10 m x 0.10 m x 0.10 m = 0.001 m³

Third Step: Calculate the buoyant force:

  • Buoyant Force (FB) = ρ x V x g = 1000 kg/m³ x 0.001 m³ x 9.81 m/s² ≈ 9.81 N

Therefore, the buoyant force acting on the wooden block is approximately 9.81 Newtons.

Archimedes’ Principle in Real Life

Archimedes’ Principle finds practical applications in various fields, ranging from engineering to everyday life. Some of the key applications include:

Ship Design and Stability

The principle plays a vital role in ship design, ensuring that ships can float and maintain stability even when carrying heavy loads. Understanding buoyancy helps naval architects design vessels that can displace enough water to stay afloat and avoid capsizing.

Hot Air Balloons

Hot air balloons work based on the principle of buoyancy. When we apply heat to the air inside the balloon, it becomes less dense than the surrounding air. This causes the balloon to rise since the buoyant force is greater than the weight of the balloon and its contents.


Archimedes’ Principle is equally essential in the functioning of submarines. By adjusting the amount of water in ballast tanks, submarines can control their buoyancy and either rise to the surface or descend to deeper depths.

Floating and Sinking

Understanding buoyancy can explain why some objects float on water, like wooden logs, while others, such as metals, sink. This principle is also vital in explaining how life jackets work to keep individuals afloat.

Calculations in Different Fluids

Archimedes’ Principle is not limited to water; it applies to any fluid. However, different fluids have varying densities, affecting the buoyant force. Here’s how the formula changes when dealing with fluids other than water:

Buoyant Force (FB) = Density of the Fluid (ρf) x Volume of the Displaced Fluid (V) x Acceleration due to Gravity (g)

Archimedes Principle and Density

The relationship between Archimedes’ Principle and density is crucial in understanding how objects float or sink. The principle states that an object will float if it is less dense than the fluid it displaces. Conversely, it will sink if it is denser than the fluid.

FAQs (Frequently Asked Questions)

Q: How does Archimedes’ Principle relate to everyday objects?
A: Archimedes’ Principle explains why objects like rubber ducks float on water but also reveals why heavy rocks sink.

Q: Can Archimedes’ Principle be applied to gases?
A: Archimedes’ Principle applies to any fluid, including gases. For example, helium balloons rise because the helium gas inside is less dense than the surrounding air.

Q: Why is the buoyant force considered an upward force?
A: The buoyant force acts in the upward direction because the pressure of a fluid increases with depth. The force pushing up is greater than the force pushing down, resulting in the net upward force.

Q: Does Archimedes’ Principle apply to objects fully submerged in a fluid?
A: Yes, Archimedes’ Principle applies to objects fully submerged in a fluid. It also applies to partially submerged objects, where only a portion of the object is submerged.

Q: Are there situations where Archimedes’ Principle does not apply?
A: Archimedes’ Principle assumes that the fluid behaves as an ideal fluid with no internal friction or viscosity. In real-life scenarios, when dealing with highly viscous fluids or compressible fluids like air, the principle may not be as accurate.

Q: Can an object have zero buoyant force?
A: Yes, an object can have zero buoyant force if it has the same density as the fluid it is submerged in. In such cases, the object neither sinks nor floats but remains suspended at a specific depth.


In conclusion, Archimedes’ Principle is a fundamental concept that helps us understand why objects float or sink in fluids. By knowing the formula and performing calculations, we can determine the buoyant force acting on an object submerged in any fluid.

From ship design to hot air balloons, this principle finds practical applications across various industries. It is an essential element in comprehending the behaviour of fluids and the interaction between objects and their environment.

Now that you’ve explored Archimedes’ Principle, its formula, and calculations, you have gained a deeper insight into the fascinating world of buoyancy and fluid mechanics.