Archimedes' Principle Formula

Archimedes' principle states that the buoyant force on an immersed object equals the weight of the fluid that the object displaces.

The Formula

F_b = W_{\text{displaced fluid}} = \rho_{\text{fluid}} g V_{\text{displaced}}

When to use: A fluid pushes up exactly as much as the displaced fluid would weigh.

Quick Example

If a submerged block displaces 2 kg of water, the water pushes up on it with the same force as the weight of 2 kg of water.

Notation

F_b

is buoyant force,

W

is weight,

\rho

is fluid density, and

V

is the displaced volume.

What This Formula Means

Archimedes' principle states that the buoyant force on an immersed object equals the weight of the fluid that the object displaces.

A fluid pushes up exactly as much as the displaced fluid would weigh.

Formal View

Archimedes' principle gives

F_b = \rho_{\text{fluid}} g V_{\text{displaced}}

, which follows from the pressure difference between the top and bottom of an immersed object.

Worked Examples

Example 1

medium

A wooden block of density

600 \text{ kg/m}^3

floats in water. What fraction of its volume is below the surface?

Answer

\dfrac{V_{sub}}{V_{block}} = 0.6

First step

Floating condition: weight = buoyant force, so

\rho_{obj} V g = \rho_f V_{sub} g

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Example 2

medium

2 \text{ kg}

metal object has volume

5 \times 10^{-4} \text{ m}^3

and is fully submerged in water. Find its apparent weight. (

\rho = 1000

g = 10

)

Example 3

medium

A boat of mass

400 \text{ kg}

floats in fresh water. Find the volume of water displaced. (

\rho=1000

g=10

)

Common Mistakes

Using the object's mass instead of the displaced fluid's mass. - Fix this by naming the system, checking "Am I reasoning about a fluid or object in a fluid, with volume, area, depth, density, or displaced fluid identified?", and attaching units or direction to the final statement.
Forgetting that only the submerged volume contributes to displaced fluid. - Fix this by naming the system, checking "Am I reasoning about a fluid or object in a fluid, with volume, area, depth, density, or displaced fluid identified?", and attaching units or direction to the final statement.
Using archimedes' principle from a keyword alone - Signal words like fluid, pressure, density only point to a possible model; the system must match too.
Substituting numbers before defining the system - A formula cannot repair a missing object, boundary, direction, medium, or circuit path.

Why This Formula Matters

Archimedes' Principle helps students explain floating, sinking, pressure changes, and fluid behavior with quantities instead of intuition alone. It is useful anywhere matter flows or surrounds an object.

Frequently Asked Questions

What is the Archimedes' Principle formula?

Archimedes' principle states that the buoyant force on an immersed object equals the weight of the fluid that the object displaces.

How do you use the Archimedes' Principle formula?

A fluid pushes up exactly as much as the displaced fluid would weigh.

What do the symbols mean in the Archimedes' Principle formula?

$F_b$ is buoyant force, $W$ is weight, $\rho$ is fluid density, and $V$ is the displaced volume.

Why is the Archimedes' Principle formula important in Physics?

What do students get wrong about Archimedes' Principle?

Students often know a formula related to archimedes' principle but skip the recognition step: Am I reasoning about a fluid or object in a fluid, with volume, area, depth, density, or displaced fluid identified? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Archimedes' Principle formula?

Before studying the Archimedes' Principle formula, you should understand: buoyancy.

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Related Concepts

Buoyancy

Related Formulas

Buoyancy Formula