Archimedes Principle Calculator
Calculate buoyant force and displaced fluid weight using Archimedes principle for floating and submerged objects.
What Is Archimedes Principle?
Archimedes principle states that the buoyant force on a submerged object equals the weight of the fluid it displaces. This upward force explains why ships float and why objects feel lighter in water.
Buoyant Force Formula
$$F_b = \rho_{fluid} \cdot V_{submerged} \cdot g$$\(\rho_{fluid}\) is fluid density, \(V_{submerged}\) is the volume of fluid displaced, and \(g\) is gravitational acceleration. The weight of displaced fluid is:
$$W_{displaced} = m_{fluid} \cdot g = (\rho_{fluid} \cdot V_{submerged}) \cdot g = F_b$$Example: \(1000\,\text{kg/m}^3\) water, \(0.01\,\text{m}^3\) submerged volume, and \(g = 9.81\,\text{m/s}^2\) give \(F_b \approx 98.1\,\text{N}\).
Floating vs. Fully Submerged Objects
For a floating body, the submerged volume is only the part below the fluid surface. For a fully submerged object, use the entire object volume. If buoyant force equals object weight, the body floats; if buoyant force exceeds weight, the body rises.
Frequently Asked Questions
Does shape affect buoyant force?
Only the submerged volume matters, not the shape. A given submerged volume displaces the same mass of fluid regardless of geometry.
Why is buoyant force equal to displaced fluid weight?
The pressure increase with depth creates a net upward force equal to the weight of the column of fluid that would fill the displaced volume.
What density should I use for seawater?
Seawater is typically about 1025 kg/m³, higher than fresh water at 1000 kg/m³ because of dissolved salts.
Can buoyant force exceed object weight?
Yes. When it does, the net force is upward and the object accelerates toward the surface until equilibrium is reached.
Does air buoyancy matter?
For everyday objects in air, buoyant force is tiny compared to weight. In water or other dense fluids, buoyancy is significant.
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