98.1
N
10
kg
48.1
N
48.1
N
1
1=Float, 0=Sink
98.1
N
10
kg
48.1
N
48.1
N
1
1=Float, 0=Sink
The Buoyancy Calculator computes the buoyant force acting on an object submerged (or partially submerged) in a fluid, and determines whether the object will float or sink. Buoyancy is the upward force that a fluid exerts on any object placed in it, and it is the reason ships float, hot-air balloons rise, and helium balloons ascend.
The buoyant force is given by Archimedes' principle:
$$F_b = \rho_{fluid} \cdot V_{displaced} \cdot g$$
where \(\rho_{fluid}\) is the density of the fluid, \(V_{displaced}\) is the volume of fluid displaced by the object, and \(g\) is gravitational acceleration. The buoyant force equals the weight of the fluid displaced.
An object floats when the buoyant force equals or exceeds its weight. It sinks when its weight exceeds the maximum possible buoyant force (achieved when fully submerged). For a floating object, only a fraction of its volume is submerged—enough to displace a weight of fluid equal to the object's weight.
This principle has extraordinary practical importance. Naval architects calculate the displacement of ships to ensure safe loading. Submarine engineers control buoyancy by adjusting ballast tanks. Geologists use buoyancy to explain why continents float on denser mantle rock (isostasy). Meteorologists apply buoyancy to understand convection currents and cloud formation.
The calculator also computes the net vertical force (buoyant force minus object weight). A positive net force means the object accelerates upward (floats); a negative value means it sinks. At equilibrium, a floating object has zero net force—it has settled to the depth where the displaced fluid weight exactly balances the object's weight.
Common examples: a steel ship floats because its hull encloses a large volume of air, displacing enough water to support its enormous weight. A solid steel ball sinks because its small volume cannot displace enough water. An ice cube floats because ice is less dense than water, so a volume of water equal to the ice cube's mass weighs the same as the cube but occupies less volume.
Archimedes' principle states that the buoyant force equals the weight of displaced fluid:
$$F_b = \rho_{fluid} \cdot V_{displaced} \cdot g$$
The mass of displaced fluid is:
$$m_{displaced} = \rho_{fluid} \cdot V_{displaced}$$
The net vertical force on the object is:
$$F_{net} = F_b - W_{object}$$
If \(F_{net} \geq 0\), the object floats (or is neutrally buoyant). If \(F_{net} < 0\), the object sinks.
For a fully submerged object, \(V_{displaced}\) equals the object's total volume. For a floating object, \(V_{displaced}\) is only the submerged portion.
The Buoyant Force is the upward force the fluid exerts on the object. The Mass of Displaced Fluid is the mass of fluid pushed aside. The Net Vertical Force shows whether the object accelerates upward (positive) or downward (negative). The Float or Sink indicator shows 1 if the buoyant force is sufficient to support the object, or 0 if the object sinks. Enter the object's weight in the advanced settings for the float/sink analysis.
Inputs
Results
A wooden block displaces 0.005 m³ of water. The buoyant force is 49.05 N, exceeding the 30 N weight. The block floats with a net upward force of 19.05 N (it would rise until only partially submerged).
Inputs
Results
A solid steel sphere (volume 0.001 m³, weight 77 N) in water. The buoyant force is only 9.81 N—far less than the 77 N weight—so it sinks.
Buoyancy is the upward force exerted by a fluid on any object placed in it. It arises because fluid pressure increases with depth, creating a net upward pressure force on the bottom of the object that exceeds the downward pressure on the top. The magnitude equals the weight of the displaced fluid: \(F_b = \rho V g\).
A steel ship has a hull that encloses a large volume of air. The total volume of the hull below the waterline displaces a huge amount of water, generating a buoyant force large enough to support the ship's weight. Even though steel is denser than water, the overall average density of the ship (steel + air) is less than water.
An object floats if its average density is less than the fluid's density, or equivalently, if the buoyant force at full submersion exceeds the object's weight. If the object's density exceeds the fluid's, it sinks. Objects with equal density are neutrally buoyant and remain at whatever depth they are placed.
Shape affects the volume of fluid displaced, which directly affects the buoyant force. A flat-bottomed boat displaces more water for its weight than a solid sphere of the same mass, which is why boats float and solid metal pieces sink. However, for a fully submerged object, only the total volume matters, not the shape.
Saltwater is denser than freshwater (about 1,025 kg/m³ vs 1,000 kg/m³). Higher density means more buoyant force for the same displaced volume. This is why objects float more easily in the ocean than in a freshwater lake, and why swimmers float effortlessly in the Dead Sea (ρ ≈ 1,240 kg/m³).
Neutral buoyancy occurs when an object's weight exactly equals the buoyant force (net force = 0). The object neither rises nor sinks but remains suspended at its current depth. Scuba divers achieve neutral buoyancy by adjusting their buoyancy compensators. Submarines use ballast tanks for the same purpose.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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