1,000
kg/m³
50
kg
490.5
N
490.5
N
50.0171
kgf
110.2688
lbf
9,810
Pa/m
1,000
kg/m³
50
kg
490.5
N
490.5
N
50.0171
kgf
110.2688
lbf
9,810
Pa/m
The Buoyant Force Calculator directly computes the upward buoyant force on an object submerged in a fluid, along with the mass and weight of the displaced fluid. This is a streamlined tool focused on the core buoyancy equation derived from Archimedes' principle.
The buoyant force formula is:
$$F_b = \rho_{fluid} \cdot V \cdot g$$
where \(\rho_{fluid}\) is the fluid density (kg/m³), \(V\) is the volume of fluid displaced by the submerged portion of the object (m³), and \(g\) is gravitational acceleration (default 9.81 m/s²). The buoyant force always acts vertically upward, opposing the gravitational pull on the object.
The physical origin of buoyancy lies in the pressure difference between the top and bottom of a submerged object. Since fluid pressure increases with depth (\(P = \rho g h\)), the upward pressure on the bottom surface of an object is greater than the downward pressure on its top surface. The net upward force from this pressure difference equals exactly \(\rho V g\)—the weight of the displaced fluid.
This calculator provides the buoyant force in three unit systems: newtons (N), kilograms-force (kgf), and pounds-force (lbf). It also computes the mass of displaced fluid and its weight. Note that the displaced fluid weight always equals the buoyant force—this is a direct statement of Archimedes' principle.
Practical applications are extensive. Marine engineers calculate buoyant forces to determine ship displacement and load capacity. Offshore platform designers must account for wave-induced buoyancy variations. Environmental scientists estimate the buoyancy of organisms to understand aquatic ecosystem dynamics. Even aerospace engineers consider buoyancy when designing lighter-than-air craft such as airships and weather balloons.
For partially submerged objects like floating boats, \(V\) represents only the volume below the waterline, not the total object volume. For fully submerged objects like submarines or anchors, \(V\) equals the object's total volume. Adjusting \(V\) appropriately is key to accurate buoyancy calculations.
The buoyant force calculation is straightforward:
$$F_b = \rho_{fluid} \cdot V \cdot g$$
The mass of displaced fluid:
$$m_{displaced} = \rho_{fluid} \cdot V$$
The weight of displaced fluid (which equals the buoyant force by Archimedes' principle):
$$W_{displaced} = m_{displaced} \cdot g = \rho_{fluid} \cdot V \cdot g = F_b$$
Unit conversions:
$$F_{kgf} = \frac{F_b}{9.80665} \quad \text{(1 kgf = 9.80665 N)}$$
$$F_{lbf} = \frac{F_b}{4.44822} \quad \text{(1 lbf = 4.44822 N)}$$
The Buoyant Force is the upward force the fluid exerts on the submerged object. The Displaced Fluid Mass and Displaced Fluid Weight confirm Archimedes' principle: the buoyant force equals the displaced fluid's weight. To determine if an object floats, compare the buoyant force to the object's weight. If \(F_b \geq W_{object}\), the object floats.
Inputs
Results
A small boat hull displaces 5 m³ of seawater (ρ = 1,025 kg/m³). The buoyant force is about 50.3 kN (5,127 kgf), meaning the boat can support up to 5,125 kg of total mass before sinking further.
Inputs
Results
A weather balloon with 10 m³ volume in air (ρ = 1.225 kg/m³) experiences a buoyant force of 120.2 N. If the balloon + payload weighs less than this, it ascends.
The buoyant force is the upward force that a fluid exerts on any object immersed in it. It equals the weight of the fluid displaced by the object: \(F_b = \rho_{fluid} \cdot V \cdot g\). This force is always directed upward, perpendicular to the fluid surface.
Because fluid pressure increases with depth, the upward pressure on the bottom of a submerged object exceeds the downward pressure on its top. When you integrate this pressure difference over the entire surface, the net upward force equals exactly the weight of the fluid that would fill the space occupied by the object—this is Archimedes' principle.
Newtons (N) are the SI unit of force. Kilograms-force (kgf) is the gravitational force on a 1 kg mass at standard gravity (1 kgf = 9.80665 N). Pounds-force (lbf) is the gravitational force on a 1-pound mass at standard gravity (1 lbf = 4.44822 N). While N is standard in physics, kgf and lbf are common in everyday engineering.
Yes, indirectly. Temperature changes the fluid's density. Warm water is less dense than cold water, so it produces a slightly smaller buoyant force for the same displaced volume. This effect is significant in oceanography, where temperature-driven density differences create ocean currents.
For a fully submerged object, the submerged volume equals the object's total volume. For a floating object, you can calculate it using the equilibrium condition: the fraction submerged equals the ratio of the object's density to the fluid's density (\(V_{sub} = V_{total} \times \rho_{object}/\rho_{fluid}\)).
No. The buoyant force is always upward (positive) as long as the fluid density and displaced volume are positive. However, the net force on an object can be downward if the object's weight exceeds the buoyant force, causing it to sink.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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