The Archimedes' Principle Calculator determines the buoyant force, net force, and whether an object floats or sinks based on object mass, fluid density, object volume, and gravitational acceleration. Applies Archimedes' principle F_b = ρ_fluid × V × g to any object-fluid combination.
49.05
N
19.62
N
29.43
N
2,500
kg/m³
100
%
0
49.05
N
19.62
N
29.43
N
2,500
kg/m³
100
%
0
"Eureka!" — according to legend, Archimedes shouted it running naked through Syracuse after realizing that a submerged object displaces fluid equal to its own volume. That insight, formalized into what we now call Archimedes' Principle, is the physical foundation for everything from ship design to submarine ballast systems to the hydrometer in your brewing kit. The calculator for Archimedes' Principle computes the buoyant force, net force, and float/sink determination for any object in any fluid.
Archimedes' Principle states: the buoyant force on an object submerged in a fluid equals the weight of the fluid displaced:
F_b = ρ_fluid × V_submerged × g
where ρ_fluid is the fluid density (kg/m³), V_submerged is the submerged volume (m³), and g = 9.81 m/s² is gravitational acceleration. The net force on the object is:
F_net = F_gravity − F_buoyancy = m × g − ρ_fluid × V × g
If F_net is positive (gravity exceeds buoyancy), the object sinks. If negative (buoyancy exceeds gravity), it accelerates upward. If zero, it is in neutral buoyancy — floating at a fixed depth. For the floating case (partial submersion), the submerged fraction equals the density ratio: V_submerged / V_total = ρ_object / ρ_fluid. Use this online calculator for any object-fluid combination. The buoyancy calculator handles the complementary fluid displacement problem.
For a completely submerged homogeneous object, the float/sink condition simplifies to a density comparison:
Water density: 1,000 kg/m³ (fresh), 1,025 kg/m³ (seawater). Objects denser than 1,025 kg/m³ sink in seawater; objects between 1,000 and 1,025 kg/m³ sink in fresh water but float in seawater. This explains why bodies of water with different salinities support different amounts of floating cargo — the Dead Sea (density ~1,240 kg/m³) makes it nearly impossible to sink.
Archimedes' Principle governs the design of any marine or submerged structure:
The hydrostatic pressure calculator and fluid properties calculators provide complementary fluid mechanics tools.
When an object is submerged and weighed on a scale (or via a spring scale), its apparent weight is reduced by the buoyant force: W_apparent = W_true − F_buoyancy = (ρ_object − ρ_fluid) × V × g. This is the basis of the hydrostatic weighing technique for body composition measurement — weighing a person in air and underwater gives the average body density, which separates fat mass (density ≈ 0.9 g/cm³) from lean mass (density ≈ 1.1 g/cm³) with high accuracy. The gold standard body composition method before DEXA scanning used Archimedes' Principle directly.
The calculator applies Archimedes' principle step by step:
1. Object weight:
$$W = m \cdot g$$
2. Buoyant force (assuming full submersion):
$$F_b = \rho_{fluid} \cdot V_{object} \cdot g$$
3. Apparent weight:
$$W_{apparent} = \max(W - F_b, \; 0)$$
If the buoyant force exceeds the weight, the apparent weight is zero (the object floats).
4. Object density:
$$\rho_{object} = \frac{m}{V_{object}}$$
5. Fraction submerged (if floating):
$$f = \frac{\rho_{object}}{\rho_{fluid}} \times 100\%$$
If \(\rho_{object} \geq \rho_{fluid}\), the object sinks and is 100% submerged.
The Apparent Weight is what a spring scale would measure when the object is fully submerged. For floating objects it reads zero because the buoyant force supports the entire weight. The Fraction Submerged tells you what percentage of the object's volume sits below the surface at equilibrium—a key value for ship loading calculations. The Status indicator shows 1 for float and 0 for sink.
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A 1-liter ice cube (917 g) in seawater. The buoyant force (10.06 N) exceeds its weight (9.0 N), so it floats with about 89.5% submerged—matching the well-known iceberg ratio.
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A 2 kg gold crown (V ≈ 104 cm³) submerged in water. Object density ≈ 19,231 kg/m³ is close to pure gold (19,320). Apparent weight is 18.6 N vs. true weight 19.62 N.
Archimedes' principle states that any object fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. Mathematically: \(F_b = \rho_{fluid} \cdot V_{displaced} \cdot g\). This principle applies to all fluids, including liquids and gases.
Apparent weight is the weight an object appears to have when submerged in a fluid. It equals the true weight minus the buoyant force: \(W_{apparent} = W - F_b\). An object feels lighter underwater because the buoyant force partially supports it. If the buoyant force exceeds the weight, the object floats and the apparent weight is zero.
According to legend, Archimedes submerged the crown in water and measured the volume of water displaced. He then compared the crown's density (mass/volume) with that of pure gold. If the goldsmith had mixed in cheaper silver (lower density), the crown would have a larger volume and lower density than pure gold of the same mass, displacing more water.
Ice has a density of about 917 kg/m³, and seawater about 1,025 kg/m³. The fraction submerged equals 917/1,025 ≈ 0.895, or about 89.5%. So roughly 90% of an iceberg is below the surface. This ratio is a direct consequence of Archimedes' principle applied to floating objects.
Yes. A helium balloon rises because the buoyant force from the surrounding air exceeds the weight of the balloon. The buoyant force equals the weight of air displaced: \(F_b = \rho_{air} \cdot V_{balloon} \cdot g\). Since helium is much less dense than air, the net force is upward.
Submarines use ballast tanks that can be filled with water (to increase weight and sink) or emptied with compressed air (to decrease weight and rise). By precisely controlling the amount of water in the tanks, the crew can achieve neutral buoyancy at any desired depth.
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