Archimedes Principle Calculator - Buoyant Force, Apparent Weight, and Float / Sink

An Archimedes principle calculator applies F_b = rho_fluid * V_submerged * g to any object in a fluid. It returns the buoyant force, the apparent weight, and the submerged fraction in one panel and tells you whether the object floats, hangs in mid-water, or sinks.

• • Floating and sinking check: Compare object density with the fluid density and read a clear float, neutral, or sink verdict.
• • Apparent weight in water: Subtract the buoyant force from the true weight to see how light the object feels when fully submerged.
• • Submerged fraction for floats: Find the share below the surface when rho_object is below rho_fluid, useful for icebergs and hull design.
• • Multiple fluids: Switch between fresh water, seawater, mercury, oil, air, or a custom density to test the same object in different surroundings.

The same relation works for any fluid, which is why a steel bolt sinks in water but floats in mercury, and why a thin-walled balloon filled with hot air rises through cool air. Only the displaced fluid weight changes.

When you already know the mass and volume of the object, the Density Calculator returns the average object density that this calculator then compares to the fluid density.

The calculator compares the object density with the fluid density, computes the buoyant force for a fully submerged object, then reports a float, neutral, or sink verdict with the submerged fraction and apparent weight.

• rho_fluid: Fluid density in kg/m³. Water at 20 °C is 998.2, seawater about 1025, air about 1.204, mercury 13,546.
• V_submerged: Volume displaced by the object in m³; equals the whole object when fully submerged and only the lower part when floating.
• V_object: Total geometric volume of the object in m³. The submerged fraction V_submerged / V_object equals rho_object / rho_fluid when the object floats.
• m_object: Object mass in kg. With V it gives rho_object = m / V, and with g it gives W_object = m * g.
• g: Local gravity in m/s². Earth sea level is 9.80665 (CODATA), the Moon about 1.62, Mars about 3.71.

If rho_object is below rho_fluid, the object is lighter per unit volume than the fluid. The buoyant force at full submersion exceeds the weight, so the object rises until only part stays below the surface.

If rho_object matches rho_fluid within 0.5 percent, the calculator reports neutral buoyancy and a zero apparent weight, the same condition submarines chase.

If rho_object is above rho_fluid, the maximum buoyant force at full submersion is below the weight and the object sinks. The apparent weight tells you how heavy the object still feels.

According to Wikipedia, Archimedes' principle, the upward buoyant force equals the weight of the displaced fluid, F_b = rho_fluid * V_submerged * g. The reference density of fresh water (998.2 kg/m³ at 20 °C) is tabulated on Wikipedia, Properties of water.

The weight W = m * g and the apparent weight W_apparent = W - F_b are both standard force calculations, and the Forces and Newton's Laws Calculator lays out the same Newton's-second-law framework when you want to combine Archimedes with horizontal or applied forces.

Four ideas come up: the displaced fluid rule, density comparison, weight versus apparent weight, and the role of local gravity.

These four ideas cover any first-year buoyancy problem: convert the object to a density, convert the fluid to a density, compare them, and read off the submerged fraction for the floating case. The math stays the same in fresh water, seawater, oil, mercury, or air.

Most textbook objects (test tubes, tin cans, storage tanks) are cylinders, and the Cylinder Volume Calculator produces the V_object value that this calculator then combines with the mass and fluid density.

Pick the object, pick the fluid, and read the result panel.

1. 1 Enter the object mass: Type the mass in kilograms. A 10 cm cube of steel is about 7.85 kg, a 1 L water bottle is 1 kg, and a 1 m³ block of wood is roughly 500 to 800 kg.
2. 2 Enter the object volume: Type the geometric volume in cubic metres. A 10 cm cube has V = 0.001 m³, a 1 L bottle has V = 0.001 m³, and a 1 m³ block has V = 1.0 m³.
3. 3 Choose a fluid preset: Pick fresh water, seawater, air, mercury, oil, or Custom. The preset fills the density field; edit it if needed.
4. 4 Adjust the fluid density if needed: Use the standard value for clean water or seawater, change it for hot brine or warm air, or pick Custom for any density between 0.1 and 20,000 kg/m³.
5. 5 Adjust gravity for non-Earth problems: Leave g at 9.80665 for Earth, drop it to 1.62 for the Moon or 3.71 for Mars. The verdict does not change.
6. 6 Read the result panel: Object density, weight, buoyant force, apparent weight, submerged fraction, and the float / sink verdict appear together.

A 920 kg iceberg with V = 1.0 m³ drifts into seawater at 1025 kg/m³. The calculator reports rho_object = 920, rho_fluid = 1025, weight ≈ 9,022 N, buoyant force ≈ 10,049 N, submerged fraction ≈ 89.8 percent, status = floats.

For a ball, a buoy, or an iceberg modelled as a sphere, the Sphere Volume Calculator returns the geometric V_object value that this calculator plugs straight into the buoyant force formula.

A dedicated buoyancy calculator saves you from redoing the same weight-versus-buoyancy algebra on every physics problem.

• • All four outputs in one panel: Read object density, weight, buoyant force, and apparent weight together instead of re-deriving them.
• • Float / sink verdict: Get a plain-language result next to the numbers, so you can answer the textbook question directly.
• • Submerged fraction for floats: See the share of the object below the surface for icebergs, hull design, and buoyancy experiments.
• • Multiple fluids and planets: Switch between fresh water, seawater, mercury, oil, air, or a custom density, and swap g between Earth, the Moon, and Mars.
• • Real-time recompute: Every keystroke updates the result panel, so it doubles as a what-if tool for lab work and homework.

Pair this calculator with the density and volume tools you already have. This Archimedes principle calculator does the buoyancy math, while a density or volume calculator supplies the inputs.

Five things can change the verdict or the numbers. Check them before you trust the result.

• • The model assumes a uniform, incompressible fluid and ignores surface tension, viscous drag, and dynamic effects such as a sinking object's wake. It is the textbook treatment, not a CFD answer.
• • The calculator treats the object as a single solid of constant density. Real objects can trap air, leak, deform, or compress under pressure; the submerged fraction only holds at static equilibrium.
• • The fluid density must match the actual fluid at the object's depth. Density drops in a thermocline, and brackish harbour water sits between fresh water and full seawater.

For viscous flows around a moving object, the simple Archimedes principle no longer covers the added drag. Use the buoyancy calculator for the steady part and pair it with a drag calculation when the object moves.

According to Wikipedia, Seawater, surface seawater at 20 °C with 35 g/kg salinity has a density of about 1025 kg/m³.

When the fluid is moving past the object, the Bernoulli Equation Calculator covers the dynamic-pressure side of the problem while this buoyancy calculator still handles the steady term.