Buoyancy Calculator

Calculate the buoyant force, net force, and whether an object floats or sinks using Archimedes' principle: F_b = ρ_fluid × V × g.

About this calculator

Built on Archimedes' principle, this calculator computes the buoyant force as the weight of fluid displaced by the object: F_b = ρ_fluid × V × g. It separately computes the object's own weight from its density and volume, and the sign of the difference between the two (net force) determines whether the object floats, sinks, or is neutrally buoyant — the calculator states this directly by comparing object density to fluid density rather than relying on the net-force sign alone. For a floating object, the fraction submerged follows directly from the density ratio (ρ_object/ρ_fluid), capped at 100% since a floating object can't be more than fully submerged; a sinking object still gets an apparent weight calculation — the weight felt underwater once buoyancy partially offsets true weight — even though it isn't actually resting at that submersion fraction.

The chart traces how buoyant force and weight both scale linearly with volume, which is why doubling an object's size doesn't change whether it floats (the density ratio is unchanged) even though the absolute forces double. Key assumptions: uniform density throughout the object (no hollow sections or internal air pockets, which is why a solid steel block sinks but a steel ship, whose average density including its hollow interior is much lower, floats), and gravitational acceleration fixed at 9.81 m/s². The most common mixup is entering an object's material density instead of its true average density — a boat hull's material might be denser than water while the boat itself, air pockets included, is not.

Inputs

Object Volume

cu yd

Object Density

kg/m³

Fluid Density

kg/m³

Tab to move between fields

Results

Buoyant Force

98.1 N

Float / Sink

Floats

Object Weight78.48 N

Net Force (+ = up)19.62 N

Fraction Submerged80%

Apparent Weight0 N

How to Use This Calculator

Enter Object Volume, Object Density, and Fluid Density.
Review Buoyant Force (N) and Float / Sink.
Use Object Weight (N) and Net Force (+ = up) to inform your decision.
Use the chart to visualize the results and explore different scenarios by adjusting inputs.

How the result changes with Object Volume

Object Volume	Buoyant Force	Float / Sink
0.01	49.05 N	Floats
0.01	73.58 N	Floats
0.02	147.15 N	Floats
0.03	245.25 N	Floats

What each input means

Object Volume: Volume of the submerged object in cubic meters. 0.01 m³ = 10 liters.
Object Density: Average density of the object. Wood ≈ 500–800, steel ≈ 7800, ice ≈ 917 kg/m³.
Fluid Density: Density of the surrounding fluid. Fresh water ≈ 1000, seawater ≈ 1025, mercury ≈ 13,546 kg/m³.

How this is calculated

Worked example, using the default values

Identify Input Parameters
Object Volume = 0.01, Object Density = 800, Fluid Density = 1000 = 3 input(s) provided
Calculate Buoyant Force
98.1 = 98.1
Calculate Float / Sink
Float / Sink
Floats = Floats
Calculate Object Weight
Object Weight
78.48 = 78.48
Calculate Net Force
Net Force
19.62 = 19.62

Engine last updated September 1, 2026. Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

The Fraction Submerged output is showing 100% for an object that sinks — why?

The submerged-fraction formula (ρ_object/ρ_fluid) is capped at 1 in the code, since a floating object physically can't submerge more than fully. When object density exceeds fluid density, that ratio would exceed 100%, so the calculator reports 100% rather than a number implying it's somehow more than fully submerged — treat that reading alongside the Float/Sink status, since 100% here on a 'Sinks' result means the object is entirely underwater, not floating with just its top exposed.

Why does the Apparent Weight output still show a number for an object that sinks?

Apparent weight is computed as object weight minus buoyant force (floored at zero), representing how much lighter the object would feel if you were holding it fully submerged — regardless of whether it's actually floating or sinking on its own. For a sinking object this is still a meaningful number (how much force you'd need to support it underwater), even though the object itself isn't resting at a partial-submersion equilibrium.

Why does a steel ship float but a solid steel block sink, when I enter the same density for both?

This calculator assumes uniform density throughout the object's entered volume — it has no way to model a hollow hull. A steel ship floats in reality because its *average* density (steel plus the large air-filled hollow interior) is far lower than solid steel, so to model a ship correctly here you'd enter that lower average density, not the density of the steel material itself.

If I double the object's volume, why doesn't it change whether it floats or sinks?

Both buoyant force and object weight scale directly with volume (F_b = ρ_fluid·V·g and weight = ρ_object·V·g), so doubling volume doubles both proportionally — the ratio between them, which is all that determines float or sink status, stays exactly the same. You can see this in the Force vs Volume chart: both lines pass through the origin and grow linearly, always maintaining the same relative gap.

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