Buoyancy (Archimedes' Principle) Calculator
Enter fluid density, object volume and mass — the buoyant force, weight, net force and floating/sinking verdict solve instantly, with a live 3D object settling at the correct submerged depth and two charts of buoyant force and submerged fraction.
Reviewed by the ToolNestr Editorial Team — July 2026
Pick a fluid, enter the object's volume and mass — buoyant force, weight, net force and the float/sink verdict solve instantly.
Two ideas that trip students up
1. Floating vs sinking
The orange block floats mostly above the translucent water line, while the red block is denser and rests fully submerged on the bottom.
2. Submerged fraction depends on density ratio
Four blocks of different density (like cork, wood, ice and steel) crossing the same water line — the denser the block, the more of it sits below the surface.
Buoyancy graphs
How it works
The core idea in one line: a submerged object is pushed up by a force equal to the weight of the fluid it shoves out of the way — whether it floats or sinks comes down to comparing that force to the object's own weight.
Fb = ρfluid × Vdisplaced × g
buoyant force = weight of fluid displaced
Fnet = Fb − mg
net force: positive means it floats, negative means it sinks
fsubmerged = ρobject / ρfluid
submerged volume fraction of a floating object
At full submersion, the maximum possible buoyant force is F_b,max = ρ_fluid × V_object × g. If that exceeds the object's weight (mg), the object floats and rises until only enough of it is submerged for F_b to exactly equal mg — giving the submerged fraction ρ_object / ρ_fluid. If F_b,max is less than or equal to the weight, no submerged depth can balance it, so the object sinks.
Worked example 1 — ice cube floating in water
Given: An ice cube has volume V = 0.001 m³ (10 cm side) and density ρ_ice = 917 kg/m³, floating in fresh water (ρ_water = 1000 kg/m³, g = 9.81 m/s²).
This is the classic "tip of the iceberg" figure — only about 8.3% of floating ice shows above the surface.
Worked example 2 — steel ball sinking in water
Given: A solid steel ball of radius r = 0.05 m (V = (4/3)πr³ ≈ 5.236 × 10⁻⁴ m³) and density ρ_steel = 7850 kg/m³, dropped in fresh water (ρ_water = 1000 kg/m³).
Submerged fraction for common floating objects (in fresh water)
Submerged fraction = ρ_object / ρ_water — a rough guide, since shape and posture (like lung volume) can shift the real-world figure.
| Object | Typical densitykg/m³ | Submerged fraction |
|---|---|---|
| Cork | ~240 | ~24% |
| Pine wood | ~500 | ~50% |
| Human body (average) | ~900–970 | ~90–97% |
| Ice ★ | 917 | 91.7% |
| Steel (solid, any shape) | 7850 | sinks — 100% submerged, rests on bottom |
★ Reference row (see worked example 1). Human submerged fraction varies with lung inflation — a full breath lowers average body density and raises buoyancy.
Where buoyancy actually matters
🚢 Ship & submarine design
A steel ship floats because its hull encloses enough air volume to bring its average density below water’s. Submarines flood or empty ballast tanks to fine-tune their average density, letting them float, hover neutrally, or sink on command.
🧊 Icebergs at sea
Because ice is about 91.7% as dense as seawater, roughly nine-tenths of an iceberg’s volume lies underwater — the visible tip is a small fraction of the total, which is why icebergs are so hazardous to shipping.
🏊 Swimming & diving
A swimmer’s body is close to water density, so buoyancy nearly cancels weight — small changes in lung volume (a deep breath vs a full exhale) are often enough to shift a person from floating to sinking.
🎈 Hot air balloons
Heating the air inside the envelope lowers its density below the surrounding cooler air, so the balloon displaces air that weighs more than the balloon system itself — the same F_b = ρ·V·g principle, just with air as the "fluid".
Common misconceptions
"Heavy objects always sink."
False — floating depends on average density, not total mass. A massive steel ship floats because its shape encloses a large air volume, keeping its overall density below water’s, while a small solid steel ball of the same material sinks.
"Buoyant force depends on the object’s mass."
It depends on the volume of fluid displaced and the fluid’s density, not on the object’s own mass or density directly: F_b = ρ_fluid × V_displaced × g. The object’s mass only matters when comparing it to F_b to decide float vs sink.
"A submerged object feels a growing buoyant force the deeper it goes."
For a fully submerged object of fixed volume in a fluid of roughly constant density, the buoyant force stays the same at any depth, because the displaced volume does not change. It is pressure, not buoyant force, that increases with depth.
"Objects that float have zero net force acting on them at all times."
A floating object at equilibrium has zero net force, but it gets there by settling to whatever submerged depth makes F_b exactly equal its weight — if pushed deeper or lifted, it briefly feels a nonzero net force pulling it back to that equilibrium level.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 1 — §14.4, Archimedes’ Principle and Buoyancy (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 14, Fluids (Archimedes’ Principle).
- • Serway & Jewett, Physics for Scientists and Engineers — Chapter 14, Fluid Mechanics.
Standard g = 9.81 m/s² is used. Fluid density presets: fresh water 1000 kg/m³, seawater 1025 kg/m³, air 1.225 kg/m³. Results are rounded for display.
How to use this calculator
Choose the fluid
Pick fresh water, seawater or air from the preset, or type a custom fluid density.
Enter volume & mass
Fill in the object’s total volume (m³) and mass (kg).
Read float or sink
See the buoyant force, weight, net force and — if it floats — the submerged fraction.
Related tools
Frequently asked questions
What is Archimedes' principle?
Archimedes’ principle states that any object submerged (fully or partly) in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces: F_b = ρ_fluid × V_displaced × g. This is why objects feel lighter in water and why some float while others sink.
How do I know if an object will float or sink?
Compare the object’s average density to the fluid’s density. If ρ_object < ρ_fluid, the buoyant force at full submersion exceeds the object’s weight, so it floats and settles at a shallower depth where the two balance. If ρ_object ≥ ρ_fluid, the maximum buoyant force can never match the weight, so it sinks and rests on the bottom.
What fraction of a floating object is submerged?
At equilibrium the buoyant force equals the object’s weight: ρ_fluid × V_submerged × g = ρ_object × V_object × g. Solving gives V_submerged / V_object = ρ_object / ρ_fluid — the submerged fraction is simply the density ratio.
Why do heavy ships float?
Buoyant force depends on the volume of fluid displaced, not on the object’s mass alone. A steel ship’s hull encloses a large volume of air, so its average density (hull + cargo + air space, divided by total hull volume) is far less than water’s, even though the steel itself is much denser than water.
Does buoyant force depend on how deep an object is submerged?
Only through how much fluid volume is displaced, not depth itself. A fully submerged object displaces its full volume no matter how deep it goes (assuming the fluid density stays constant), so the buoyant force stays the same at any depth — it does not grow with depth the way pressure does.