Buoyancy & Archimedes’ Principle Simulator
Fb = ρfluid · Vdisp · g — Drop, Float, Sink • Simulate • Explore • Practice • Quiz
Σ Live equations — values substituted from current state
⚖ Material comparison — floats vs sinks at current fluid
💡 What-if coach — insights from current values
1 Overview
The Buoyancy Simulator brings Archimedes’ principle to life. Drop a cube, sphere, or cylinder of any material into a tank of fluid and watch it find its natural resting depth, with live force arrows for weight (red, downward) and buoyant force (blue, upward). Eight objects (cork through lead) and six fluids (alcohol through mercury) cover the full density spectrum from 250 kg/m³ to 13 534 kg/m³ — including the famous result that lead floats on mercury.
This tool is built for high-school physics, technical-college fluid-mechanics, and engineering trainees learning hydrostatics. Four modes (Simulate, Explore, Practice, Quiz) cover concept building, problem solving, and self-testing. Both SI (kg/m³, N, L) and Imperial (lb/ft³, lbf, gal) units are supported with live conversion.
2 Getting Started
The simulator opens in Simulate mode with an Ice cube (917 kg/m³) ready to be dropped into Fresh Water (1000 kg/m³). Click the orange 🔹 Drop Object button — the cube falls, splashes, and settles with about 91.7% below the waterline. That fraction is exactly ρobject / ρfluid — the iceberg ratio.
To explore further, switch the Object to Lead and the Fluid to Mercury — Lead (11 340) actually floats on Mercury (13 534). Or pick Steel in Water — it sinks and the green apparent weight arrow appears, showing how much the buoyant force has lightened it.
3 Simulate Mode
The canvas shows a glass tank with animated waves, an object resting at its equilibrium depth, and force vectors. The readout cards report Object Density, Fluid Density, Mass, Weight, Buoyant Force, Apparent Weight, Submerged %, and V displaced. Adjust Volume (0.1–20 L) and Shape (Cube / Sphere / Cylinder) and watch the displaced fluid grow.
Six presets set up classic scenarios in one click: Default (ice on water), Iceberg Tip, Lead Floats Mercury, Steel Sinks, Salt vs Fresh, and Cork Bobber. Use the + Custom button to add your own material with a user-defined density (50–25 000 kg/m³).
4 Explore Mode
Switch to Explore for concept cards across four categories: Basics (Archimedes’ principle, density, why things float), Formulas (Fb = ρVg, submerged-fraction derivation, apparent weight), Applications (ships, hot-air balloons, hydrometers, submarines), and Common Errors (mass vs weight, density vs specific gravity, units).
Each card has a worked example with real numbers, so you see how the formula behaves before attempting Practice problems.
5 Practice & Quiz
Practice generates random problems — find the buoyant force on a 2 L cube of aluminium in water, find the submerged fraction of an unknown wood, or calculate apparent weight of a sinking sphere. Enter your answer (tolerances are appropriate for the unit system) and click Check. Show Solution walks through the full calculation step-by-step.
Quiz presents five questions per session, mixing conceptual (does it float? what changes if salt is added?) and numerical problems. Star rating is awarded based on correct answers.
6 SI vs Imperial
Click the SI / Imperial pill at the top to convert every readout, slider label, badge, canvas axis, and calc-modal line. SI uses kg/m³, N, kg, L, m. Imperial uses lb/ft³, lbf, lb, gal (US), ft. Internal calculations always use SI base units, so accuracy is preserved across switches.
Useful conversions: 1 kg/m³ ≈ 0.0624 lb/ft³; 1 N ≈ 0.2248 lbf; 1 L ≈ 0.2642 US gal.
7 Power Tools
Action bar: Drop Object animates a fall and splash; Reset places the object above the fluid; Undo / Redo step through your last edits (Ctrl+Z / Ctrl+Shift+Z).
Canvas toggles: Hide/show Forces, Particles, Equation, Grid, and Waterline for focused screenshots or simpler views.
Show Calculations opens a step-by-step modal: density → mass → weight → submerged volume → buoyant force → apparent weight — the exact work a student would show on paper.
Export: CSV saves the current state as a row; PNG saves a labelled snapshot. Right-click the canvas for the same actions plus Copy Result.
Sound feedback: Click on drag, splash on drop, success/error chimes in Practice and Quiz.
8 Tips & Best Practices
- An object floats when ρobject < ρfluid and sinks otherwise — volume and shape do not change this rule for a uniform solid.
- For a floating object, the submerged fraction equals the density ratio: Vsub/V = ρobject/ρfluid.
- For a sinking object, the buoyant force still acts but is less than the weight; the apparent weight is W − Fb.
- Salt water (1025 kg/m³) is denser than fresh water, so the same boat sits slightly higher in the sea than in a lake.
- Pair this simulator with the Pascal’s Law and Fluid Flow tools to cover statics and dynamics together.
Understanding Buoyancy and Archimedes’ Principle
Buoyancy is the upward force a fluid exerts on any object placed in it. The magnitude of this force, given by Archimedes’ principle, equals the weight of the fluid displaced by the object: Fb = ρfluid · Vdisplaced · g. This single equation predicts whether a steel ship floats, why hot-air balloons rise, and how submarines control depth.
Densities of Common Materials & Fluids
| Material / Fluid | ρ (kg/m³) | ρ (lb/ft³) | Behaviour in Water |
|---|---|---|---|
| Cork | 250 | 15.6 | Floats — 25% submerged |
| Pine wood | 450 | 28.1 | Floats — 45% submerged |
| Ice | 917 | 57.2 | Floats — 91.7% submerged |
| Fresh Water | 1000 | 62.4 | Reference fluid |
| Salt Water (sea) | 1025 | 63.99 | Reference fluid |
| Aluminium | 2700 | 168.6 | Sinks (Wapp ≈ 63% of W) |
| Iron / Steel | 7870 | 491.4 | Sinks (Wapp ≈ 87% of W) |
| Lead | 11 340 | 708.0 | Sinks — but floats on Mercury |
| Mercury (fluid) | 13 534 | 845.0 | Densest common liquid |
The Float-or-Sink Rule
The behaviour of a uniform solid in a fluid is determined entirely by the density ratio ρobject / ρfluid. If the ratio is less than 1, the object floats and the submerged fraction equals the ratio itself. If it is greater than 1, the object sinks but still receives an upward buoyant force equal to its full weight in displaced fluid. This is why a 1 kg steel cube placed on a kitchen scale submerged in water reads only about 0.873 kg — the buoyant force of 1.247 N supports a portion of its weight.
The Iceberg Ratio — A Worked Example
Ice has a density of 917 kg/m³ and floats on sea water (ρ = 1025 kg/m³). The submerged fraction is 917 / 1025 ≈ 0.895, meaning about 89.5% of an iceberg is hidden below the waterline — only the famous “tip” is visible. For a 1 000 m³ iceberg, that is 895 m³ submerged, exerting a buoyant force Fb = 1025 × 895 × 9.81 ≈ 9.0 MN, exactly equal to the iceberg’s weight.
Why Steel Ships Float
Steel has a density 7.87 times greater than water, so a solid steel block sinks. A ship floats not because steel becomes lighter but because its average density — including the air-filled hull — is less than 1000 kg/m³. Naval architects design hulls to displace many times the boat’s actual mass in water, generating enough buoyant force to support the entire vessel plus cargo. The same logic explains how a hot-air balloon (warm low-density air inside a balloon) floats in the surrounding cooler atmosphere.
Apparent Weight and Submarines
For an object that sinks, its apparent weight in the fluid is Wapp = (ρobject − ρfluid) · V · g. Submarines exploit this by adjusting their average density: pumping water into ballast tanks increases density and the submarine sinks, while pushing the water out with compressed air decreases density and it rises. At neutral buoyancy, the submarine’s density exactly equals the surrounding water’s, and it can hover at any depth.
Who Uses This Simulator?
This buoyancy simulator is used by high-school and undergraduate physics students learning Archimedes’ principle, technical-college trainees in hydrostatics and fluid mechanics, naval-architecture and marine-engineering students sizing hulls and pontoons, and instructors who need a fast visual to compare densities, demonstrate the iceberg ratio, or illustrate why ships float and submarines submerge. The Practice and Quiz modes let students self-test before exams.
Explore Related Simulators
If you found this buoyancy simulator helpful, explore our Pascal’s Law Simulator, Fluid Flow in Pipes, Bernoulli’s Principle, Specific Heat Capacity, and Thermal Expansion for more hands-on practice.
Enter a positive value. Range: 50–25 000 kg/m³.