A small pebble sinks but a 100,000-ton ship floats. Both are denser than water on the inside — yet only one floats. The key is in how density compares to the surrounding fluid, plus a clever physics principle called Archimedes' principle.
The basic rule
Anything denser than the surrounding fluid sinks. Anything less dense floats. The exact density of the object compared to the fluid determines whether and how much it floats.
Water density: 1000 kg/m³ = 1 g/cm³ = 1 specific gravity unit.
- Wood: 600-800 kg/m³. Floats.
- Plastic: typically 900-1500 kg/m³. Some float, some sink.
- Most fruits: ~1000 kg/m³. Float (barely).
- Iron: 7,800 kg/m³. Sinks.
- Lead: 11,300 kg/m³. Sinks fast.
Specific gravity
Specific gravity (SG) is density relative to water. Easier than absolute densities for everyday use.
- SG < 1: floats in water.
- SG = 1: neutral (suspended).
- SG > 1: sinks.
Examples:
- Cork: SG 0.24. Floats easily.
- Pine wood: SG 0.5.
- Oak: SG 0.75.
- Plastic: SG 0.9-1.5 depending on type.
- Aluminum: SG 2.7.
- Iron: SG 7.8.
- Gold: SG 19.3.
Why a ship floats
A 100,000-ton steel ship is made of metal denser than water. So why doesn't it sink?
Because the ship is hollow. The total volume of the ship (including air inside) is what matters, not just the steel.
Average density = total mass / total volume.
If the ship's average density (steel + air inside the hull) is less than water, it floats. The hull design lowers the average density by including a lot of air.
If you crushed the ship into a solid metal cube, it would sink immediately.
Archimedes' principle
The buoyant force on an object equals the weight of the fluid it displaces.
- If the object weighs less than the displaced water, it floats.
- If it weighs more, it sinks.
- If equal, it floats neutrally suspended.
An object that's exactly water's density (a hollow ball partly submerged, just like its average density equals water) hangs suspended.
How much an object sinks
For floating objects, the amount submerged depends on density ratio:
- Density 0.5 (oak): half submerged.
- Density 0.75 (denser oak): three-quarters submerged.
- Density 0.9 (water-logged wood): 90% submerged.
An iceberg has density 0.9, so 90% is underwater. The famous tip is the visible 10%.
Salt water vs fresh water
Salt water has higher density than fresh water (~1025 kg/m³ vs 1000). So:
- Things float higher in salt water (you can see this in the ocean).
- The Dead Sea (very salty, density 1240 kg/m³) lets you float effortlessly.
- Ships sink slightly more in fresh water than salt water — there's an actual line on cargo ships ("plimsoll mark") for this.
Density of air
Air at sea level: 1.225 kg/m³. Vastly less than water (1000).
So things float in air just like in water — they need to be less dense than air. Hydrogen and helium are lighter than air; that's why hydrogen blimps float, and helium balloons rise.
Hot air is less dense than cold air. Hot air balloons work because heated air inside the balloon weighs less than the cold air around it.
Practical applications
Hot tub testing: if you can't tell whether a wood is cedar or pine by density, weigh it dry and measure displacement to compare against published densities.
Pearl identification: real pearls and many gemstones have specific densities. Specific gravity testing helps identify them.
Fluid mechanics: chemists and physicists characterize fluids by density. Some chemistry experiments need specific densities.
Mining: gold's density (19.3) makes it stand out from common rocks (2-3). Gold panners use density-based separation.
Hydrometers: floating instruments calibrated to water that show fluid's specific gravity. Used in beer brewing to measure sugar dissolution, and in batteries to test acid concentration.
Density of liquids and oils
| Liquid | Density (g/cm³) |
|---|---|
| Gasoline | 0.74 |
| Olive oil | 0.92 |
| Vegetable oil | 0.92 |
| Water | 1.00 |
| Milk | 1.03 |
| Sea water | 1.025 |
| Honey | 1.42 |
| Mercury | 13.5 |
Why oil and water don't mix: different densities (oil is less dense and floats on water), and they're chemically immiscible. Both reasons.
Honey at 1.42 sinks in water but stays on the bottom of a glass.
Mercury at 13.5 is so dense that iron floats in it.
Will it float?
Quick test:
- Estimate or look up density.
- Compare to fluid's density.
- If lower, floats; if higher, sinks.
If hollow, average density of the object (including any internal cavities) is what matters.
Why ice floats
Water is unusual: solid water (ice) is less dense than liquid water. Ice has SG 0.92.
So ice floats on water. This is rare among substances — most solids are denser than their liquid forms.
This anomalous behavior of water is critical for life — fish survive frozen lakes because the ice forms on top, insulating the water below.
Density of air at altitude
Atmospheric pressure (and density) decreases with altitude:
- Sea level: 1.225 kg/m³
- 1500 m (Denver): 1.06 kg/m³ (87% of sea level)
- 4000 m: 0.82 kg/m³ (67%)
- 10000 m (cruising altitude): 0.41 kg/m³ (33%)
This is why hot air balloons climb — heated less-dense air rises, and as it rises, surrounding air gets less dense too. Balloon must be hotter to climb further.
Calculate density
Our density calculator takes mass and volume and returns density in multiple units plus specific gravity. Useful for materials science, fluid mechanics, or just checking whether something will float.