Physics
Density Calculator
Solve for density, mass, or volume using ρ = mass ÷ volume. Enter any two values in any units, get the third instantly, and see whether it floats in water — plus a lookup table for the density of common materials.
Solve for
Density
2
Sinks in waterSG 2
in kg/m³
2000
in g/cm³
2
vs. fresh water at 1000 kg/m³ (1 g/cm³).
Try an example
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The basics
What is density?
Density measures how tightly matter is packed into space — the mass contained in each unit of volume. It is what makes a small lead fishing weight feel heavy and a large foam block feel like nothing. The relationship is one short formula, and it can be rearranged to find whichever quantity you are missing.
ρ = m ÷ V
Mass per unit volume
Density (ρ, the Greek letter rho) is the mass m divided by the volume V. It is an intensive property — it does not depend on how much of the material you have.
20 g ÷ 10 cm³ = 2 g/cm³
float if ρ < ρ_water
The water benchmark
Water sets the reference. Anything less dense than water floats on it; anything denser sinks. The ratio of a material's density to water's is its specific gravity.
ice 917 < 1000 → floats
Method
How to calculate density by hand
Three steps, whichever quantity you are solving for.
- 1
Get matching units
Measure the mass and the volume, then make sure their units belong to the same family — grams with cm³, or kilograms with m³. Convert first if they don't.
20 g and 10 cm³ - 2
Pick the right form
Use ρ = m ÷ V for density, rearrange to m = ρ × V for mass, or V = m ÷ ρ for volume.
ρ = m ÷ V - 3
Substitute and solve
Plug the two known numbers in and do the single multiplication or division. The unit of the answer follows from the units you put in.
ρ = 20 ÷ 10 = 2 g/cm³
Worked examples
See it solved every direction
The same formula, rearranged for each of the three quantities you might be missing.
Given m = 20 g, V = 10 cm³
Rearrange: ρ = m ÷ V
Substitute: ρ = 20 ÷ 10
ρ = 2 g/cm³
Reference chart
Density of common materials
Look up the density of everyday substances, metals, liquids, and gases — sorted lightest to densest, with each one's specific gravity and whether it floats or sinks in water. Search by name or filter by group.
Materialkg/m³g/cm³vs. water
HeliumGas · SG 0.0001790.17860.000179Floats
Air (sea level)Gas · SG 0.0012251.2250.001225Floats
StyrofoamEveryday · SG 0.05500.05Floats
Balsa woodWood · SG 0.161600.16Floats
CorkEveryday · SG 0.242400.24Floats
Pine woodWood · SG 0.515100.51Floats
Oak woodWood · SG 0.757500.75Floats
EthanolLiquid · SG 0.7897890.789Floats
IceEveryday · SG 0.9179170.917Floats
Olive oilLiquid · SG 0.929200.92Floats
Water (fresh)Liquid · SG 110001Neutral
SeawaterLiquid · SG 1.02510251.025Sinks
MilkLiquid · SG 1.03510351.035Sinks
RubberEveryday · SG 1.111001.1Sinks
BrickMineral · SG 1.919001.9Sinks
ConcreteMineral · SG 2.424002.4Sinks
GlassMineral · SG 2.525002.5Sinks
AluminumMetal · SG 2.727002.7Sinks
DiamondMineral · SG 3.5135103.51Sinks
TitaniumMetal · SG 4.50645064.506Sinks
SteelMetal · SG 7.8578507.85Sinks
IronMetal · SG 7.87478747.874Sinks
BrassMetal · SG 8.585008.5Sinks
CopperMetal · SG 8.9689608.96Sinks
SilverMetal · SG 10.491049010.49Sinks
LeadMetal · SG 11.341134011.34Sinks
MercuryLiquid · SG 13.5341353413.534Sinks
GoldMetal · SG 19.31930019.3Sinks
PlatinumMetal · SG 21.452145021.45Sinks
Values at roughly 20 °C and 1 atm; real samples vary with temperature, purity, and porosity.
Unit conversions
Density units, side by side
Density units look different but scale by clean factors. These are the conversions the calculator applies under the hood.
1 g/cm³=1000 kg/m³the density of water
1 g/cm³=1 g/mL = 1 kg/Lidentical by definition
1 kg/m³=1 g/Lthe metric “light” scale
1 g/cm³=62.43 lb/ft³metric to imperial
1 lb/ft³=16.018 kg/m³imperial to metric
Worth knowing
Rules worth remembering
A handful of facts that catch people out when they work with density.
ρ is independent of size
Density doesn't change with amount
Break a brick in half and each piece has the same density as the whole. Density is an intensive property — it describes the material, not how much of it you have.
SG = ρ ÷ ρ_water
Specific gravity drops the units
Dividing by water's density cancels the units, leaving a pure ratio. It is the quickest float test: above one sinks, below one floats.
warmer → usually less dense
Temperature shifts density
Most materials expand when heated, spreading the same mass over more volume, so density falls. Reference values are always quoted at a stated temperature.
ice < water
Water is the odd one out
Water is densest at 4 °C and expands as it freezes, so ice is less dense than liquid water and floats — the reason ponds freeze top-down and aquatic life survives winter.
gases ≪ liquids ≪ solids
State sets the scale
Gases are roughly a thousand times less dense than liquids and solids because their molecules are spread far apart. Air is about 1.2 kg/m³ against water's 1000.
mixtures average out
Alloys land between their parts
The density of a mixture or alloy sits between its ingredients, weighted by how much of each is present — useful for spotting fake gold by its specific gravity.
Where it shows up
Why density matters
One ratio that decides what floats, how ships are loaded, and whether a coin is counterfeit.
ρ_object vs ρ_fluid
Ships & submarines
A steel hull floats because its average density — steel plus the air inside — is less than water. Submarines flood tanks to raise their density and dive.
SG of metal
Spotting fakes
Jewellers and mints weigh a piece in air and in water to find its density. A gold coin must match gold's specific gravity of 19.3, or it isn't solid gold.
hot air rises
Weather & flight
Warm air is less dense than cold air, so it rises — driving wind, storms, and the lift of a hot-air balloon.
In practice
How to measure density yourself
You always need two numbers — a mass and a volume. Mass is easy: a scale. Volume depends on the shape.
V = l × w × h
Regular solids
For a box, cylinder, or sphere, measure the dimensions and use the geometry formula for its volume. Weigh it, then divide.
V = volume of water pushed up
Irregular objects
Drop the object into a measured amount of water and read how far the level rises. The rise is the object's volume — Archimedes' displacement trick, the way to volume an odd shape like a stone or a crown.
SG from two weighings
Weigh in air and water
Weigh the object hanging in air, then submerged. The apparent weight it loses equals the weight of the water it displaces, which gives volume and density without a measuring jug.
Common mistakes
Where density calculations go wrong
Most bad density answers come from one of these four slips — all easy to avoid.
g with cm³, kg with m³
Mismatched units
Dividing grams by m³, or kg by cm³, throws the answer off by a factor of a million. Put mass and volume in matching families first — the calculator does this for you.
mL = cm³, not m³
Confusing mL and m³
A millilitre is one cubic centimetre, not one cubic metre. Treating a litre as a cubic metre (1,000× too big) is the single most common volume error.
mass ÷ V, not V ÷ mass
Flipping the formula
Density is mass over volume. Dividing volume by mass gives the reciprocal — a number that looks plausible but is upside down.
quote the temperature
Ignoring temperature
Density shifts with temperature, so comparing a hot sample to a 20 °C table value can mislead. Reference figures always assume a stated temperature.
FAQ
Common questions
Density is how much mass is packed into a given volume — mass per unit volume. Two objects can be the same size, but the denser one weighs more because more matter is crammed into the same space. The formula is ρ = mass ÷ volume.
Divide the mass by the volume: ρ = mass ÷ volume. For 20 grams occupying 10 cm³, the density is 20 ÷ 10 = 2 g/cm³. Make sure mass and volume are measured in matching unit families before you divide, or convert them first — the calculator above does the conversion for you.
Density is mass over volume, so its units combine a mass unit with a volume unit: g/cm³, kg/m³, kg/L, and lb/ft³ are the common ones. They scale directly — 1 g/cm³ equals 1000 kg/m³. Water is about 1 g/cm³, or 1000 kg/m³.
Rearrange the formula to mass = density × volume, then multiply. For a density of 19.3 g/cm³ (gold) and a volume of 50 cm³, mass = 19.3 × 50 = 965 g. Switch the calculator to “Mass” to do this automatically.
Rearrange to volume = mass ÷ density and divide. For 5000 g of water at 1 g/cm³, volume = 5000 ÷ 1 = 5000 cm³ (5 litres). Switch the calculator to “Volume” for this.
Compare its density to water’s 1000 kg/m³ (1 g/cm³). Anything less dense than water floats; anything denser sinks. That is why ice (917 kg/m³) floats and a steel bolt (7850 kg/m³) sinks. The calculator shows a float/sink verdict next to every result.
Specific gravity is an object’s density divided by the density of water — a dimensionless ratio. Gold has a specific gravity of about 19.3, meaning it is 19.3 times as dense as water. A specific gravity above 1 sinks; below 1 floats.
Yes. Heating most materials makes them expand, so the same mass fills more volume and density drops. Water is the famous exception near freezing — it is densest at 4 °C, which is why lakes freeze from the top down. Reference tables quote density at a stated temperature, usually 20 °C.
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Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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