How to Calculate Density: Formula, Mass & Volume

Density is one of those ideas that sounds abstract until you hold two objects the same size — a block of foam and a block of steel — and feel the difference. That difference is density: how much mass is packed into a given volume. It's why ice floats, why a hot-air balloon rises, and why a small bag of coins feels so heavy. This guide explains how to calculate density, the formula and how to rearrange it to find mass or volume, worked examples in metric and US units, and a reference table of common materials. When you just need the number, the density calculator solves for density, mass, or volume the moment you enter the other two.

What is density?

Density is the amount of mass per unit of volume of a substance. Two objects can be the same size but have very different masses — a litre of water weighs 1 kilogram, while a litre of mercury weighs over 13 kilograms — and density is the number that captures that. It is an intensive property, which means it doesn't depend on how much of the material you have: a teaspoon of gold and a gold bar have exactly the same density. That makes density a kind of fingerprint for a material, which is why it's used to identify metals, check the purity of liquids, and work out whether something will float.

The density formula

The formula is short and worth memorising:

Density = Mass ÷ Volume

Or in symbols, ρ = m / V, where ρ (the Greek letter "rho") is density, m is mass, and V is volume. That single relationship is the whole of it — everything else is just rearranging the same equation to solve for whichever quantity you're missing.

The formula for mass, volume and density (all three forms)

Because the three quantities are linked by one equation, knowing any two gives you the third. Here are all three rearrangements:

To find…	Formula	In words
Density (ρ)	ρ = m ÷ V	mass divided by volume
Mass (m)	m = ρ × V	density times volume
Volume (V)	V = m ÷ ρ	mass divided by density

A handy memory trick is the "density triangle": draw a triangle with m on top and ρ and V in the two bottom corners. Cover the quantity you want, and the position of the other two tells you whether to multiply (side by side) or divide (one over the other). The density calculator applies whichever of these three forms you need automatically — you just leave the unknown field blank.

Units of density

Density units are always a unit of mass over a unit of volume. The common ones are:

• g/cm³ (grams per cubic centimetre) — the everyday metric unit, handy because water is almost exactly 1 g/cm³.
• kg/m³ (kilograms per cubic metre) — the SI unit, used in physics and engineering. Water is 1000 kg/m³.
• lb/ft³ (pounds per cubic foot) — common in US construction and HVAC work. Water is about 62.4 lb/ft³.

To convert between the two metric units, remember that 1 g/cm³ = 1000 kg/m³. Mixing units is the single most common cause of a wrong answer, so always check that your mass and volume units match the density unit you want before you divide.

How to calculate density: a worked example

Suppose you have a metal block with a mass of 600 grams and a volume of 76 cm³. Plug the numbers into ρ = m / V:

ρ = 600 g ÷ 76 cm³ = 7.9 g/cm³

A density of 7.9 g/cm³ is very close to the density of iron or steel, so that's almost certainly what the block is made of. This is exactly how density is used to identify an unknown material: measure the mass on a scale, find the volume, divide, and compare against a reference table.

Finding mass from density and volume

Now suppose you know a liquid's density is 0.8 g/cm³ and you have 250 cm³ of it. To get the mass, use m = ρ × V:

m = 0.8 g/cm³ × 250 cm³ = 200 g

Finding volume from density and mass

And if you have 500 g of a substance with a density of 2.5 g/cm³, the volume is V = m ÷ ρ:

V = 500 g ÷ 2.5 g/cm³ = 200 cm³

Three problems, one equation, three rearrangements. Once the formula is second nature, the only real work is measuring mass and volume accurately and keeping your units consistent.

How to measure mass and volume

Mass is the easy part: put the object on a balance or kitchen scale and read it in grams or kilograms. Volume takes a little more care, and how you find it depends on the shape:

• Regular solids (a cube, a cylinder, a sphere) — use the geometry formula. A box is length × width × height; a cylinder is π × radius² × height.
• Irregular solids — use water displacement. Fill a measuring cylinder, drop the object in, and the rise in the water level equals the object's volume (1 mL = 1 cm³). This is the famous "Eureka" method attributed to Archimedes.
• Liquids — pour into a graduated cylinder or measuring jug and read the volume directly.

Common material densities (reference table)

Here are approximate densities for everyday materials, all at room temperature in g/cm³:

Material	Density (g/cm³)
Balsa wood	0.16
Ice	0.92
Water (4 °C)	1.00
Seawater	1.03
Aluminium	2.70
Glass	2.5
Iron / steel	7.8–7.9
Copper	8.96
Silver	10.49
Lead	11.34
Mercury	13.53
Gold	19.32

Notice that ice (0.92) is less dense than water (1.00) — that's why ice floats, and why icebergs sit mostly below the surface. Anything with a density below 1 g/cm³ will float in water; anything above it will sink.

Why density matters: floating, sinking and buoyancy

An object floats if it is less dense than the fluid it sits in, and sinks if it is denser. A steel ship floats — despite steel being eight times denser than water — because its hull encloses a large volume of air, dropping the average density of the whole vessel below that of water. Hot-air balloons rise for the same reason: heating the air inside lowers its density compared with the cooler air outside. Oil floats on water, cream rises on milk, and a helium balloon climbs through the air — all of it is density at work.

Density and temperature

Density isn't quite fixed: most substances expand when heated, so their volume goes up while their mass stays the same, which means density drops as temperature rises. Water is the famous exception — it is densest at about 4 °C, and expands as it freezes, which is why pipes burst in winter and lakes freeze from the top down. For everyday calculations the change is small enough to ignore, but in precise scientific or engineering work, density is always quoted at a stated temperature.

Specific gravity and relative density

Density is often discussed alongside a related but distinct concept: specific gravity, also called relative density. Where density is an absolute quantity expressed in units such as kg/m³ or g/cm³, specific gravity is a pure ratio with no units. It compares the density of a substance to the density of a reference, almost always water at 4°C, which is very close to 1,000 kg/m³ or 1 g/cm³.

The formula is simply the density of your substance divided by the density of water. Because water's density is approximately 1 g/cm³, the specific gravity of a material expressed in those units is numerically almost identical to its density in g/cm³. A substance with a density of 2.7 g/cm³ has a specific gravity of about 2.7. This convenient overlap is why geologists and gemmologists lean on specific gravity so heavily: a single dimensionless number tells you instantly whether a mineral will sink in water and roughly how heavy it is for its size.

Material	Specific gravity	Behaviour in water
Cork	0.24	Floats high
Ice	0.92	Floats, mostly submerged
Water (reference)	1.00	Neutral
Aluminium	2.70	Sinks
Iron	7.87	Sinks rapidly
Gold	19.30	Sinks rapidly

Any value below 1 means the substance floats in water, and any value above 1 means it sinks. This single rule explains why ice floats, why oil pools on top of water, and why a gold nugget drops straight to the bottom of a pan.

Density of mixtures and solutions

Real-world substances are rarely pure. When you blend two materials, the resulting density is not a simple average unless the volumes combine cleanly. For a mixture where total mass and total volume are known, you still apply the core relationship of mass divided by volume, but you must add the masses and the volumes of each component first.

Consider mixing 200 g of ethanol (density 0.79 g/cm³, so about 253 cm³) with 200 g of water (density 1.00 g/cm³, so 200 cm³). The combined mass is 400 g. In an ideal case the volume would be 453 cm³, giving a density of about 0.88 g/cm³. In reality ethanol and water molecules pack together more tightly than expected, so the true volume is slightly less and the measured density slightly higher. This volume contraction is a famous example of why you should measure the density of a finished solution rather than assume it.

For salt solutions, sugar syrups and antifreeze mixtures, density rises as you dissolve more solute. This is the principle behind a hydrometer, which measures the density of a liquid by how high it floats. Brewers, winemakers and battery technicians all use density readings to infer concentration without any chemical analysis.

Density gradients and layering liquids

Because liquids of different densities resist mixing, you can stack them in visible layers, a popular demonstration that turns the density formula into something you can see. The denser a liquid, the lower it settles. A classic density column, from bottom to top, might run honey, corn syrup, washing-up liquid, water, vegetable oil and rubbing alcohol.

• Honey sits at the bottom with a density near 1.42 g/cm³.
• Water takes the middle at 1.00 g/cm³.
• Vegetable oil floats above water near 0.92 g/cm³.
• Rubbing alcohol rides on top near 0.79 g/cm³.

Small objects dropped into the column come to rest at the layer matching their own density, a vivid way to estimate an unknown object's density without calculation. This same physics drives ocean stratification, where cold salty water sinks beneath warm fresh water, and it underpins industrial separation processes that sort plastics for recycling by floating them in fluids of carefully chosen density.

Population density and other non-physical densities

The word density extends well beyond physics, and the underlying idea is always the same: an amount divided by the space it occupies. Recognising this pattern helps you apply the concept across fields.

Type of density	Quantity	Per unit of	Typical units
Mass density	Mass	Volume	kg/m³
Population density	People	Area	people/km²
Charge density	Electric charge	Volume or area	C/m³
Bone mineral density	Mineral content	Area	g/cm²
Data density	Information	Storage area	bits/in²

Population density divides a number of people by an area rather than a volume, but the conceptual machinery is identical to mass density. Whenever you see "density" you can ask: what is being counted, and over what space is it spread? That instinct makes the physical density formula feel less like an isolated rule and more like one instance of a broad principle.

Measuring the density of irregular objects

Regular shapes let you calculate volume with geometry, but most real objects are irregular. The reliable method is water displacement, an idea credited to Archimedes. Submerge the object in a graduated container of water and read how much the water level rises; that rise equals the object's volume.

The procedure has four steps. First, weigh the dry object to get its mass. Second, fill a measuring cylinder with enough water to fully cover the object and record the starting level. Third, lower the object in completely and record the new level. Fourth, subtract to find the displaced volume, then divide mass by that volume. For a stone weighing 85 g that raises the water level from 50 cm³ to 80 cm³, the volume is 30 cm³ and the density is 85 / 30, or about 2.83 g/cm³, consistent with common rock.

A few precautions improve accuracy. Remove trapped air bubbles, since they exaggerate the displaced volume. Account for objects that float by gently pushing them under or attaching a known sinker and subtracting its volume. And avoid water-soluble or porous materials, which absorb water and distort the reading. Once you have a clean mass and volume, our density calculator will return the result instantly and let you rearrange the formula to solve for any unknown.

Common density measurement mistakes to avoid

Accurate density depends on careful technique. The following errors account for most wrong answers in classrooms and labs alike.

• Mixing unit systems. Combining grams with cubic metres, or kilograms with cubic centimetres, produces nonsense. Convert everything into one consistent system before dividing.
• Reading the meniscus wrong. In a glass cylinder, read the bottom of the curved water surface at eye level. Reading the top inflates your volume and lowers your density.
• Ignoring temperature. Liquids expand when warm, so a density quoted without a temperature is incomplete for precise work.
• Forgetting buoyancy of air. For everyday work it is negligible, but in high-precision weighing the air your object displaces slightly reduces its apparent mass.
• Trapped air or porosity. Bubbles clinging to a submerged object, or water soaking into a porous one, both corrupt the volume measurement.

Catching these issues early is far easier than diagnosing a strange final number. When a result looks implausible, retrace the measurement of volume first, since volume is almost always where density calculations go wrong.

Density in engineering and material selection

Engineers treat density as a first-class design property because it drives weight, which in turn affects cost, performance and safety. The goal is rarely the lowest density or the highest, but the best strength-to-weight ratio for the job. This is why a racing bicycle frame, an aircraft wing and a bridge each reach for very different materials despite all needing to be strong.

Consider why aluminium displaced steel in aviation. Steel is far stronger pound for pound in some respects, but its density of about 7.87 g/cm³ makes a steel airframe punishingly heavy. Aluminium, at roughly 2.70 g/cm³, offers enough strength at a third of the weight, and modern carbon-fibre composites push the ratio further still at densities near 1.6 g/cm³. Every gram saved in an aircraft reduces fuel burn over its entire service life.

Material	Density (g/cm³)	Typical engineering use
Carbon fibre composite	1.6	Aerospace, racing frames
Aluminium alloy	2.7	Aircraft, drink cans
Titanium	4.5	Implants, jet engines
Steel	7.9	Construction, tools
Lead	11.3	Radiation shielding, ballast

Density also matters where you deliberately want weight, such as the lead keel of a sailing yacht or the tungsten in a dart, where high density concentrates mass in a small space. Reading a density table is therefore the first step of nearly every material-selection decision an engineer makes.

Bulk density vs true density of powders and solids

For powders, granules and porous materials, a single density figure is ambiguous, and confusing the two common definitions leads to serious errors in shipping, storage and chemistry. The distinction is between true density and bulk density.

True density measures the mass of the solid material itself divided by the volume of just that solid, excluding any air gaps. Bulk density divides mass by the total volume the material occupies in a container, including the air between particles. Flour illustrates the gap vividly: its true density is over 1.4 g/cm³, but a loosely poured cup has a bulk density closer to 0.5 g/cm³ because so much of the cup is air.

• Bulk density determines how much a sack of grain weighs and how big a silo you need.
• True density tells you whether a particle will sink or float and how it behaves chemically.
• Tap density is a third variant, measured after settling the powder by tapping, and sits between the two.

Whenever you see a density quoted for a powder, ask which definition applies. A reading that seems too low for the material is usually a bulk density inflated by trapped air, not an error in your calculation.

The physics behind why some things float: Archimedes' principle

We touched earlier on the idea that less dense objects float, but the precise reason deserves its own explanation, because it underpins everything from shipbuilding to hot air balloons. The governing rule is Archimedes' principle, which states that the upward buoyant force on an object equals the weight of the fluid that object displaces. Whether the object floats or sinks comes down to a simple contest between that buoyant force and the object's own weight.

When you lower an object into a fluid, it pushes aside a volume of that fluid equal to the portion of the object that is submerged. The fluid pushes back with a force equal to the weight of what was displaced. If the displaced fluid weighs more than the object, the object floats and bobs up until only enough of it is submerged to balance its weight. If the displaced fluid weighs less, the object keeps sinking. Because weight depends on density, the whole question reduces to comparing the density of the object with the density of the fluid.

This is exactly why a steel ship floats even though steel is far denser than water. The hull is mostly hollow, so the average density of the ship, counting all the air inside, is lower than that of water. The ship sinks into the sea only until it has displaced a weight of water equal to its own total weight, then it floats. Load it with heavy cargo and it settles lower, displacing more water, until once again the forces balance. A submarine exploits the same idea deliberately, flooding tanks to increase its average density and sink, then blowing them clear to rise.

• Floats: object's average density is less than the fluid's density.
• Neutrally buoyant: densities are equal, so the object hovers at any depth, like a balanced submarine.
• Sinks: object's average density exceeds the fluid's density.

Understanding the principle as a comparison of densities, rather than a vague notion of heaviness, makes buoyancy predictable. A bowling ball and a beach ball can be the same size, but only the beach ball floats because its average density, dominated by the air inside, is far below that of water.

How density underpins everyday weather and ocean currents

Density is not just a laboratory curiosity; it drives some of the largest movements on the planet. Both the atmosphere and the oceans circulate largely because warm, less dense fluid rises while cool, denser fluid sinks. This continual overturning, called convection, redistributes heat across the globe and shapes the climate we live in.

In the air, the sun heats the ground, the ground warms the air just above it, and that warm air expands and becomes less dense than the cooler air higher up. The warm parcel rises, cooler air rushes in to take its place, and the cycle repeats. This is the engine behind sea breezes, thunderstorms and the towering thermals that gliders and birds ride for free lift. The same density difference explains why a hot air balloon climbs: heating the trapped air lowers its density below that of the surrounding atmosphere.

The oceans run on the same logic, but with two ingredients controlling density rather than one. Both temperature and salinity matter. Cold water is denser than warm water, and salty water is denser than fresh water. In the polar regions, surface water becomes cold and, as sea ice forms and leaves its salt behind, increasingly salty. This dense water sinks and flows along the ocean floor, driving a slow, global conveyor belt of currents that carries heat between the equator and the poles over centuries.

Factor	Effect on density	Everyday consequence
Higher temperature	Lowers density	Warm air and water rise
Higher salinity	Raises density	Salty water sinks beneath fresh
Higher pressure	Slightly raises density	Deep ocean water is marginally compressed

Once you see density as the hidden lever behind rising air and sinking seawater, weather maps and ocean diagrams start to make intuitive sense. The fluid that is denser sinks, the fluid that is lighter rises, and the resulting circulation does the rest.

Calculating the density you need for a specific job

Sometimes the practical question is reversed. Rather than measuring an object to find its density, you know the density you want and need to work out how much material to use or what volume a given mass will occupy. This comes up constantly in cooking, shipping, fuel storage and home projects, and it relies on the same single formula rearranged to suit the unknown.

If you know the density of a material and the mass you have, you can find the volume it will fill by dividing mass by density. That tells a shipper whether a heavy but compact load will fit in a container, or a homeowner how many litres of a material a certain weight represents. If instead you know the density and the volume of a container, multiplying the two gives the mass it will hold, which is how fuel tanks, water cisterns and grain silos are rated. Plugging your two known values into a density calculator removes the arithmetic and the risk of slipping a decimal place.

The recurring trap in these calculations is unit consistency. Mixing grams with cubic metres, or millilitres with kilograms, produces answers that are wrong by factors of a thousand or a million. Before you calculate, convert everything into a matching system: grams with cubic centimetres, or kilograms with cubic metres. Doing so guarantees that the density figure you arrive at lands in a sensible range, and that the mass or volume you work back to is one you can actually trust when something practical, like whether a load is safe to lift, depends on it.

Frequently asked questions

What is the formula for density?

Density equals mass divided by volume: ρ = m / V. Measure the mass in grams and the volume in cubic centimetres, divide, and the result is the density in g/cm³.

How do you calculate density?

Measure the object's mass on a scale, find its volume (by geometry for regular shapes or water displacement for irregular ones), then divide mass by volume. For example, 600 g ÷ 76 cm³ = 7.9 g/cm³. The density calculator does the division and unit handling for you.

How do you find mass from density and volume?

Rearrange the formula to mass = density × volume. If a liquid has a density of 0.8 g/cm³ and a volume of 250 cm³, the mass is 0.8 × 250 = 200 g.

How do you find volume from density and mass?

Use volume = mass ÷ density. For 500 g of a material with a density of 2.5 g/cm³, the volume is 500 ÷ 2.5 = 200 cm³.

What is the density of water?

Water has a density of about 1 g/cm³, which is the same as 1000 kg/m³ or roughly 62.4 lb/ft³. It is densest at 4 °C. Because water is exactly 1 g/cm³, any material with a higher number sinks and any lower number floats.

What units is density measured in?

Commonly g/cm³, kg/m³, or lb/ft³. They're interchangeable — 1 g/cm³ equals 1000 kg/m³ — as long as you keep your mass and volume units consistent with the density unit you want.