Audited —·Last updated 27 Jul 2026·8 citations·Tier 1·0 uses

Density Calculator

Free density calculator — solve ρ = m / V for density, mass, or volume. SI units, worked examples, and reference tables for water, gold, aluminium, and more.

Density Calculator

Solve for
Mass of the object in kilograms. For grams divide by 1000 (e.g. 250 g = 0.25 kg); for tonnes multiply by 1000. Leave blank when solving for mass.
kg
Volume of the object in cubic metres. 1 litre = 0.001 m³; 1 cm³ = 0.000001 m³. Leave blank when solving for volume.
m³
Density in kilograms per cubic metre. Water at 4 °C = 1000 kg/m³; aluminium ≈ 2700; gold ≈ 19320. Leave blank when solving for density.
kg/m³
Density
1,000
Mass per unit volume ρ, computed from ρ = m / V when solving for density and echoed back when solving for mass or volume. Reported in SI base units of kilograms per cubic metre (kg/m³).
Mass
1 kg
Volume
0.001 m³

Background.

This density calculator solves the defining equation of bulk-matter physics — ρ = m / V — for whichever of the three quantities you do not already know. Pick a 'solve for' mode, enter the two known values in SI units (kilograms for mass, cubic metres for volume, kilograms per cubic metre for density), and the tool returns the missing quantity together with the full self-consistent set. The reason density matters far beyond an introductory physics homework question is that it is the single number that decides whether a steel hull floats, whether a balloon rises, whether a sample of gold is genuine or counterfeit, whether a stratified atmosphere holds together or convects, whether a sealed concrete tanker can be lifted by a forklift, and whether the manifest weight a logistics firm pays for a container of catalyst pellets matches the volume it actually occupies. Density is the bridge between the two quantities humans measure most easily — how heavy something is and how much space it takes up — and once you know it for a given material you can immediately solve countless downstream problems: buoyant force in a fluid (Archimedes' principle), pressure at depth (the hydrostatic equation), terminal velocity in air (Stokes drag), bulk modulus from sound-speed measurements, and the loading capacity of any structural member.

The concept is ancient — Archimedes' famous 'Eureka' moment in the bath was a density measurement, performed to determine whether King Hieron II's crown was pure gold by comparing its mass-to-volume ratio against a known gold reference. The modern SI definition expresses density in kilograms per cubic metre (kg/m³), but several other units survive in working laboratories and industries: grams per cubic centimetre (g/cm³) in chemistry and metallurgy (numerically equal to a thousand times the kg/m³ value, so water is 1.000 g/cm³ or 1000 kg/m³), pounds per cubic foot in US construction, and specific gravity — the dimensionless ratio of a substance's density to that of water at 4 °C — across petrochemicals and geology.

Density is also temperature- and pressure-dependent. Water reaches its maximum density (999.972 kg/m³) at 3.98 °C, expands when frozen (ice is 917 kg/m³, which is why icebergs float and why water pipes burst in winter), and falls smoothly to about 958 kg/m³ at its 100 °C boiling point. Gases are far more sensitive — air at 1 atm and 15 °C is 1.225 kg/m³ but at the same pressure and 100 °C only 0.946 kg/m³, a 23% drop that drives every hot-air balloon and chimney updraft on the planet.

Below the widget you will find reference density tables for common solids, liquids, and gases at standard conditions; the derivation of ρ = m / V from the SI definitions of the kilogram and the metre; worked examples covering the gold-crown problem, sea-water displacement for ship loading, hot-air-balloon lift, and the conversion arithmetic between g/cm³, kg/m³, and specific gravity; an honest treatment of the difference between bulk density, true (skeletal) density, and apparent density for porous materials like soils, powders, and foams; and a discussion of where the simple ρ = m / V model breaks down — anisotropic composites, multi-phase mixtures, and the relativistic regime where mass itself becomes frame-dependent. The calculator is a thin wrapper around a pure-function solver registered at density.solve, exercised by the same unit-test suite used elsewhere in the Quanta engineering toolset, so the values you read here are bit-for-bit identical to the ones produced upstream.

What is density calculator?

Density (symbol ρ, Greek lowercase rho) is the mass of a substance per unit volume. It is an intensive property, meaning it does not depend on how much of the material you have: a 1 g grain of salt and a 1 kg sack of salt share the same density (about 2160 kg/m³), even though their masses differ by three orders of magnitude. This makes density a fingerprint of the material itself — useful for identification, quality control, and material substitution. Mathematically, ρ = m / V where m is mass and V is volume. The SI unit of density is the kilogram per cubic metre (kg/m³). One litre of pure water at 4 °C has a mass of very nearly 1 kg, so water's density is 1000 kg/m³ — a convenient round number that anchors most everyday density intuition. Densities span an enormous range: interstellar gas is around 10⁻²¹ kg/m³, air is about 1.2 kg/m³, liquid water is 1000 kg/m³, structural steel is around 7850 kg/m³, gold is 19320 kg/m³, the centre of the Sun reaches about 1.5 × 10⁵ kg/m³, atomic nuclei are around 2 × 10¹⁷ kg/m³, and a neutron star is comparable to nuclear density. For solids and liquids, three subtly different densities are used in industry. True density (or skeletal density) is the density of the material with all internal voids excluded — measured by helium pycnometry. Bulk density is the mass of a granular or porous sample divided by the total volume including internal pores and the space between grains — what you measure by weighing a known volume of soil or powder. Apparent density sits between the two, including closed pores but excluding open ones. For homogeneous, non-porous solids and pure liquids these are all the same number; for soils, coffee grounds, foams, and rock cores they can differ by 30% or more, and confusing them is one of the most common mistakes in soil mechanics, pharmaceutics, and food engineering.

How to use this calculator.

  1. Pick the quantity you want the calculator to compute from the 'Solve for' menu — density, mass, or volume.
  2. Enter the two known quantities in SI units. Mass goes in kilograms, volume in cubic metres, density in kilograms per cubic metre.
  3. Convert before entering if needed: 1 litre = 0.001 m³, 1 cm³ = 10⁻⁶ m³, 1 g = 0.001 kg. Multiply g/cm³ by 1000 to get kg/m³ (water is 1.0 g/cm³ = 1000 kg/m³).
  4. Leave the field for the unknown quantity blank — the calculator ignores it and computes the missing value from the other two.
  5. Read the headline density value (kg/m³) and cross-check it against the reference table below to identify or verify the material.
  6. For a buoyancy check, compare the calculated density against the fluid density: 1000 kg/m³ for fresh water, 1025 kg/m³ for sea water, 1.225 kg/m³ for air at sea level. If the object density is lower, it floats; if higher, it sinks.

The formula.

ρ = m ⁄ V
ρ · densitym · massV · volume

The core relationship and its three algebraic forms are:

ρ = m / V (definition of density) m = ρ × V (solve for mass) V = m / ρ (solve for volume)

Given any two of {ρ, m, V}, the third follows immediately. The calculator implements all three rearrangements and routes to the correct one based on your 'solve for' selection. Three conventions are baked in. First, all quantities are taken as positive scalars — densities are bulk averages and have no signed direction. Second, the calculator refuses to divide by zero: if you ask for density with volume = 0, or for volume with density = 0, it raises an InvalidInputError rather than silently returning Infinity. Third, the units must be consistent. The widget assumes SI (kg, m³, kg/m³) but the algebra itself is unit-agnostic — feed it grams and cubic centimetres and you will get g/cm³ out the other side, and feed it pounds and cubic feet and you will get lb/ft³. The conversion arithmetic is straightforward but worth memorising: 1 g/cm³ = 1000 kg/m³, 1 lb/ft³ ≈ 16.0185 kg/m³, and specific gravity (relative to water at 4 °C) is the kg/m³ value divided by 1000. For variable-density problems — atmospheric layers, salinity-stratified ocean, the interior of a planet — ρ becomes a field ρ(x, y, z, T, p) and the simple ρ = m / V becomes a volume integral m = ∫∫∫ ρ dV. The calculator does not perform that integration; for stratified problems, feed it the average density of the layer you care about, or treat each layer separately and add the masses.

A worked example.

Example

The Archimedes problem, retold. A jeweller hands you a small crown said to be pure gold. You put it on a kitchen scale and read 500 g, so mass = 0.5 kg. You lower it into a graduated cylinder of water and the water level rises by 25.9 mL, so the displaced volume is 25.9 cm³ = 25.9 × 10⁻⁶ m³ = 0.0000259 m³. Enter solveFor = 'density', mass = 0.5, volume = 0.0000259. The calculator returns ρ = 0.5 / 0.0000259 ≈ 19305 kg/m³, which rounds to 19.3 g/cm³ — within rounding of pure gold's accepted density of 19320 kg/m³ at 20 °C. The crown checks out. Run the same experiment on a crown that comes back at 15000 kg/m³ and you have evidence of dilution — silver (10490 kg/m³), copper (8960 kg/m³), or lead (11340 kg/m³) alloyed in. Archimedes used exactly this trick on King Hieron II's crown in Syracuse around 250 BCE, with a balance scale and a brimming vessel rather than a graduated cylinder, but the maths is identical. Note the precision required: a 1% impurity reading would need volume measurements accurate to about 0.25 mL on a 25 mL sample, which is at the limit of a teaching-grade graduated cylinder but routine for a calibrated burette or modern hydrostatic balance.

volume0
mass0.5
solve Fordensity

Frequently asked questions.

What is the formula for density?
Density equals mass divided by volume, written ρ = m / V, where ρ is density (typically in kg/m³ or g/cm³), m is mass (kg or g), and V is volume (m³ or cm³). Rearranging gives m = ρ × V when you know the density and volume and want the mass, and V = m / ρ when you know the mass and density and want the volume. All three forms are algebraically identical — you pick whichever isolates your unknown.
What are the units of density?
The SI unit is kilograms per cubic metre (kg/m³). In chemistry and metallurgy you will more often see grams per cubic centimetre (g/cm³), which is exactly 1000 times smaller — so water is 1.000 g/cm³ = 1000 kg/m³. US engineering uses pounds per cubic foot (lb/ft³, where 1 lb/ft³ ≈ 16.02 kg/m³) and pounds per gallon. Specific gravity is the dimensionless ratio of a substance's density to that of water at 4 °C, so steel at 7850 kg/m³ has specific gravity 7.85.
What is the density of water?
Pure water at 4 °C and 1 atm has a density of 999.972 kg/m³, conventionally rounded to 1000 kg/m³. Density falls slightly as water warms (997.0 kg/m³ at 25 °C, 958.4 kg/m³ at 100 °C) and rises slightly as it cools — except below 4 °C, where it begins to drop again because hydrogen bonds force the molecules into an increasingly open lattice. Ice at 0 °C is 917 kg/m³, about 9% less dense than the liquid, which is why ice floats and why winter pipe-burst happens. Sea water averages 1025 kg/m³ thanks to its 3.5% dissolved-salt content.
Why does ice float on water?
Because solid water is less dense than liquid water — an anomaly shared by very few substances. As liquid water cools below 4 °C, its molecules begin to settle into the open hexagonal arrangement of the ice lattice, in which every oxygen atom is hydrogen-bonded to four neighbours at the corners of a tetrahedron. That arrangement is geometrically less efficient than the disordered packing of the liquid, so the same number of molecules occupies more volume. Ice is 917 kg/m³ versus liquid water's 1000 kg/m³, so by Archimedes' principle about 8.3% of an iceberg's volume rides above the waterline (the famous 'tip of the iceberg') and 91.7% sits below.
How do I convert g/cm³ to kg/m³?
Multiply by 1000. The conversion is exact because 1 g/cm³ = (10⁻³ kg) / (10⁻⁶ m³) = 10³ kg/m³. So water at 1.00 g/cm³ is 1000 kg/m³, aluminium at 2.70 g/cm³ is 2700 kg/m³, gold at 19.32 g/cm³ is 19320 kg/m³, and air at 1.225 × 10⁻³ g/cm³ is 1.225 kg/m³. Going the other way (kg/m³ to g/cm³) you divide by 1000. The two units are interchangeable for any density calculation as long as you stay consistent within a single problem.
How do I measure the density of an irregular object?
Use water displacement, the same method Archimedes used. Weigh the object on a calibrated scale to get its mass. Then submerge it fully in a graduated cylinder, beaker, or overflow can filled with water and measure the volume of water it displaces — for a graduated cylinder, that is the rise in water level; for an overflow can, it is the volume of water that pours into a collection vessel. Density is mass divided by displaced volume. The object must sink completely (push it under with a thin wire if it tries to float), must not absorb water (or you will under-read the volume), and must not dissolve. For porous materials you need helium pycnometry instead of water; for shapes that fit a known geometric formula (cylinder, cube, sphere) you can skip displacement and compute the volume directly.
What is the difference between density and specific gravity?
Density is an absolute quantity with units (kg/m³, g/cm³, lb/ft³). Specific gravity is a dimensionless ratio: the density of a substance divided by the density of a reference, usually water at 4 °C (1000 kg/m³). So specific gravity numerically equals the density expressed in g/cm³ — gold (19.32 g/cm³) has SG 19.32, ethanol (0.789 g/cm³) has SG 0.789. The unitless form is convenient because it survives any consistent unit system and because the rule of thumb 'SG > 1 means it sinks in water, SG < 1 means it floats' falls out immediately. Petroleum, brewing, and battery industries quote SG almost exclusively.
How does density change with temperature and pressure?
Liquids and solids change density modestly with temperature (typically a few parts per thousand per degree Celsius) because of thermal expansion — heat the material, the molecules vibrate more energetically, and the average inter-particle spacing grows. The effect is captured by the volumetric thermal expansion coefficient β (per kelvin): ρ(T) ≈ ρ₀ × (1 − β × ΔT). Liquids and solids are almost incompressible, so pressure has only a tiny effect on their density (water's density rises about 4.6% from atmospheric to the deepest ocean trench at 1100 atm). Gases are the opposite: they expand and compress almost without limit, and their density is dictated by the ideal-gas law, ρ = pM / (RT), where p is pressure, M is molar mass, R is the universal gas constant, and T is absolute temperature. Air at sea level is about 1.225 kg/m³ at 15 °C; at the cruise altitude of 11 km it is about 0.36 kg/m³ — roughly a third — which is why jet engines need to inhale much more air at altitude to deliver the same thrust.
What is the densest naturally occurring element?
Osmium, at 22590 kg/m³ at 20 °C (about 22.59 g/cm³), narrowly beating iridium at 22560 kg/m³. The two metals were neck-and-neck for decades until X-ray crystallography on highly purified samples settled the question in osmium's favour in the 1990s. Both are about 13% denser than lead and roughly 17% denser than gold. They sit at the bottom of group 8 and 9 of the periodic table, where the combination of small atomic radius (lanthanide contraction) and large atomic mass produces an unusually compact crystal lattice. Higher densities exist among synthetic transuranic elements — hassium is predicted to top 40000 kg/m³ — but only microscopic quantities have ever been produced.
Why does my calculated density not match the textbook value?
Five common causes. First, units — verify you have kg and m³ (or g and cm³) consistently; mixing kg with cm³ will give a value 10⁶ off. Second, temperature — textbook tables typically quote 20 °C or 25 °C, so a hot or cold sample will read 1–5% different for liquids and far more for gases. Third, porosity — bulk density of a powder or porous solid can be 30–50% below the true (skeletal) density of the parent material; if you weighed sand in a cup, you measured bulk density, not the density of the quartz grains themselves. Fourth, impurity or alloying — commercial aluminium alloys span 2640 to 2800 kg/m³ depending on copper, silicon, and magnesium content. Fifth, measurement error — a 1 mL miscount on a 10 mL graduated cylinder is a 10% volume error and therefore a 10% density error; for accuracy below 1% you need a calibrated pycnometer or hydrostatic balance, not a kitchen jug.

References& sources.

  1. [1]Bureau International des Poids et Mesures (BIPM) (2019). The International System of Units (SI), 9th edition. Definitions of the kilogram (in terms of the Planck constant h) and the metre (in terms of the speed of light c), which together fix the SI unit of density as kg/m³.
  2. [2]Newell, D. B. & Tiesinga, E., eds. (2019). The International System of Units (SI). NIST Special Publication 330, 2019 Edition. National Institute of Standards and Technology, Gaithersburg, MD. The US edition of the SI brochure, covering base unit definitions and derived quantities including density.
  3. [3]Rumble, J. R., ed. (2023). CRC Handbook of Chemistry and Physics, 104th Edition. CRC Press, Boca Raton. The standard reference for tabulated densities of pure elements, common alloys, organic and inorganic compounds, and gases at standard temperature and pressure.
  4. [4]Tanaka, M., Girard, G., Davis, R., Peuto, A. & Bignell, N. (2001). Recommended table for the density of water between 0 °C and 40 °C based on recent experimental reports. Metrologia, 38(4), 301–309. Peer-reviewed paper underlying the modern reference table for water density, including the 999.972 kg/m³ maximum at 3.98 °C used by national metrology institutes.
  5. [5]Serway, R. A. & Jewett, J. W. (2018). Physics for Scientists and Engineers with Modern Physics, 10th ed., Cengage Learning. Chapter 1 §1.1 'Standards of Length, Mass, and Time' and Chapter 14 'Fluid Mechanics', covering the definition of density, Archimedes' principle, and the buoyancy applications used throughout this calculator.
  6. [6]U.S. Geological Survey (USGS). Densities of Common Rocks and Minerals — Mineral Resources Program reference data. Tabulated bulk and grain densities for sedimentary, igneous, and metamorphic rock types used in seismic interpretation and ore-body estimation.
  7. [7]Picard, A., Davis, R. S., Gläser, M. & Fujii, K. (2008). Revised formula for the density of moist air (CIPM-2007). Metrologia, 45(2), 149–155. The CIPM-adopted equation for the density of humid air as a function of temperature, pressure, humidity, and CO₂ content — the basis for the 1.225 kg/m³ ISA sea-level air-density value used in aerospace and meteorology.
  8. [8]Heath, T. L., trans. (1897). The Works of Archimedes, edited in modern notation with introductory chapters. Cambridge University Press. Includes 'On Floating Bodies' Books I and II, the foundational text on buoyancy and the principle behind the gold-crown density measurement.
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