Density Calculator
Calculate density from mass and volume, or solve for mass or volume when density is known. Supports kg, g, lb, L, m³, gal and more, with instant unit conversion.
Density from Mass and Volume
Density Formula
Where:
- \(\rho\) — density of the substance (kg/m³)
- \(m\) — mass of the object or sample (kg)
- \(V\) — volume the object occupies (m³)
Density is the mass packed into each unit of volume. The first form finds density from mass and volume; the other two rearrange the same relationship to solve for mass or volume when density is known.
Density – Calculation Example
Example: a container holds 1 litre of a liquid with a mass of 1 kilogram. What is its density?
\[ V = 1\ \text{L} = 0.001\ \text{m}^3 \]
\[ \rho = \frac{m}{V} = \frac{1\ \text{kg}}{0.001\ \text{m}^3} = 1000\ \text{kg/m}^3 \]
Result: \(\rho = 1000\ \text{kg/m}^3\), which equals 1 g/cm³ — the same density as pure water at 4 °C.
How to use the calculator
- Choose what you want to Solve for: Density (ρ), Mass (m) or Volume (V). The fields for the two known quantities stay visible; the one being solved for is hidden.
- To find density, enter Mass (m) and Volume (V) with their units (kg, g, lb, oz for mass; m³, L, mL, cm³, ft³, in³, gal for volume).
- To find mass or volume instead, enter Density (ρ) in kg/m³, g/cm³, g/L, lb/ft³ or lb/in³ together with the other known quantity.
- Read the headline answer, then check the results table, which shows all three quantities converted into SI units and common alternatives, plus the formula with your numbers substituted.
- The note below the table compares the result with the density of water (1000 kg/m³) and tells you whether the substance would float or sink.
What is density?
Density describes how much matter is packed into a given amount of space: a brick and a foam block can have the same size, but the brick contains far more mass per cubic centimetre. Because density is an intrinsic property, it does not depend on how much of a substance you have — a drop of mercury and a litre of mercury have exactly the same density. This makes density a reliable way to identify substances, check the purity of materials, or convert between mass and volume in practical work.
The SI unit of density is kilograms per cubic metre (kg/m³), but you will often meet g/cm³ in chemistry (numerically the same as kg/L), g/L for gases, and lb/ft³ or lb/in³ in US engineering. Water is a useful anchor point: at 4 °C it has a density of 1000 kg/m³, or 1 g/cm³. Anything with a lower average density floats in water; anything denser sinks — which is why steel ships float (their hollow hulls give a low average density) while a solid steel bolt drops straight down.
The ratio of a substance's density to that of water is called specific gravity. The calculator shows this value automatically: a result of 2.5× the density of water means the substance has a specific gravity of 2.5 and will sink. Dividing density by 1000 also gives g/cm³ directly, since 1000 kg/m³ = 1 g/cm³.
Reference densities of common materials
| Material | Density (kg/m³) | Density (g/cm³) |
|---|---|---|
| Air (sea level, 15 °C) | 1.225 | 0.0012 |
| Ice (0 °C) | 917 | 0.917 |
| Water (4 °C) | 1000 | 1.000 |
| Seawater | 1025 | 1.025 |
| Aluminium | 2700 | 2.70 |
| Steel | 7850 | 7.85 |
| Copper | 8960 | 8.96 |
| Lead | 11340 | 11.34 |
| Gold | 19300 | 19.3 |
Assumptions, limitations and tips
- Uniform density: the calculator assumes the material is homogeneous. For composite objects, the result is an average density, which is what determines floating and sinking.
- Temperature matters: most materials expand when heated, so their density falls slightly. Values in the table above are typical room-temperature figures; water itself varies from 999.8 kg/m³ to about 958 kg/m³ between 0 °C and 100 °C.
- Watch the units: mixing units carelessly is the most common source of error. The calculator converts everything internally (1 lb = 0.45359237 kg, 1 ft³ ≈ 0.0283168 m³, 1 US gal = 3.785 L), so you can enter values exactly as measured.
- Porosity and voids: for granular materials like sand or gravel, the measured density includes air gaps. Multiply by the packing fraction or use the bulk density if that is what your application needs.
- Negative or zero inputs: mass and density cannot be negative, and volume or density must be greater than zero when they appear in a denominator — the calculator flags these cases rather than returning a nonsensical answer.
If you need related quantities, the Mass calculator and the Force calculator can extend these results — for example, multiplying mass by \(g = 9.81\ \text{m/s}^2\) gives the weight of your sample. For energy problems involving density, the Kinetic Energy and Potential Energy calculators take mass directly as an input.
Frequently Asked Questions
How do I calculate density by hand without a calculator?
Divide mass by volume after converting both to matching units. For example, 250 g of salt occupying 200 cm³ gives \( \rho = 250 / 200 = 1.25\ \text{g/cm}^3 \). If your units don't match (e.g. grams and litres), convert first: 1 L = 1000 cm³ and 1 kg = 1000 g. Always divide the mass unit by the volume unit to get a sensible density unit.
How do I find the density of an irregularly shaped object?
Use water displacement. Fill a graduated container with water, note the level, submerge the object completely, and read the rise — that difference is the object's volume. Then weigh the object dry and divide mass by the displaced volume. This works for waterproof solids like stones or coins. For absorbent or soluble materials, coat them or use a liquid such as sand or alcohol in which they won't dissolve.
How do I convert between kg/m³, g/cm³ and lb/ft³?
Move the decimal point rather than memorising formulas: since 1000 kg/m³ = 1 g/cm³, dividing kg/m³ by 1000 gives g/cm³, and multiplying g/cm³ by 1000 gives kg/m³. For imperial units, 1 lb/ft³ ≈ 16.018 kg/m³, so 62.4 lb/ft³ (water at room temperature) is about 1000 kg/m³. Doing both conversions by hand is a common source of rounding errors, which is why the calculator keeps full precision internally.
What is the difference between density and specific gravity?
Density has units (e.g. kg/m³), while specific gravity is a dimensionless ratio: a substance's density divided by the density of water (1000 kg/m³). A specific gravity of 2.5 simply means the substance is 2.5 times denser than water. Because water's density is 1000 kg/m³, specific gravity numerically equals density in g/cm³ — which is why the two are often confused in lab reports.
Is density the same as weight or heaviness?
No. Density is mass per unit volume, while weight is the gravitational force on that mass (mass times \( g = 9.81\ \text{m/s}^2 \)). A small gold coin is heavier than a large foam block in everyday language, but more precisely it is denser — it packs more mass into less space. Two objects of identical size differ in weight exactly in proportion to their densities.
Why does ice float if water and ice are the same substance?
When water freezes, its molecules arrange into an open crystal structure that takes up about 9% more space, so ice has a density of about 917 kg/m³ — roughly 8% less than liquid water (1000 kg/m³). Because it is less dense, ice floats with about 92% of its volume submerged. Most substances are denser as solids than as liquids, making water a notable exception.
What is a common mistake when calculating density?
Mixing unit systems is the top error — for example dividing pounds by litres and labelling the result kg/m³. Other frequent slips include using a container's total volume instead of the liquid volume inside it, forgetting that gases need temperature and pressure to be specified (air density varies with altitude), and confusing US gallons (3.785 L) with imperial gallons (4.546 L). Double-check units before trusting any result.