Density Calculator
A density calculator divides mass by volume: ρ = m / V. A 27 g block that takes up 10 cm³ has a density of 27 ÷ 10 = 2.7 g/cm³ (2,700 kg/m³), close to aluminum. That is more than water’s 0.998 g/cm³, so it sinks. Rearranged, m = ρ × V and V = m / ρ.
Show steps
- Density: ρ = m / V = 27.00 g ÷ 10.00 cm³ = 2.700 g/cm³.
- Compare with water: 2.700 > 0.99821 g/cm³, so it sinks in fresh water at 20 °C.
How to use the density calculator
- Choose what to find: Density, Mass or Volume. The Shipping tab gives freight density in pounds per cubic foot.
- For density, enter the mass and get the volume one of three ways: type it, measure a rectangular block (length × width × height), or read the water level before and after dropping the object into a graduated cylinder.
- For mass or volume, pick a material from the list to fill in its density, or type your own value. Every field has its own unit, and you choose the unit of the answer.
The result shows the answer in several units, specific gravity, a float-or-sink check against fresh water and seawater, the closest materials in the reference table, and the steps with units shown.
Density formula
Density is mass per unit volume:
- ρ = m / V (density)
- m = ρ × V (mass)
- V = m / ρ (volume)
ρ (the Greek letter rho) is density, m is mass and V is volume. The SI unit is kg/m³; chemistry classes use g/cm³, which is the same as g/mL. Specific gravity is density divided by the density of water at 4 °C (0.99997 g/cm³), so it has no unit and is almost equal to the density in g/cm³.
Density unit conversions
| 1 g/cm³ equals | Value |
|---|---|
| g/mL | 1 |
| kg/m³ (or g/L) | 1,000 |
| kg/L | 1 |
| lb/ft³ | 62.43 |
| lb/gal (US) | 8.345 |
The pound and inch are exact by definition (1 lb = 0.45359237 kg, 1 in = 2.54 cm), and a US gallon is exactly 231 in³, so these factors follow from NIST’s SI guide.
Worked examples
Density of a block
A metal block measures 5 cm × 4 cm × 5 cm and has a mass of 270 g. V = 5 × 4 × 5 = 100 cm³, so ρ = 270 g ÷ 100 cm³ = 2.70 g/cm³. That matches aluminum (2.699 g/cm³).
Density of a rock by water displacement
A rock has a mass of 84 g. The water in a graduated cylinder rises from 40 mL to 71 mL when the rock is dropped in, so V = 71 − 40 = 31 mL = 31 cm³. ρ = 84 ÷ 31 = 2.71 g/cm³. This method works for any shape that sinks and does not absorb water.
Mass from density
Mercury has a density of 13.55 g/cm³. One liter is 1,000 cm³, so m = 13.55 × 1,000 = 13,550 g = 13.55 kg, about 13.6 times the mass of a liter of water.
Volume from density
How big is 1 kg of gold (19.32 g/cm³)? V = 1,000 g ÷ 19.32 g/cm³ = 51.76 cm³, a cube only about 3.73 cm on each side.
Freight density
A pallet measures 48 × 40 × 36 inches and weighs 600 lb. Volume = 69,120 in³ ÷ 1,728 = 40 ft³, so density = 600 ÷ 40 = 15 lb/ft³. Carriers use this number, along with handling and other factors, to set the freight class.
Will it float or sink?
An object floats in a liquid when its average density is lower than the liquid’s. Fresh water at 20 °C is 0.99821 g/cm³; seawater with 35 g/kg of salt at the same temperature is about 1.0248 g/cm³. A floating object sits with the fraction ρobject / ρliquid below the surface. For ice in seawater that is 0.9167 ÷ 1.0248 ≈ 0.89, which is why most of an iceberg is hidden. A steel ship floats because its average density, steel plus the air inside the hull, is less than water’s.
Densities of common materials
| Material | Density (g/cm³) | Source |
|---|---|---|
| Air, dry, near sea level | 0.001205 | NIST table 2 |
| Polyethylene | 0.93 | NIST table 2 |
| Ice, 0 °C | 0.9167 | IAPWS R10-06 |
| Water, 4 °C | 0.99997 | NIST WebBook |
| Water, 20 °C | 0.99821 | NIST WebBook |
| Seawater, 20 °C, 35 g/kg | 1.0248 | TEOS-10 |
| Polystyrene | 1.06 | NIST table 2 |
| Acrylic (PMMA) | 1.19 | NIST table 2 |
| Pyrex glass | 2.23 | NIST table 2 |
| Concrete, ordinary | 2.30 | NIST table 2 |
| Aluminum | 2.699 | NIST table 1 |
| Iron | 7.874 | NIST table 1 |
| Copper | 8.96 | NIST table 1 |
| Silver | 10.50 | NIST table 1 |
| Lead | 11.35 | NIST table 1 |
| Mercury | 13.55 | NIST table 1 |
| Gold | 19.32 | NIST table 1 |
| Platinum | 21.45 | NIST table 1 |
The calculator’s list has 29 materials, including titanium, zinc, tin, nickel, tungsten, PVC, PET and Teflon from the same NIST tables. NIST notes that some of its values are nominal, and real samples vary with purity, temperature and porosity, so treat them as typical values. Wood, soil and food vary too much for a single number; measure your own sample.
Common mistakes
- Mixing units. Grams with cubic meters gives a tiny, meaningless number. Convert first, or let the calculator do it.
- Using the container’s volume. For a liquid, measure only the liquid. For displacement, subtract the starting water level.
- Confusing weight and mass. In everyday use a weight in pounds or kilograms is the mass; in physics, weight is a force in newtons.
- Ignoring temperature. Most liquids and gases expand when warmed, so their density drops. Water is densest near 4 °C.
Sources
- NIST, X-Ray Mass Attenuation Coefficients, Table 1 (element densities) and Table 2 (compounds and mixtures), checked November 2026.
- NIST Chemistry WebBook, Thermophysical Properties of Fluid Systems: water at 0.101325 MPa (IAPWS-95), checked November 2026.
- IAPWS, R10-06(2009) equation of state for ice Ih: density at 0 °C and 1 atm computed from it, checked November 2026.
- IOC, SCOR and IAPSO, TEOS-10 seawater standard: density at 20 °C, 35.165 g/kg, 1 atm computed with the GSW toolbox, checked November 2026.
- NIST, Special Publication 811, Appendix B conversion factors, checked November 2026.
Density practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
Volume = 42 − 30 = 12 mL, so ρ = 96 ÷ 12 = 8 g/mL. Dividing by 30 or 42 is the common mistake.
The submerged fraction equals ρ_object / ρ_liquid = 0.917 / 1.00 ≈ 0.92.
Quiz complete
Frequently asked questions
How do you calculate density?
Measure the mass and the volume, then divide mass by volume. 50 g in 20 mL is 50 ÷ 20 = 2.5 g/mL. Keep the units: the answer is in mass units per volume unit.
What is the density of water?
About 1 g/cm³. More precisely 0.99997 g/cm³ at 4 °C, 0.99821 g/cm³ at 20 °C and 0.99705 g/cm³ at 25 °C, which is 997 to 1,000 kg/m³.
How do you find the density of an irregular object?
Weigh it, then find its volume by water displacement: note the water level in a graduated cylinder, drop the object in, and subtract. Divide the mass by that volume. Choose Displacement in the calculator.
Is density the same as specific gravity?
Not quite. Specific gravity is density divided by the density of water, so it has no unit. Numerically it is almost the same as the density in g/cm³: aluminum is 2.699 g/cm³ and has a specific gravity of 2.699.
Why does density not depend on the size of the sample?
Density is an intensive property: doubling the amount doubles both mass and volume, so their ratio stays the same. A paper clip and a steel beam made of the same steel have the same density.
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