Density is how much mass is packed into each unit of volume. A block of 540 g that takes up 200 cm³ has a density of 540 ÷ 200 = 2.7 g/cm³ (2,700 kg/m³): heavier than water, so it sinks. The calculator solves the formula for whichever value you are missing, takes mass and volume in metric or US units, and gives the density in four units and compared with water.
Rearranging ρ = m ÷ V
| You want | Formula | Example |
|---|---|---|
| Density | ρ = m ÷ V | 540 g ÷ 200 cm³ = 2.7 g/cm³ |
| Mass | m = ρ × V | 7.87 g/cm³ × 50 cm³ = 393.5 g of iron |
| Volume | V = m ÷ ρ | 1,000 g ÷ 19.32 g/cm³ = 51.8 cm³ of gold |
A kilogram of gold fits in a cube 3.7 cm on a side; a kilogram of water fills a liter carton.
Densities to compare with
| Substance | g/cm³ | kg/m³ | Floats on water? |
|---|---|---|---|
| Air (20 °C, sea level) | 0.0012 | 1.2 | – |
| Ethanol | 0.789 | 789 | yes |
| Ice | 0.917 | 917 | yes |
| Water (20 °C) | 0.998 | 998 | – |
| Aluminum | 2.70 | 2,700 | no |
| Iron | 7.87 | 7,870 | no |
| Copper | 8.96 | 8,960 | no |
| Lead | 11.3 | 11,300 | no |
| Gold | 19.3 | 19,300 | no |
Element densities as listed by the Royal Society of Chemistry; water from standard tables. Real objects are often less dense than the pure metal, because alloys and hollow parts change the average.
Measuring density at home or in class
- Weigh the object on a kitchen or lab scale.
- Fill a measuring jug part way, note the level, lower the object in and note the new level: the difference is its volume in mL, which equals cm³.
- Divide the mass by the volume.
For a liquid, weigh an empty jug, fill it to a known volume and weigh again. Temperature matters for liquids and a lot for gases, so a precise result names the temperature.
The calculator does its arithmetic on your device and works offline once zet4u is saved, so it is ready in a lab with no Wi-Fi.
Frequently asked questions
What is the formula for density?
Density = mass ÷ volume (ρ = m ÷ V). A 540 g block that takes up 200 cm³ has a density of 2.7 g/cm³, the density of aluminum.
How do I find the volume of an odd-shaped object?
Lower it into water in a measuring jug and read how much the level rises: that rise is its volume. Then weigh it and divide.
What is the density of water?
About 1 g/cm³: 0.9998 at 0 °C, 0.9982 at 20 °C and 0.9584 at 100 °C. Ice is lighter, about 0.917 g/cm³, which is why it floats.
How do I convert g/cm³ to kg/m³?
Multiply by 1,000. 2.7 g/cm³ = 2,700 kg/m³. In US units, 1 g/cm³ = 62.43 lb/ft³ = 8.345 lb per US gallon.
Will it float?
An object floats in water if its average density is below the water's. A steel ship floats because its hull, full of air, has an average density well under 1 g/cm³.
Sources
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