How the Mass Calculator Works
Mass is the amount of matter in an object. Density tells you how tightly that matter is packed. Volume is the space the object takes up. The three are linked by one simple rule, and the Mass Calculator uses it to find any one of them when you know the other two.
The formula
mass = density x volume volume = mass / density density = mass / volume
What you enter
- What to find: the mass, the volume or the density.
- The two values you know, each with its unit.
- A material (optional), such as water, steel or gold, which fills in a typical density for you.
Every value is changed to kilograms, cubic meters and kilograms per cubic meter before the calculation. The answer is then changed to the unit that you chose, so the units can be mixed freely.
Worked examples
| You know | Calculation | Result |
|---|---|---|
| Density 2.5 g/cm³, volume 20 cm³ | 2.5 x 20 | Mass 50 g |
| Steel (7.85 g/cm³), mass 1 kg | 1000 g / 7.85 | Volume 127.39 cm³ (0.1274 L) |
| Mass 100 lb, volume 1 ft³ | 100 / 1 | Density 100 lb/ft³ (1.602 g/cm³) |
| Aluminum (2.7 g/cm³), volume 20 cm³ | 2.7 x 20 | Mass 54 g |
- You know: Density 2.5 g/cm³, volume 20 cm³
Calculation: 2.5 x 20
Result: Mass 50 g - You know: Steel (7.85 g/cm³), mass 1 kg
Calculation: 1000 g / 7.85
Result: Volume 127.39 cm³ (0.1274 L) - You know: Mass 100 lb, volume 1 ft³
Calculation: 100 / 1
Result: Density 100 lb/ft³ (1.602 g/cm³) - You know: Aluminum (2.7 g/cm³), volume 20 cm³
Calculation: 2.7 x 20
Result: Mass 54 g
Chart: density of common materials in g/cm³
Each block is about 0.48 g/cm³. Blue floats in water, green is up to about 3 g/cm³, amber is a heavy metal, and red is a very heavy one.
Oak wood ██ 0.75 Ice ██ 0.917 Water ██ 1.00 Concrete █████ 2.40 Glass █████ 2.50 Aluminum ██████ 2.70 Steel ████████████████ 7.85 Copper ███████████████████ 8.96 Silver ██████████████████████ 10.49 Lead ███████████████████████ 11.34 Gold ████████████████████████████████████████ 19.32
Gold is about 25 times as dense as oak. A material is denser than water if its density is more than 1 g/cm³, and it sinks. If it is less, it floats. The calculator tells you which one it is.
Chart: the space taken by 1 kg
Because a dense material packs a lot of mass into a small space, the same 1 kg takes very different volumes. Each block is about 33 cm³.
Oak wood ████████████████████████████████████████ 1,333 cm³ Ice █████████████████████████████████ 1,091 cm³ Water ██████████████████████████████ 1,000 cm³ Aluminum ███████████ 370 cm³ Steel ████ 127 cm³ Lead ███ 88 cm³ Gold ██ 52 cm³
Density units
| Unit | Equal to |
|---|---|
| 1 g/cm³ (= 1 g/mL = 1 kg/L) | 1,000 kg/m³ |
| 1 lb/ft³ | 16.018 kg/m³ |
| 1 lb/in³ | 27,680 kg/m³ |
| 1 lb per US gallon | 119.83 kg/m³ |
Water at about 4 °C has a density of 1 g/cm³, which is 62.4 lb/ft³ or about 8.34 lb per US gallon.
Mass and weight
People often say weight when they mean mass. Mass is measured in kilograms or pounds and does not change from place to place. Weight is the force of gravity on the mass, and it is smaller on the Moon. This calculator finds the mass.
Tips
- Keep the units in mind. A density in g/cm³ and a volume in liters give a confusing answer if you forget the change. The calculator does the change for you.
- Hollow objects are lighter. The density of the material is for a solid piece. A hollow pipe or a foam has less mass for its outside volume.
- Use the volume of the material only. The volume of a box is not the volume of what is inside it.
- Temperature matters a little. Water is slightly lighter when it is hot.
What this calculator does not include
- Alloys and mixtures whose density you do not know. Use a density from a data sheet.
- The volume of a shape from its measurements. Work out the volume first, then enter it.
- Gases, whose density changes a lot with pressure and temperature.
- Weight as a force in newtons.
The densities of materials are typical values near room temperature. Real samples can differ a little, so use this tool as a guide.