How the Density Calculator Works
Density tells you how much matter is packed into a space. A lump of lead and a lump of wood of the same size have very different masses, because lead is much denser. Density is one of the properties that is used to tell materials apart, to know if something will float, and to check a purchase, from a piece of metal to a jar of oil.
The formula
density = mass / volume
Mass is how much matter there is (in grams, kilograms, pounds or ounces), and volume is the space it takes up (in cubic centimeters, liters, cubic feet and so on). The calculator changes every unit to kilograms and cubic meters inside, and then shows the density in the unit that you choose.
What you enter
- The mass of the object, and its unit.
- The volume, in one of two ways: type it in directly, or let the calculator work it out from the size of a box, a cylinder or a sphere.
- The unit that you want for the density.
Volume from the size
| Shape | Volume |
|---|---|
| Box | length x width x height |
| Cylinder | 3.1416 x (diameter / 2) x (diameter / 2) x height |
| Sphere | 4/3 x 3.1416 x (diameter / 2) x (diameter / 2) x (diameter / 2) |
Worked examples
| You know | Calculation | Density |
|---|---|---|
| 50 g in 10 cm³ | 50 / 10 | 5 g/cm³ (5,000 kg/m³) |
| 1 kg in a box of 10 x 10 x 10 cm | 1,000 g / 1,000 cm³ | 1 g/cm³, the same as water |
| 540 g in a cylinder 4 cm across and 15 cm high | 540 / 188.5 cm³ | 2.86 g/cm³, close to aluminum |
| 4.19 kg in a sphere 10 cm across | 4,190 / 523.6 cm³ | 8.0 g/cm³, close to iron |
- You know: 50 g in 10 cm³
Calculation: 50 / 10
Density: 5 g/cm³ (5,000 kg/m³) - You know: 1 kg in a box of 10 x 10 x 10 cm
Calculation: 1,000 g / 1,000 cm³
Density: 1 g/cm³, the same as water - You know: 540 g in a cylinder 4 cm across and 15 cm high
Calculation: 540 / 188.5 cm³
Density: 2.86 g/cm³, close to aluminum - You know: 4.19 kg in a sphere 10 cm across
Calculation: 4,190 / 523.6 cm³
Density: 8.0 g/cm³, close to iron
Chart: the density of common materials
Each block is about 0.54 g/cm³. Blue floats in water, green is up to 3 g/cm³, amber is a heavy metal, and red is a very heavy one.
Cork █ 0.24 g/cm³ Pine wood █ 0.5 g/cm³ Water ██ 1 g/cm³ Aluminum █████ 2.7 g/cm³ Iron ███████████████ 7.87 g/cm³ Copper █████████████████ 8.96 g/cm³ Lead █████████████████████ 11.34 g/cm³ Gold ████████████████████████████████████ 19.32 g/cm³ Platinum ████████████████████████████████████████ 21.45 g/cm³
| Material | g/cm³ | kg/m³ | lb/ft³ |
|---|---|---|---|
| Cork | 0.24 | 240 | 15.0 |
| Pine wood | 0.5 | 500 | 31.2 |
| Water | 1 | 1,000 | 62.4 |
| Aluminum | 2.7 | 2,700 | 168.6 |
| Iron | 7.87 | 7,870 | 491.3 |
| Copper | 8.96 | 8,960 | 559.4 |
| Lead | 11.34 | 11,340 | 707.9 |
| Gold | 19.32 | 19,320 | 1206.1 |
| Platinum | 21.45 | 21,450 | 1339.1 |
These are typical values near room temperature. The exact density changes a little with the temperature, the mix of a metal (its alloy) and the type of wood.
Will it float?
An object floats in a liquid if it is less dense than the liquid. Fresh water has a density of 1 g/cm³, so anything with a density below 1 floats in it, and anything above 1 sinks. The calculator tells you which one it is. A floating object sinks into the water until the weight of the water that it moves is equal to its own weight, so the share of its volume that is below the surface is equal to its density in g/cm³. Each block of the chart is 2.5% of the object.
Cork ██████████ 24% under water Pine wood ████████████████████ 50% under water Oak wood ██████████████████████████████ 75% under water Ice █████████████████████████████████████ 91.7% under water
This is why an iceberg has most of its bulk under the water, and why steel ships float: their shape holds a lot of air, so the whole ship is less dense than water.
Which material is it?
The calculator compares your density with a list of common materials, and names the one that is closest, if it is within 25%. The chart draws your density next to the three closest ones and water, on a log scale, where each step to the right is the same ratio. Density alone does not prove a material, so use it as a clue:
- Two different materials can have almost the same density, such as steel and iron.
- An alloy or a plated object has a density between those of its metals.
- A hollow object or one with holes has a lower density than its material.
Units of density
| Unit | Equal to |
|---|---|
| 1 g/cm³ (= 1 g/mL = 1 kg/L) | 1,000 kg/m³ |
| 1 lb/ft³ | 16.02 kg/m³ |
| 1 lb/in³ | 27,680 kg/m³ |
| 1 lb per US gallon | 119.8 kg/m³ |
Tips
- Measure the volume with care. For an odd shape, put the object in water and measure how much the level rises. The rise is the volume.
- Use the same system. The calculator changes units for you, so a mass in pounds and a volume in liters are fine.
- Weigh dry objects. A wet or porous object weighs more than it should.
What this calculator does not include
- The change of density with the temperature and the pressure, which is large for gases.
- Objects of odd shapes. Enter their volume yourself.
- A test that proves what a material is.
This tool gives an estimate for study and general use. Densities of materials are typical values.