Density Calculator
Solve density, mass, or volume from the other two. Units are converted for you, so you can mix grams with liters or kilograms with cubic centimeters.
The formula
Density = mass ÷ volume
Density tells you how much matter is packed into a given space. It is what people mean when they say lead is "heavier" than aluminum. A tonne of lead and a tonne of aluminum weigh the same, but the lead takes up far less room.
Rearranged, the same relationship gives you the other two quantities:
| To find | Use |
|---|---|
| Density | d = m ÷ V |
| Mass | m = d × V |
| Volume | V = m ÷ d |
Units, and why g/cm³ equals g/mL
Solids and liquids are usually quoted in grams per cubic centimeter or grams per milliliter. These are the same thing, because one cubic centimeter is defined as exactly one milliliter.
Gases are far less dense, so they are normally given in grams per liter instead. Air at room temperature is about 1.2 g/L, which is roughly a thousand times less dense than water. Quoting a gas in g/cm³ gives an awkward number like 0.0012, which is why the unit changes.
In SI units density is kilograms per cubic meter. Water is 1000 kg/m³, which is the same as 1.00 g/cm³.
Worked example
A metal block has a mass of 135 g and measures 2.0 cm by 3.0 cm by 2.5 cm. What is its density, and what metal might it be?
Step 1. Find the volume.
V = 2.0 × 3.0 × 2.5 = 15 cm³
Step 2. Divide.
d = 135 g ÷ 15 cm³ = 9.0 g/cm³
Checking the table below, that is very close to copper at 8.96 g/cm³. Density is often used this way, as a quick identity test for an unknown material.
Measuring the volume of an odd shape
Regular blocks are easy. For an irregular object, use water displacement.
- Part fill a measuring cylinder with water and note the reading.
- Lower the object in gently so it is fully submerged.
- Note the new reading.
- The difference is the object's volume.
This only works if the object sinks and does not absorb water or dissolve. For something that floats, push it under with a thin pin and subtract the pin's own volume.
Densities worth knowing
| Substance | Density |
|---|---|
| Air at 20 °C | 0.0012 g/cm³ |
| Cork | 0.24 g/cm³ |
| Ethanol | 0.789 g/cm³ |
| Ice at 0 °C | 0.917 g/cm³ |
| Water at 4 °C | 1.000 g/cm³ |
| Aluminum | 2.70 g/cm³ |
| Iron | 7.87 g/cm³ |
| Copper | 8.96 g/cm³ |
| Lead | 11.3 g/cm³ |
| Mercury | 13.5 g/cm³ |
| Gold | 19.3 g/cm³ |
Why ice floats
Notice that ice is less dense than liquid water. Almost every other substance is denser as a solid, because cooling packs particles closer together.
Water is unusual because of hydrogen bonding. As it freezes, each molecule locks into an open hexagonal arrangement that holds its neighbors slightly further apart than they sit in the liquid. The result is that ice takes up about 9% more space than the water it came from, so it floats.
This has large consequences. Lakes freeze from the top down, and the floating ice layer insulates the water below, which is why fish survive winter. If ice sank, ponds would freeze solid from the bottom.
Temperature, and why water peaks at 4 °C
Density changes with temperature because volume does. Warm almost anything and it expands, so its density falls slightly. This is why a density value should always come with a temperature.
Water has a quirk here too. It reaches its maximum density at about 4 °C, not at its freezing point. Cool water below 4 °C and it starts to expand again as those open ice-like structures begin to form.
Density and specific gravity
Specific gravity, also called relative density, compares a substance with water:
Specific gravity = density of substance ÷ density of water
Because it is a ratio of two densities, the units cancel and it has none. Since water is 1.00 g/cm³, the number is numerically the same as a density in g/cm³, which is why the two get confused. Anything with a specific gravity below 1 floats on water.
Mistakes worth avoiding
- Mixing units. Grams with liters gives an answer a thousand times off. Convert first.
- Confusing density with mass. A large block of foam has more mass than a small ball bearing but far less density.
- Quoting density without a temperature. It matters, especially for gases.
- Measuring displacement with a floating object. It has to be fully submerged.
- Using cm³ for a gas. The number becomes unhelpfully small. Use g/L.
Frequently asked questions
What is the formula for density?
Density equals mass divided by volume. Rearranged, mass equals density times volume, and volume equals mass divided by density.
Is g/cm3 the same as g/mL?
Yes. One cubic centimeter is defined as exactly one milliliter, so the two units are interchangeable for solids and liquids.
What is the density of water?
Water is 1.000 g per cubic centimeter at 4 degrees Celsius, which is its densest point. At normal room temperature it is very slightly less, about 0.997.
Why does ice float on water?
Ice is about 9 percent less dense than liquid water. Hydrogen bonds lock the molecules into an open hexagonal structure as water freezes, holding them further apart than in the liquid, so the solid takes up more space and floats.
How do I find the volume of an irregular object?
Use water displacement. Note the water level in a measuring cylinder, lower the object in until it is fully submerged, then note the new level. The difference between the two readings is the object's volume.
What is the difference between density and specific gravity?
Density is mass per unit volume and carries units. Specific gravity is the ratio of a substance's density to that of water, so it has no units. The numbers match when density is given in grams per cubic centimeter.
Related terms
Next: convert temperatures on the Celsius to Fahrenheit calculator.