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Density Calculator
Use this free density calculator to solve for density, mass, or volume — whichever one you do not know. Enter any two of the three values, pick your units, and it works out the third, in g/cm³, kg/m³, and lb/ft³ at once. Material presets for water, steel, aluminum, gold, oak, and air fill in the density for you, so you can find the weight of a block, the volume of a liquid, or whether an object will float.
How it works
Density is how much mass is packed into a given volume, and the formula is a single division: density equals mass divided by volume. A block with a mass of 500 grams and a volume of 250 cubic centimetres has a density of 500 divided by 250, or 2 grams per cubic centimetre. The same triangle of three quantities works in every direction: if you know the density and the volume, the mass is density times volume, and if you know the mass and the density, the volume is mass divided by density. This calculator solves for whichever of the three you leave unknown, so you never have to rearrange the formula yourself.
Units are where density calculations usually go wrong, because the same material has very different-looking numbers in different unit systems. Water is 1 g/cm³, which is the same as 1,000 kg/m³ and 62.4 lb/ft³. The conversions are fixed: 1 g/cm³ equals 1,000 kg/m³, and 1 g/cm³ equals 62.43 lb/ft³. This calculator converts your inputs to grams and cubic centimetres first, does the division, and then shows the answer in all three density units, so you can copy the one your textbook, datasheet, or recipe uses without converting by hand.
The material presets cover the values people look up most often. Water is 1.00 g/cm³, seawater is 1.025 g/cm³, and ice is 0.917 g/cm³, which is why ice floats: it is less dense than the water it sits in. Steel is 7.85 g/cm³, aluminum is 2.70 g/cm³, copper is 8.96 g/cm³, lead is 11.34 g/cm³, and gold is 19.32 g/cm³, so a gold bar the size of a smartphone weighs far more than you would expect. Oak is about 0.75 g/cm³ and pine about 0.50 g/cm³, which is why both float, and air at sea level is only 0.001225 g/cm³. Pick a preset, and the calculator fills in the density and solves for the mass or volume you need.
Density is also the test for whether something floats. An object floats if its average density is less than the fluid it is in, and sinks if it is greater. A ship floats even though it is made of steel, because its average density, counting the air inside the hull, is less than water. A hot air balloon rises because hot air is less dense than the cool air around it. The same idea explains why oil floats on water in a salad dressing bottle: oil is about 0.92 g/cm³, a little less dense than water, so it sits on top.
Temperature changes density a little, because most materials expand when heated and the same mass then occupies more volume. Water is the famous exception near freezing: it reaches its maximum density at about 4 °C, and as it cools further toward 0 °C it expands, so ice is less dense than liquid water. That quirk is why lakes freeze from the top down and fish survive the winter underneath. For most everyday work, the room-temperature densities in this calculator are accurate enough, but if you are working with hot liquids or gases, look up the density at your actual temperature.
Mass = density × volume
Volume = mass ÷ density
1 g/cm³ = 1,000 kg/m³ = 62.43 lb/ft³
Common densities
| Material | g/cm³ | kg/m³ |
|---|---|---|
| Air | 0.001225 | 1.225 |
| Ice | 0.917 | 917 |
| Water | 1.00 | 1,000 |
| Aluminum | 2.70 | 2,700 |
| Steel | 7.85 | 7,850 |
| Copper | 8.96 | 8,960 |
| Lead | 11.34 | 11,340 |
| Gold | 19.32 | 19,320 |
Worked example
A metal block weighs 500 grams and measures 250 cm³. What is its density, and how much would a 1-litre block of water weigh?
Step 1: Density — 500 ÷ 250 = 2.00 g/cm³.
Step 2: Convert — 2.00 g/cm³ × 1,000 = 2,000 kg/m³, and 2.00 × 62.43 = 124.86 lb/ft³.
Step 3: Water mass — 1 litre is 1,000 cm³, so mass = 1.00 × 1,000 = 1,000 g, or 1 kg.
Enter 500 g and 250 cm³ in the calculator and it gives exactly 2.00 g/cm³. Switch to Solve for mass, pick the water preset, enter 1,000 cm³, and it gives 1,000 g. The block, at 2 g/cm³, is denser than water, so it would sink.
FAQ
How do you calculate density?
Divide mass by volume: density = mass ÷ volume. A block with a mass of 500 grams and a volume of 250 cubic centimetres has a density of 500 ÷ 250 = 2 grams per cubic centimetre. The same formula rearranged gives mass = density × volume and volume = mass ÷ density.
What is the density of water?
Water has a density of 1 gram per cubic centimetre, which is 1,000 kilograms per cubic metre, or 62.4 pounds per cubic foot. That is why 1 millilitre of water weighs 1 gram and 1 litre weighs 1 kilogram. Seawater is slightly denser, about 1.025 g/cm³, because of the dissolved salt.
How do I find mass from density and volume?
Multiply density by volume: mass = density × volume. A 2-litre bottle of water has a volume of 2,000 cm³ and water's density is 1 g/cm³, so its mass is 2,000 × 1 = 2,000 grams, or 2 kilograms. Choose Solve for mass in this calculator and enter the density and volume.
What is the density of steel and aluminum?
Steel has a density of about 7.85 g/cm³ (7,850 kg/m³) and aluminum about 2.70 g/cm³ (2,700 kg/m³). That is why aluminum is used where weight matters: a part of the same size weighs roughly a third as much in aluminum as in steel. Gold is far denser at 19.32 g/cm³.
Does density change with temperature?
Yes, slightly. Most materials expand when heated, so the same mass takes up more volume and the density falls. Water is the famous exception near freezing: it is densest at about 4 °C, and ice at 0 °C is less dense at 0.917 g/cm³, which is why ice floats. For most everyday calculations, the room-temperature values in this calculator are accurate enough.