Density tells you how tightly matter is packed. Enter the mass and volume of an object to get its density in g/cm³ and kg/m³ and find out whether it floats in water.
Enter the mass in grams.
Enter the volume in cm³.
Read the density.
Density: ρ = m ÷ V
Density tells you how much mass is packed into each unit of volume. This calculator takes a mass in grams and a volume in cubic centimetres, divides one by the other, and gives the density in g/cm³ and in the SI unit kg/m³. It then compares the result with water, at 1 g/cm³, and tells you whether the object would sink or float.
Class 8 and Class 9 students meet density through floating and sinking and through Archimedes' principle. Jewellers use it to check whether gold is pure, builders use it to estimate the weight of sand and concrete, and dairies use a related reading to check milk. A density value is also a quick fingerprint that helps identify an unknown material in a school lab.
1. Weigh the object and write its mass in grams.
2. Find its volume in cm³. For a regular block, multiply length × breadth × height. For an irregular object, lower it into a measuring cylinder and read the rise in water level, since 1 mL = 1 cm³.
3. Divide: ρ = m ÷ V to get the density in g/cm³.
4. Multiply by 1000 to convert g/cm³ to kg/m³.
5. Compare with water at 1 g/cm³. A larger value means a solid lump will sink; a smaller one means it will float.
6. For relative density, divide the density by that of water; the result has no units.
One gram is 1/1000 of a kilogram, and one cubic centimetre is 1/1,000,000 of a cubic metre, since a metre is 100 cm and 100³ = 1,000,000. So 1 g/cm³ equals 0.001 kg ÷ 0.000001 m³, which is 1000 kg/m³. That is why water is quoted as 1 g/cm³ in lab work and 1000 kg/m³ in physics and engineering. Litres fit neatly too: 1 g/mL equals 1 kg/L, because 1 mL is 1 cm³.
An object in water feels an upward buoyant force equal to the weight of water it pushes aside. If the object is fully submerged, that displaced water has the same volume as the object, so buoyancy beats weight only when the object's density is less than water's. That is why a steel ship floats: its hollow hull encloses air, so its average density, total mass over total enclosed volume, is below 1 g/cm³. An object exactly as dense as water stays suspended wherever it is placed.
Density is not a fixed number for every sample. Most substances expand when heated, so density drops slightly with temperature. Water is unusual: it is densest near 4 °C, and ice at about 0.92 g/cm³ floats on liquid water. Gases change density a lot with pressure and temperature. Mixtures and porous materials depend on how they are packed, so loose sand and compacted sand give different values. Seawater, at about 1.025 g/cm³, supports floating objects slightly better than fresh water.
Ishaan finds a small metal block in the school lab with a mass of 356 g, and when he lowers it into a measuring cylinder the water level rises by 40 cm³.
Density = mass ÷ volume: = 356 ÷ 40 = 8.9 g/cm³
In SI units: 8.9 g/cm³ × 1000 = 8,900 kg/m³
Compared with water (1 g/cm³): Denser than water → sinks
Answer: Density 8.9 g/cm³; In kg/m³ 8,900 kg/m³
Mixing kg with cm³ or g with m³, which gives numbers off by factors of 1000 or more.
Using the outer volume of a hollow object when judging whether the material itself would sink.
Reading the measuring cylinder from above or below the meniscus rather than at eye level.
Assuming a floating object must be light; floating depends on density, not mass.
Forgetting air bubbles clinging to an irregular object, which make the measured volume too large.
Class 8 to 11 lab work on density, floating and Archimedes' principle.
Checking the purity of gold or silver jewellery against the known density of the pure metal.
Identifying unknown metals or plastics from their density.
Converting between mass and volume for sand, cement and aggregate orders.
Estimating loads on shelves and floors from the volume of stored materials.
How do I find the volume of an irregular object?
Submerge it in water and measure the rise in water level.
What is relative density?
Density divided by the density of water; it has no units.