What this density calculator does
This tool applies the density formula ρ = m / V in all three rearrangements. If you know mass and volume, it computes density. If you know density and volume, it computes mass. If you know mass and density, it computes volume. Every input is unit-aware: mass in grams or kilograms, volume in cubic centimetres, cubic metres, litres or millilitres, density in g/cm³ or kg/m³. The calculator converts to SI internally, computes the result, and returns it in whichever unit you chose — with a cross-conversion to the other natural unit for reference. Because density is a material property, the result page includes a materials comparison table so you can identify what substance your sample is likely to be, and the tool highlights the closest match.
Formulas — three rearrangements
Variable definitions
- ρ (rho) — density, in kg/m³ or g/cm³.
- m — mass, in kg or g.
- V — volume, in m³ or cm³ (or their liquid equivalents, L and mL).
Unit conversions you need to know
- 1 kg = 1000 g
- 1 m³ = 1,000,000 cm³ = 1000 L
- 1 L = 1000 mL = 1000 cm³
- 1 g/cm³ = 1000 kg/m³
The g/cm³ unit is convenient for small samples — a 200 cm³ block of aluminium (density 2.7 g/cm³) has a mass of 540 g, which is easier to write than 0.54 kg. Both units describe the same physical quantity; picking the right one is a matter of scale.
Worked examples
Example 1: Find density — a metal block
- ρ = m / V = 540 / 200.
- ρ = 2.7 g/cm³ = 2700 kg/m³.
- This matches the density of aluminium — the block is likely aluminium.
Example 2: Find density — a gold ring
- ρ = 9.65 / 0.5.
- ρ = 19.3 g/cm³ = 19300 kg/m³.
- This is the density of pure gold. If a "gold" ring gave a much lower value, it would be a fake.
Example 3: Find mass — a steel beam
- m = ρ × V = 7850 × 0.05.
- m = 392.5 kg.
- The beam weighs nearly 400 kg — solid steel is heavy.
Example 4: Find mass — a bottle of water
- Convert: 1500 mL = 1500 cm³.
- m = 1.0 × 1500.
- m = 1500 g = 1.5 kg.
- This is why a 1.5 litre bottle of water weighs exactly 1.5 kg — the density of water is 1 g/cm³.
Example 5: Find volume — a mercury sample
- V = m / ρ = 1360 / 13.6.
- V = 100 cm³.
- 100 cm³ of mercury has a mass of 1.36 kg — a small volume of a very dense liquid.
Example 6: Find volume — working in SI units
- V = m / ρ = 27 / 2700.
- V = 0.01 m³ = 10,000 cm³ = 10 L.
- Same aluminium sample as Example 1, just viewed at a larger scale.
Materials and their densities
Density is a diagnostic property — it can identify a substance. These values are standard at room temperature.
| Material | g/cm³ | kg/m³ | Category |
|---|---|---|---|
| Air (20 °C) | 0.0012 | 1.2 | Gas |
| Cork | 0.24 | 240 | Light solid |
| Pine wood | 0.40 | 400 | Light solid |
| Petrol / gasoline | 0.70 | 700 | Liquid |
| Ice (0 °C) | 0.92 | 920 | Solid |
| Water (4 °C) | 1.000 | 1000 | Reference |
| Sea water | 1.03 | 1030 | Liquid |
| Concentrated sulphuric acid | 1.84 | 1840 | Liquid |
| Aluminium | 2.70 | 2700 | Metal |
| Iron / steel | 7.87 | 7870 | Metal |
| Copper | 8.96 | 8960 | Metal |
| Lead | 11.30 | 11300 | Metal |
| Mercury | 13.60 | 13600 | Liquid metal |
| Gold | 19.30 | 19300 | Precious metal |
| Osmium (densest element) | 22.60 | 22600 | Precious metal |
The calculator highlights the closest match when you compute a density. A density of 2.7 g/cm³ almost certainly means aluminium; 19.3 means gold; 7.87 means iron or steel. Being within ±5% of a standard value is usually enough to make a confident identification.
Common mistakes to avoid
- Mixing g with m³, or kg with cm³. The g/cm³ unit pairs with grams and cm³; kg/m³ pairs with kilograms and m³. Mixing the two systems (grams with m³, or kg with cm³) gives an answer that is off by a factor of 1000. The calculator handles conversions internally, but exam answers need the pairing done correctly by hand.
- Forgetting to convert litres to cm³ or m³. 1 litre is 1000 cm³, not 100 cm³ and not 1 cm³. A 2-litre bottle has a volume of 2000 cm³ or 0.002 m³.
- Confusing mass and weight. Mass is in kilograms or grams. Weight is a force, in newtons. Density uses mass. If a problem gives weight, divide by g (9.8 m/s²) first.
- Using the wrong density for water. Water's density is 1000 kg/m³ = 1 g/cm³ at 4 °C. Using 1 kg/L is fine (same thing). Using 1 g/mL is also correct because 1 mL = 1 cm³.
- Assuming density is constant everywhere. Density changes with temperature (gases dramatically, liquids and solids slightly) and pressure (gases). For most BISE problems at room temperature, the standard values are accurate enough.
- Forgetting that ice floats. Ice has a density of about 0.92 g/cm³, less than water's 1.0. This is why ice floats — a classic exam question that the density comparison explains.
- Mixing up volume of the substance with volume of the container. A 500 mL bottle filled halfway holds 250 mL of liquid. Use the liquid's volume, not the container's.
- Rounding too aggressively. Density comparisons often require two or three significant figures. Rounding 2.698 to 2.7 is fine, but rounding 2.68 to 3 is not.
FAQ
What is the formula for density?
Density is mass per unit volume: ρ = m / V, where ρ (rho) is density, m is mass and V is volume. The SI unit is kilograms per cubic metre (kg/m³). A more common small-scale unit is grams per cubic centimetre (g/cm³). 1 g/cm³ = 1000 kg/m³.
What is the density of water?
The density of water at 4 °C is 1000 kg/m³ = 1 g/cm³. This is the reference density against which the relative density (or specific gravity) of other substances is measured. Water is slightly less dense at higher temperatures.
What is the difference between density and specific gravity?
Density is an absolute quantity with units (kg/m³ or g/cm³). Specific gravity (also called relative density) is a dimensionless ratio: the density of a substance divided by the density of water. A substance with specific gravity 2.7 has a density of 2700 kg/m³.
How do I find mass from density and volume?
Rearrange ρ = m / V to get m = ρ × V. Multiply the density (kg/m³) by the volume (m³) to get mass in kilograms. If you are using g/cm³ and cm³, the result is in grams.
How do I find volume from density and mass?
Rearrange ρ = m / V to get V = m / ρ. Divide the mass (kg) by the density (kg/m³) to get volume in cubic metres. If mass is in grams and density in g/cm³, the result is in cm³.
Why can density not be zero?
Density is mass divided by volume. Every real substance has a positive mass and positive volume. When solving for mass or volume, dividing by a zero density would be a domain error — the calculator flags this and explains why.
Related tools
Related Hira Academy resources
Revise the theory of matter and measurement with our Class 9 notes and Class 10 notes, and track term progress with the free Student Portal.