Density Calculator (ρ = m/V)
Calculate density from mass and volume using ρ = m/V, or rearrange to solve for mass or volume instead — with step-by-step working shown.
Density formula
Density measures how much mass is packed into a given volume:
- ρ (rho) — density, in kilograms per cubic metre (kg/m³) — always positive
- m — mass, in kilograms (kg) — always positive
- V — volume, in cubic metres (m³) — always positive
Enter any two values and leave the third blank; the calculator solves for it and shows the substitution step.
Worked example
A block has a mass of 100 kg and a volume of 50 m³. What is its density?
- Formula: ρ = m/V
- Substitute: ρ = 100 / 50
- Result: ρ = 2 kg/m³
Solving in reverse
The same formula rearranges to find mass or volume when density is known:
- Mass: m = ρV — enter ρ and V, leave m blank.
- Volume: V = m/ρ — enter m and ρ, leave V blank.
For example, a density of 2 kg/m³ and a volume of 50 m³ gives m = 2 × 50 = 100 kg. Given that same density and a mass of 100 kg, V = 100 / 2 = 50 m³.
Common mix-ups
- Confusing mass and weight. Density uses mass (kg), not weight (N) — see the weight calculator if you have a weight in newtons and need mass first.
- Mixed units. Grams per cubic centimetre (g/cm³) is a common non-SI density unit — multiply by 1000 to convert to kg/m³.
- Treating volume as area. Volume (m³) is a 3D measure; don't substitute a 2D area (m²) into this formula.
Where this shows up
Density explains why a steel ship can float (its overall shape displaces enough water despite steel being denser than water) and why oil floats on water. It also connects to other physics quantities: pressure in a fluid depends on density, and mass itself relates to gravitational force through F = ma.
Frequently asked questions
- What is the formula for density?
- Density is ρ = m/V, where ρ (rho) is density in kilograms per cubic metre (kg/m³), m is mass in kilograms (kg), and V is volume in cubic metres (m³).
- How do I find mass if I know density and volume?
- Rearrange the formula to m = ρV. Enter the density and volume values and leave the mass field blank, and the calculator multiplies them for you automatically.
- How do I find volume if I know density and mass?
- Rearrange the formula to V = m/ρ. Enter the mass and density, leave volume blank, and the calculator divides mass by density to solve for it.
- Can density, mass, or volume be negative?
- No — mass and volume are physical quantities that must be greater than zero, and since density is mass divided by volume, a valid density is always positive too.
- What units does this calculator use?
- SI units throughout — kilograms per cubic metre (kg/m³) for density, kilograms (kg) for mass, and cubic metres (m³) for volume. Convert grams, litres, or other units to SI before entering them.
- How is density used to tell if something floats?
- An object floats in a fluid if its density is lower than the fluid's density — water is about 1000 kg/m³, so anything with a lower density than that floats on water and anything denser sinks.