How to Calculate Density (ρ = m/V): Mass ÷ Volume

Calculate density with ρ = m/V. Unit traps (g/cm³ vs kg/m³), float vs sink, worked examples, and a free density calculator.

What Density Asks

Density tells you how much mass is packed into a given volume. A kilogram of steel takes less space than a kilogram of foam — steel has higher density.

The formula is ρ = m / V (rho = mass over volume). With mass in kilograms and volume in cubic metres, density is in kg/m³. Water is about 1000 kg/m³; many woods are less, most metals are more.

If you already have m and V (or ρ and one unknown), open the free density calculator first, then return here for unit traps and the link to buoyancy.

The Formulas

  • ρ = m / V — density from mass and volume.
  • m = ρ V — rearrange for mass.
  • V = m / ρ — rearrange for volume.

    • Keep units consistent. If mass is in grams and volume in cm³, density comes out in g/cm³. 1 g/cm³ = 1000 kg/m³ (same as water).

    Density and Floating

    Buoyant force uses fluid density: Fb = ρ V g. See buoyant force and the

    buoyancy guide.

    An object denser than the fluid tends to sink when fully submerged; less dense materials float. Compare object density to fluid density, or compare weight to maximum Fb.

    Object weight is W = mg — use the weight calculator when you need newtons from kilograms.

    Units

  • m → kg (or g if V is in cm³).
  • V → m³ (1 L = 0.001 m³; 1 cm³ = 1×10⁻⁶ m³).
  • ρ → kg/m³ (or g/cm³).
  • Convert liters and cm³ before using SI water density 1000 kg/m³.

    • Worked Examples

    Example 1: 12 kg in 0.003 m³

    ρ = m/V = 12 / 0.003 = 4000 kg/m³.

    Example 2: find mass

    ρ = 7800 kg/m³ (steel-like), V = 0.002 m³. m = ρV = (7800)(0.002) = 15.6 kg.

    Example 3: find volume

    m = 2.0 kg, ρ = 1000 kg/m³ (water). V = m/ρ = 2.0/1000 = 0.002 m³ = 2.0 L.

    Example 4: g/cm³ to kg/m³

    ρ = 2.7 g/cm³ (aluminum). In SI: 2.7 × 1000 = 2700 kg/m³.

    Common Mistakes

  • Mixing grams with m³, or kilograms with cm³, without converting.
  • Using liters as if they were m³ (off by 1000).
  • Putting object density into Fb = ρVg instead of fluid density.
  • Comparing density in kg/m³ to weight in newtons.

    • Check It on the Calculator

    Density calculator — ρ = m/V.

    Buoyancy force calculator.

    Weight calculator.

    Learn ρ = m/V and confirm every homework number on the calculator.

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