The Mass Formula
Mass is calculated using the density formula rearranged to solve for mass:
m = ρ × V
Where m is mass, ρ (rho) is density, and V is volume. This is one of three rearrangements of the density equation:
- Find mass: m = ρ × V
- Find density: ρ = m / V
- Find volume: V = m / ρ
Mass vs Weight
| Property | Mass | Weight |
|---|---|---|
| Definition | Amount of matter | Gravitational force on matter |
| SI Unit | kilogram (kg) | newton (N) |
| Changes with location? | No | Yes (depends on gravity) |
| On the Moon | Same as Earth | ~1/6 of Earth weight |
| In zero gravity | Same as Earth | Zero |
| Measured with | Balance scale | Spring scale |
Common Material Densities
| Material | Density (kg/m³) | 1 m³ mass (kg) |
|---|---|---|
| Air (20°C) | 1.2 | 1.2 |
| Wood (oak) | 750 | 750 |
| Water | 1,000 | 1,000 |
| Concrete | 2,400 | 2,400 |
| Aluminum | 2,700 | 2,700 |
| Steel | 7,850 | 7,850 |
| Copper | 8,960 | 8,960 |
| Gold | 19,320 | 19,320 |
Practical Examples
- Shipping: A crate 1.2 m × 0.8 m × 0.6 m filled with water weighs 1,000 × 0.576 = 576 kg
- Construction: A concrete slab 3 m × 2 m × 0.15 m weighs 2,400 × 0.9 = 2,160 kg
- Cooking: 500 mL of olive oil weighs 911 × 0.0005 = 0.456 kg (456 g)
- Metalwork: A steel rod 2 m long, 5 cm diameter weighs 7,850 × 0.00393 = 30.8 kg
Unit Conversion Reference
| From | To kg |
|---|---|
| 1 gram (g) | 0.001 kg |
| 1 milligram (mg) | 0.000001 kg |
| 1 pound (lb) | 0.4536 kg |
| 1 ounce (oz) | 0.02835 kg |
| 1 metric ton (t) | 1,000 kg |