Library / Foundations: Physics / FPH-12
Foundations: Physics
Density
Mass per unit volume.
- Ref
- FPH-12
- Rev
- v1
- Field
- Foundations: Physics
- Result
- ρ [kg/m³]
For kg/m³ use mass in kg and volume in m³. The calculator takes volume in cm³ (1 m³ = 10⁶ cm³).
Density tells how much mass is packed into each unit of volume.
Calculator
kg/m³
kg
cm³
- Density in g/cm³7.8 g/cm³
- Relative density (water = 1)7.8
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
Density (kg/m³) current value 7,800 kg/m³
VVolumeKey driver
787,800,000
mMass
101,000,000
- Objects with a density above that of water (1000 kg/m³) sink in water.
- A factor of 1000 separates g/cm³ and kg/m³ values.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kg/m³) | Local step | Change in result |
|---|---|---|---|---|---|---|
| V Volume | 1 to 100,000 cm³ | 78 | 7,800,000 | 7,800,000 | +10% | −9.09 % |
| m Mass | 0.01 to 1,000 kg | 10 | 1,000,000 | 1,000,000 | +10% | +10 % |
Sweep of Volume
| Volume (cm³) | Density (kg/m³) |
|---|---|
| 1 | 7,800,000 |
| 4.217 | 1,850,000 |
| 17.78 | 438,600 |
| 74.99 | 104,000 |
| 316.2 | 24,670 |
| 1,334 | 5,849 |
| 5,623 | 1,387 |
| 23,710 | 328.9 |
| 100,000 | 78 |
Sweep one variable
Density (kg/m³)Hover, touch, or use the arrow keys on the chart
Variables and how each one contributes
ρ
Density
What the equation gives you. Everything else feeds it.
m
Mass
Mass of the sample. Directly proportional.
V
Volume
Volume of the sample. Inversely proportional.
Worked example with the values above
- Convert volume: 1,000 cm³ = 0.001 m³.
- Divide: 7.8 / 0.001.
- ρ = 7,800 kg/m³.
Assumptions and limits
- Uniform material.
- Mass and volume in the stated units.
Common mistakes
- Using cm³ with kg and forgetting the 10⁶ factor.
- Mixing g/cm³ with kg/m³.
Statistics and uncertainty
Volume of irregular objects measured by displacement has a few per cent error, which sets the density uncertainty.
Where it is used
- Identifying materials.
- Mass estimates of parts from volume.
Maths you need
- Mass and volume: basic quantities
- Unit conversion: cm³ to m³