The SI unit of density is the kilogram per cubic meter (kg/m³), which means mass in kilograms divided by volume in cubic meters

. However, in many practical contexts, especially in chemistry and materials science, density is often expressed in grams per cubic centimeter (g/cm³), which is a CGS unit

Relationship between kg/m³ and g/cm³

• 1 kg/m³ is equal to 0.001 g/cm³.
• Conversely, 1 g/cm³ equals 1000 kg/m³.

This conversion arises because:

• 1 kilogram (kg) = 1000 grams (g).
• 1 cubic meter (m³) = 1,000,000 cubic centimeters (cm³).

So when converting density units:

1kgm3=1000 g1,000,000 cm3=0.001gcm31\frac{kg}{m^3}=\frac{1000,g}{1,000,000,cm^3}=0.001\frac{g}{cm^3}1m3kg​=1,000,000cm31000g​=0.001cm3g​

and

1gcm3=1000kgm31\frac{g}{cm^3}=1000\frac{kg}{m^3}1cm3g​=1000m3kg​

This means that the gram per cubic centimeter unit is numerically 1000 times larger than the kilogram per cubic meter unit for the same density value

Why use g/cm³ instead of kg/m³?

• For solids and liquids, g/cm³ is more convenient because the values typically range around 1 (e.g., water is about 1 g/cm³), making it easier to handle than large numbers like 1000 kg/m³.
• For gases or larger-scale measurements, kg/m³ is more practical.

Summary

Unit| Symbol| Relation to SI unit (kg/m³)| Typical use
---|---|---|---
Kilogram/cubic meter| kg/m³| SI unit of density| Standard scientific use
Gram/cubic centimeter| g/cm³| 1 g/cm³ = 1000 kg/m³; 1 kg/m³ = 0.001 g/cm³| Common in chemistry, materials science

Thus, although the SI unit of density is kg/m³, g/cm³ is widely used for convenience in many fields