To change density from g/cm³ to kg/m³, multiply by 1000. To change from kg/m³ to g/cm³, divide by 1000. Both units describe the same quantity, mass per unit volume, written with different building blocks.
This skill appears whenever a question gives data in g and cm³ but asks for an answer in kg/m³. It belongs with mass, weight and density.
Where does the factor of 1000 come from?
Build it from two conversions. Mass: 1 g = 0.001 kg. Volume: 1 cm³ = 0.000 001 m³ = 10⁻⁶ m³, because 1 m = 100 cm and 100³ = 1 000 000.
So 1 g/cm³ = 0.001 kg ÷ 0.000 001 m³ = 1000 kg/m³.
How do you convert step by step?
- Write the starting unit next to the number.
- Decide the direction. Going to kg/m³ gives a bigger number, going to g/cm³ gives a smaller one.
- Multiply or divide by 1000 accordingly.
- Sense check against water: 1 g/cm³ = 1000 kg/m³.
Worked example
A steel sample has density 7.8 g/cm³. Give its density in kg/m³.
Step 1: 7.8 g/cm³ needs to go to kg/m³, so the number should grow.
Step 2: 7.8 × 1000 = 7800.
Answer: 7800 kg/m³.
Check by the long route: 7.8 g in 1 cm³ means 7.8 g × 1 000 000 = 7 800 000 g in 1 m³. Then 7 800 000 g = 7800 kg. The same answer.
The mistake to watch for
Mistaken working: 7.8 g/cm³ = 7.8 × 100 × 100 × 100 = 7 800 000 kg/m³
The student cubed the length conversion to fix the volume, but forgot to convert grams into kilograms.
Cubing the length factor correctly gives 1 000 000 for the volume. The mass conversion then divides by 1000, so the net factor is 1000, not 1 000 000. A quick sense check helps: steel cannot be seven million kilograms in a cubic metre when water is 1000 kg/m³.
Check yourself
1. Convert 2.7 g/cm³ to kg/m³.
Show answer
2.7 × 1000 = 2700 kg/m³.
2. Convert 13 600 kg/m³ to g/cm³.
Show answer
13 600 ÷ 1000 = 13.6 g/cm³.
3. A cooking oil has density 0.92 g/cm³. Will it float on water (1000 kg/m³)? Explain with a conversion.
Show answer
0.92 × 1000 = 920 kg/m³. This is less than 1000 kg/m³, so the oil floats.
Where this leads next
Use this conversion in calculating an unknown volume from mass and density. If the units in that lesson still feel slippery, practise with the mixed practice set.
A teacher watching you convert can see in seconds whether the gap is the factor or the habit of writing units. That is the kind of detail covered in online one-to-one Physics tuition.