# Whis my planetary volume formula wrong? (volume = mass/density)

I'm having trouble with this and am unsure what I'm doing wrong. Let's use Earth as an example.

Earth has a mass of 5,972,168,000,000,000,000,000,000 (5.97E+27) kg and a density of 5513.4 kg/m3 or 5.5134 g/cm3.

Volume = mass / density.

The calculation gives me a result of 1,086,109,090,909,090,000,000,000.00 (1.09E+24) m3. However, the Earth's volume is 1,083,210,000,000,000.00 m3. That's a 1 billion times difference.

Is there a discreprancy with the units this question advised to always use kg and m2?

• Earth's volume from wikipedia is $1.0832 \times10^{12}$ km, not $1.0832 \times10^{12}$ m. Correct this error and you'll see you calculated approximately the right answer the first time. Jun 17, 2023 at 20:13
• I cannot correct the volume as this is the value I'm trying to calculate from the forumla. I can only change the mass or density. I can however fix my reference to know what the value should be, so thank you for pointing that out. Jun 17, 2023 at 20:53
• Your Earth mass is off by a factor 1000, that's jupiter mass. The mass of earth is is $6\cdot 10^{24}$kg. Jun 18, 2023 at 0:29

As @planetmaker has pointed out, the mass of the earth is $$6⋅10^{24}$$ kg, instead of $$6⋅10^{27}$$.
Second, $$km^{3}$$ and $$m^{3}$$ are different things. $$km^{3}$$ is off $$m^{3}$$ by a factor of 1 billion ($$1km^{3}$$=$$10^9m^{3}$$).
Correct your calculations using these factors. If calculations are correct, you should obtain $$1.08321 × 10^{21}m^3$$ as your correct answer.