"Its hit point maximum equals its normal maximum or four times your ranger level, whichever is higher."

This may be a redundant question but here it goes.

If I take a Panthar at 3rd level its hp's would be 24 (3d8 with Con 10), at 10th level it would be 40 (4hp x 10th level).

If I took a Hawk at 3rd level it's hp's would be 12 (4hp × 3rd level which is greater than 3 from 1d4-1 with Con 8), at 10th level it would be 40 (4hp x 10th level).

Does this seem correct ? Or am I going about this wrong?

*edited for clarification*

 Its hit point maximum equals the hit point number in its stat block or four times your ranger level, whichever is higher.

The semantics between what you posted and what it actually says is important. 

                             |----------------------------------------------------------- Hit Points ----------------------------------------------------------------|

Creature              | Stat Block | 3rd Level Ranger | 5th Level Ranger | 10th Level Ranger | 20th Level Ranger |

Hawk                   |          1        |            12               |             20               |                40           |                80                |

Panther               |        13        |             13              |             20               |                40           |                80                |

Dimetrodon        |        19        |             19              |            20                |               40            |                80                 |

Swarm of Bats* |        22        |             22              |             22               |              40             |                 80                |

Tiger**                 |       37         |             37             |              37              |              40             |                 80                 |

Cave Bear**        |       42         |            42              |                42             |              42            |                 80                 |

*not RAI https://rpg.stackexchange.com/questions/153769/can-a-beast-master-ranger-choose-a-swarm-as-an-animal-companion 

**If you're allowed a higher CR and Large size

You were on the right track though. Here all beast companions eventually have the same HP.

I was at work when working on this, the wording on line is different then whats in the Players Handbook. Thanks. Makes a lot more since now.

So I am going to temporarily redact my statement. I have been using dndbeyond almost exclusively, so I forget about the errata sometimes. My physical and .pdf PHB both say the same as what you posted, but according to this thread here, there is no errata to the Beast Companion's HP that reflects what it says on this site. If the website is wrong and beast companion HP is "its normal maximum" then your calculations would be correct.

Edit: Good ol' Stormknight has clarified the issue here.