Trial Calculator (Make a copy of the sheet or download to use in Excel):
https://docs.google.com/spreadsheets/d/1NgYDFakUm0GLcMdwxVBOT8gWQ4fS_gi841i23A-Fe18/edit#gid=0
Trial - Par Time in Seconds - Max Vitality - Base Score - Base Score with HM
Aetherian Archive - 900 - 24 - 84300 - 124300
Hel Ra Citadel - 900 - 24 - 93100 - 133100
Sanctum Ophidia - 1500 - 24 - 104100 - 144100
Maw of Lorkhaj - 2700 - 36 - 68150 - 108150
Halls of Fabrication - 2700 - 36 - 120100 - 160100
Asylum Sanctorium - 1200 - 36 - 15000 (+0) - 30000 (+1) - 70000 (+2)
Maelstrom Arena - 5400 - 15 - 426000
Dragonstar Arena - 3600 - 24 - 20000
To calculate scores on your own:
Trial Score = (Base Score + Vitality x 1000) x [1 + (Par time - Your time)/10000] (times should be in seconds)
Score Example 1
Asylum Sanctorium +2 with a trial time of 10:33 (633 seconds) and 36 vitality. The in-game score is 112008. The par time for Asylum is 20 minutes or 1200 seconds and the base score for +2 and 36 vitality is 70000 + 36000. Since 633 seconds is 567 seconds ahead of the par time, the base score + vitality bonus is increased by 567/10000 or 5.67%.
Final Score = 106000 x 1.0567 = 112010.2
The 2.2 points difference is because the game calculates trial times to 3 decimal places, while the formula we're using as well as the in-game score display does not use any decimal places.
Score Example 2
Aetherian Archive HM with a trial time of 15:25 (925 seconds) and 24 vitality. The in-game score is 147926. The par time for Aetherian Archive is 15 minutes or 900 seconds and the base score for HM and 24 vitality is 124300 + 24000. Since 925 seconds is 25 seconds behind the par time, the base score + vitality bonus is decreased by 25/10000 or 0.25%.
Final Score = 148300 x 0.9975 = 147929
From Code65536 in the comments: "Also note that the time adjustment (i.e., 1 + time diff/10000) has a floor of 0.001, which means that if you take more than 2h46m30s beyond the par time, your score will not drop any further. E.g., if you see someone clearing vHoF with a score of 120, that means they took at least 3h31m30s".
Hopefully this post is informative. I decided to make it because I wasn't able to find up to date information elsewhere.