If you search in the forum on 'archive size sql' you will find several scripts.

I use the below: Replace YourVaultStoreDatabase with the name of your VaultStoreDatabase

SELECT A.ArchiveName,
       COUNT(S.IdTransaction) "Num. Items Archived",
       SUM(S.ItemSize)/1024 "Archived Items Size (MB)",
       SUM(SP.OriginalSize)/1024/1024 "Original Email Size (MB)"
FROM   EnterpriseVaultDirectory.dbo.Archive A,
       EnterpriseVaultDirectory.dbo.Root R,
YourVaultStoreDatabase.dbo.ArchivePoint AP,
YourVaultStoreDatabase.dbo.Saveset S,
YourVaultStoreDatabase.dbo.SavesetProperty SP
WHERE  S.SavesetIdentity = SP.SavesetIdentity
  AND  S.ArchivePointIdentity = AP.ArchivePointIdentity
  AND  AP.ArchivePointId = R.VaultEntryId
  AND  R.RootIdentity = A.RootIdentity
GROUP BY A.ArchiveName

Also if you have EV reporting ( on a SQL reporting server), there are SIS reports.

Gertjan
 

Do I run this as an SQL query against the vault store database?

Oh and the SQL query Gertjan posted goes across directory and vault store database, you will have to change yourVaultStore to the name of your vault store database