Source from : https://gallery.technet.microsoft.com/scriptcenter/f1df9f50-9cd9-4c75-a8d9-e2faba6b8574
-- Transact-SQL script to analyse the database size growth using backup history.
DECLARE @endDate datetime, @months smallint;
SET @endDate = GetDate(); -- Include in the statistic all backups from today
SET @months = 6; -- back to the last 6 months.
;WITH HIST AS
(SELECT BS.database_name AS DatabaseName
,YEAR(BS.backup_start_date) * 100
+ MONTH(BS.backup_start_date) AS YearMonth
,CONVERT(numeric(10, 1), MIN(BF.file_size / 1048576.0)) AS MinSizeMB
,CONVERT(numeric(10, 1), MAX(BF.file_size / 1048576.0)) AS MaxSizeMB
,CONVERT(numeric(10, 1), AVG(BF.file_size / 1048576.0)) AS AvgSizeMB
FROM msdb.dbo.backupset as BS
INNER JOIN
msdb.dbo.backupfile AS BF
ON BS.backup_set_id = BF.backup_set_id
WHERE NOT BS.database_name IN
('master', 'msdb', 'model', 'tempdb')
AND BF.file_type = 'D'
AND BS.backup_start_date BETWEEN DATEADD(mm, - @months, @endDate) AND @endDate
GROUP BY BS.database_name
,YEAR(BS.backup_start_date)
,MONTH(BS.backup_start_date))
SELECT MAIN.DatabaseName
,MAIN.YearMonth
,MAIN.MinSizeMB
,MAIN.MaxSizeMB
,MAIN.AvgSizeMB
,MAIN.AvgSizeMB
- (SELECT TOP 1 SUB.AvgSizeMB
FROM HIST AS SUB
WHERE SUB.DatabaseName = MAIN.DatabaseName
AND SUB.YearMonth < MAIN.YearMonth
ORDER BY SUB.YearMonth DESC) AS GrowthMB
FROM HIST AS MAIN
ORDER BY MAIN.DatabaseName
,MAIN.YearMonth
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