Which Sql Version do you have? If you do not use Backup Compression, below query can help to calculate backup size (approximately 90%)

-- Data Size

Declare @dataSize Float

Select @dataSize= (SUM(used_pages) * 8) / (1024.00) From sys.allocation_units -- Run it in YourDatabase

-- Log Size

Create Table #Log_info ( FieldId Int, FileSize Bigint, Startoff Bigint, FseqNo int, Status smallint,

Parity Bigint, CreateLsn numeric)

Declare @sql nvarchar(100)

Set @sql = 'dbcc loginfo(YourDatabase)'

Insert into #log_info

Exec sp_executesql @sql

Declare @LogSize Float

Select @LogSize= FileSize/ (1024.00 * 1024.00) From #Log_info where [Status] = 2 -- Only Active VLFs

Select @dataSize DataSize_inMB, @LogSize LogSize_inMB, @dataSize+ @LogSize As 'BackupSize_Approx[90%]'

Drop Table #log_info