Run the following script in your database
SELECT RTRIM(name) AS NameOfFile,
size/128.0 as TotalSizeInMB,
CAST(FILEPROPERTY(name, 'SpaceUsed' )AS int)/128.0 AS SpaceUsedInMB,
size/128.0 -CAST(FILEPROPERTY(name, 'SpaceUsed' )AS int)/128.0 AS AvailableSpaceInMB, filename AS PhysicalLocation
FROM dbo.sysfiles
In the output sum the values of the column SpaceUsedInMB. This will be the size of your backup. If your database is in FULL recovery model then sum all the values in the column and if it is in SIMPLE sum the values of only your data files.