Is there any method from which we can manually calculate wallet privatekey from a protected bitcoin core wallet.dat file ?
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Is there any method from which we can manually calculate wallet privatekey ...
You can't calculate the private-key.
You can extract the key if the wallet is unprotected or if the wallet is protected and you know the wallet passphrase (also known as the wallet "password").
You can also do this using the equivalent methods in other tools such as pywallet.
... from a protected bitcoin core wallet.dat file?
Only if you know the passphrase for the protected wallet. Bitcoin core uses the password to encrypt the private key.
If you don't know the passphrase, you can't extract the private key.