Can I send BCH to the same public address as I would BTC?

[B4RF]

If thats not the case, is there a way to calculate the BCH public key from my private key without importing the key into an external online software?

[shunyata]

yes and no.

the private and public keys are the same. however for it to be considered BCH the transaction has to be created for and broadcast on the BCH chain instead of the BTC chain. BCH transactions will not be accepted on the BTC chain and vice versa which is why it's no longer required to split your coins for security sake.