how to find the block height from merkle root?
The block hash is the output obtained when hashing the header of a bitcoin block. The header of a bitcoin block is comprised of several pieces of data, one of which is the merkle root.
So having the merkle root alone is not sufficient to calculate the block hash, you would need additional information (the rest of the block header).
You could write some code to query the block database for a specific merkle root, but otherwise I am not aware of any software that currently includes this functionality.
(this seems odd to me though: if you have calculated the merkle root, you assumedly have all the transaction data from the block in question. I'm not sure in what situation you would have all of this data, but not the rest of the block header data)