Java Security

Let's say that I have an RSA key pair that has been generated in a keystore using the keytool utility.

I am now accessing this key pair through some java code (using the Keystore class) and I want to encrypt/decrypt data using this public/private key.
In order to encrypt/decrypt arbitray length data, I need to know the maximum block size that I can encrypt/decrypt.
Based upon my experiment, this block size seems to be the size of the key divided by 8 and minus 11.

But how can I determine all that programatically when the only thing that I have is the keystore?
I did not find a way to figure out the size of the key from the keystore (unless it can be computed from the RSA exponent or modulus, but this is where my knowledged of RSA keys stops) and I did not find a way to figure out where this "magic" number 11 is coming from.

I can always encrypt 1 byte of data and look at the size of the result. This will give me the blocksize and the key size by multiplying it by 8. But it means that I always need the public key around to compute this size (I cannot do it if I have only the private key).
And this is not helping much on the number 11 side.

Am I missing something obvious?

Thanks.