The size in bytes of one “encrypted” block matches the size of the key, which matches the size of the module. A private exponent is usually the same size, but may be smaller. A public exponent can be up to a key size in size, but usually much smaller to provide more efficient encryption or verification. Most of the time this is Farm's fourth number, 65537.
Please note that this is the bit size of the encrypted data. Simple data should be supplemented. PKCS # 1 v1.5 uses no more than a key size - 11 bytes for plain text. Of course, it is smarter to keep a higher margin, although, say, a 19-bit minimum interval (16-byte random rather than 8-byte random to fill).
For this reason and because of the expensive encryption / decryption performance of RSA, RSA is mainly used in conjunction with a symmetric primitive such as AES — in the case of AES, the random symmetric AES secret key is encrypted instead of plain text. This key is then used to encrypt plain text.