calculate dipole antenna
You are asking about a dual-band antenna. For the frequencies you just mentioned, 1800MHz is a harmonic of 900MHz so the same antenna would work for both, but performance would be degraded a bit at the higher frequency.
There are simple ways to get much better performance out of a dual band dipole and it involves loading it somewhere in the middle. A simple qualitative explanation is this. If you add an inductor (RF choke) at the center of each arm of your dipole, the high frequency would be confined to the shorter dipole, but the longer wavelength would see the full dipole. In this way, each wavelength sees a perfect half wave dipole. You can this driving on the road. Hams, police, and emergency vehicles will use this technique on their UHF/VHF radio antennas. You will see long whips with "black blobs" in the middle of whip.
-Tip