Antenna Design Calculator
The upper section relates antenna diameter and frequency to gain and beamwidth. Using the scroller, set the beamwidth against the 3 dB or 10 dB marker, and read off the corresponding frequency and diameter; or set the frequency against the diameter and read off the beamwidth.

The gain can also be read off; most antennas have efficiencies of 50 to 60 %. Note the antenna diameter is taken to be diameter of the aperture of the antenna.

The lower nomogram relates far field range (the distance at which the antenna pattern is properly formed) to the frequency and antenna diameter. Set the range against the marker and read off frequency and diameter, or set frequency against diameter and read off the far field range.

From http://www.q-par.com/antenna-calculator/Antenna_calc_instructions.htm