It's called calibration. That's why $3 worth of bent metal sells for hundreds of dollars.
One approach is to build a 'standard gain antenna' where, if you follow the plans exactly, the gain is well known. Then you can use that antenna, and your own antenna range, to transfer the calibration to your certain dipole.
A simple dipole would probably only hold a reliable calibration over a narrow range. Most calibrated EMC antennas are wide band designs (not simple thin dipoles).
If you want to do a calibration against a spectrum analyser and a signal generator you ideally need three antennas (google "three antenna method")
Alternatively you can do it roughly if you use two "identical" antennas.
Or you can beg/steal/borrow a known calibrated antenna and measure some ambient signal with both antennas and thereby get some sort of idea of the calibration factor. Any EMC test house would be able to do something of the sort for you for a few hundred pounds.
Antenna Factor requires a distance from the antenna, usually 1m or 3meters. It converts gain to field strength. You need to measure the antenna, then add math to get the antenna factor.
I recently purchased a dipole from AHSystems which had gain and antenna factor at 1,3 and 10 meters away from the antenna. Maybe contact them for more details on how they measure and calculate their results.
