it's called dose rate coefficient for photons. You find it tabulated or can compute it from absorption coefficients. An online calculator is here: http://www.radprocalculator.com/Gamma.aspx

The coefficient is strongly energy dependend.

https://hps.org/publicinformation/ate/q4148.html

above link gives the relationship

Each detector has its own cps to dose rate conversion factor - it is called calibration factor. The dose rate coefficient mentioned above by Patrick Eschle refers to the conversion from the activity (disintegrations per second) of a given isotopic source to the dose rate.

For each detector the response cps / dose rate will depend on various factors like the energy of the incident radiation (most detectors have an energy dependence), angle of incidence, type of detector (intrinsic efficiency), etc.

The link given by Mushtaq Ahmad is very good for someone who wants to have an overview about the response of various detectors.

Radu A. Vasilache is right and I was too quick in answering ignoring detector response - sorry!

 Measuring Radiation Dose

When a person is exposed to radiation, energy is deposited in the tissues of the body. The amount of energy deposited per unit of weight of human tissue is called the absorbed dose. Absorbed dose is measured using the conventional rad or the SI Gy.

One rad is equal to 100 erg/gm of tissue.

One R is equal to 87.7 erg/gm of air.

The rad, which stands for radiation absorbed dose, was the conventional unit of measurement, but it has been replaced by the Gy.

One Gy is equal to 100 rad.

To determine a person's biological risk, scientists have assigned a number to each type of ionizing radiation (alpha and beta particles, gamma rays, and x-rays) depending on that type's ability to transfer energy to the cells of the body. This number is known as the Quality Factor (Q).

When a person is exposed to radiation, scientists can multiply the dose in rad by the quality factor for the type of radiation present and estimate a person's biological risk in rems. Thus, risk has been evaluated as

rem = rad X Q.

The rem has been replaced by the Sv.

One Sv is equal to 100 rem

Here is the details about Measuring Radiation Dose according to file attached document  herewith. However, we always measure CPS/CPM simply counts not the RAD or REM. Is there any mathematical/emperical relation available to calculate that?

Or CPS = (Factor?)*RAD/REM

I got the best answer from Mushtaq Ahmad's link as 5 cps per μSv h-1. Its a very helpful information. Thank you.