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The measurement of ionizing radiation is sometimes expressed as being a rate of counts per unit time registered by a radiation monitoring instrument, of which counts per minute and counts per second are commonly used. Count rates are normally associated with the measurements of particles, such as alpha particles and beta particles. For gamma ray and X-ray dose measurements a unit such as the sievert is normally used.
This measurement is the rate of events registered by the measuring instrument, not the rate of events at the point of original emission. For radioactive decay measurements it must not be confused with disintegrations per unit time (dpm), which represents the rate of atomic disintegration events at the source of the radiation. 
Counts can be expressed as a total amount integrated over any time period, but cps and cpm are generally accepted practical count rate measurements. They are not an SI unit, but are a de facto radiological unit of measure. Note that radiation intensity is the count rate which takes into account the energy levels of the radiation being measured.
Counts per minute (abbreviated to cpm) is a measure of the detection rate of ionization events per minute. Counts are only manifested in the reading of the measuring instrument, and are not an absolute measure of the strength of the source of radiation. Whilst an instrument can display at a rate of cpm, it does not have to detect counts for one minute, as it can infer the total per minute.
Counts per second (abbreviated to cps) is used for measurements when higher count rates are being encountered, or if hand held radiation survey instruments are being used which can be subject to rapid changes of count rate when the instrument is moved over a source of radiation in a survey area.
In Radiation Protection Instrumentation practice, an instrument which reads a rate of detected events is normally known as a ratemeter, whereas an instrument which totalises the events detected over a time period is known as a scaler. This colloquial use stems from the early days of electronic counting, when a scaling circuit was required to reduce count rate to that which mechanical counters could register. 
Count rate does not universally equate to dose rate, and there is no simple universal conversion factor. Any conversions are instrument-specific.
Counts is the number of events detected, but dose rate relates to the amount of ionising energy deposited in the sensor of the radiation detector. The conversion calculation is dependent on the radiation energy levels, the type of radiation being detected and the radiometric characteristic of the detector.
The continuous current ion chamber instrument can easily measure dose but cannot measure counts. However the Geiger counter can measure counts but not the energy of the radiation, so a technique known as energy compensation of the detector tube is used to produce a dose reading. This modifies the tube characteristic so each count resulting from a particular radiation type is equivalent to a specific quantity of deposited dose.
Disintegrations per minute (dpm) and disintegrations per second are measures of the activity of the source of radioactivity. The SI unit of radioactivity, the becquerel, is equivalent to one disintegration per second, it should not be confused with cpm. Becquerels is the strength of the source of radiation, but cpm is the number of counts received by an instrument from that source.
The efficiency of the radiation detector (e.g. scintillation counter) and its relative position to the source of radiation must be accounted for when relating cpm to dpm. Dpm is the number of atoms that have decayed, not the number of atoms that have been measured as decayed.