Count Rate Calculator
Calculate CPS, CPM, and Statistical Uncertainty
Understanding Count Rate Calculations
The Count Rate Calculator is an essential tool for nuclear physics, health physics, and radiochemistry. It determines the frequency of radiation events detected over a specific period. Whether you are using a Geiger-Müller counter, a scintillation detector, or analyzing radioactive decay data, converting raw counts into a standardized rate (like CPS or CPM) is the first step in analysis.
What is Count Rate?
Count rate is simply the number of events (counts) detected per unit of time. Unlike a total count, which depends on how long you measure, the count rate allows you to compare the intensity of radiation sources regardless of the measurement duration.
- CPS (Counts Per Second): The standard SI-adjacent unit for intensity.
- CPM (Counts Per Minute): Commonly used in handheld survey meters and Geiger counters.
The Count Rate Formula
To calculate the count rate ($R$), divide the total number of detected events ($N$) by the time interval ($t$) during which measurement took place.
Where:
- R = Count Rate (CPS or CPM)
- N = Total measured counts (dimensionless integer)
- t = Time elapsed
Statistical Uncertainty in Counting
Radioactive decay is a random process governed by Poisson statistics. The reliability of your count rate depends on the total number of counts collected. The standard deviation ($\sigma$) of a single measurement of $N$ counts is approximated by the square root of $N$.
The uncertainty in the count rate ($\sigma_R$) is calculated as:
This calculator provides this uncertainty value, allowing you to report results as Rate ± Error. The Relative Standard Deviation (RSD), expressed as a percentage, helps determine the precision of your measurement. Collecting more counts generally reduces the RSD, improving statistical confidence.
How to Use This Calculator
- Enter Total Counts: Input the raw number of radiation events detected by your instrument.
- Enter Duration: Input the time elapsed during the measurement.
- Select Unit: Choose whether your time input is in seconds, minutes, or hours.
- Calculate: Click the button to see the normalized rates (CPS/CPM) and the statistical error associated with your measurement.