These comments explain the calculation of sample rate. Sample frequency in Hz is 1/(sample time in seconds).
// sampling rate is [ADC clock] / [prescaler] / [conversion clock cycles]
// for Arduino Uno ADC clock is 16 MHz and a conversion takes 13 clock cycles
Sampling rate = ADC clock / prescaler / conversion clock cycles
For example, with a prescaler of 32 the sampling rate is, 16MHz/32/13 = 38.462 kHz
and the ADC clock is 500kHz
Is that clear?
@jafal
38.4kHz is the sampling frequency.
The maximum frequency you can sample is always 1/2 of the sampling frequency
The the max input frequency on the ADC pin is 38.4kHz / 2 = 19.2kHz