A little bit of necromancy, but this thread is still the #1 result when searching "Rigol DS2000 frequency counter" on google.
I have played a bit with smallish signals and low frequency and have started to establish some minimum specs.
My signal source is an old but well performing HP 8903B Audio Analyzer.
When testing for calibration this unit has always been better than the manual specs by a healthy margin.
Tests have been made with the counter source set to channel 1.
20MHz bandwidth limit was active.
1x probes where used (BNC T connection between 8903B source and analyzer).
Scope Input impedence set to 1Mohm.
Accuracy
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The Rigol counter is a 6 digit unit of unknown accuracy.
The HP counter is a 5 digit unit with a specified accuracy of .004% + 1 digit.
In testing with sine waves of 200mV (RMS) amplitude, The Rigol's first 5 digits match the HP from 20Hz to 100KHz, plus or minus one 5th digit, thus at least matching that spec, might be even better, but I have no way to confirm if the last digit is any good.
Sensitivity
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The Rigol's sensitivity is unspecified
The HP is specified as 5.0mV (RMS) in AC level and signal-to-noise modes
Using a 400Hz sine wave, with the scope set to 100mV/div, the counter is stable for signals down to 25mV (RMS) amplitude. 24mV jumps by several Hz and 23mV jumps all over the place.
I consider the counter output stable when the first 4 digits are constant.
At 1KHz the rigol's needs 26mV (RMS) to stabilize.
10KHz needs 27mV (RMS).
50KHz needs 27mV (RMS).
100KHz needs 27mV (RMS).
If at any time I set the scope to 50mV/div and hear the relay click, the counter becomes jumpy and innacurate with signals smaller than 600mV, thus being rather useless for signals you might wish to observe at that setting.
Conclusion
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After these experiments I think it is safe to describe the counter in the Rigol DS2000 series as a 6 digits counter with an accuracy of at least 0.004 percent and a sensitivity better than 30mV (RMS) for a sine-wave input when the scope's vertical amplifier is set to 100mV per division. The counter was accurate from 20 Hz to 100KHz and as been reported to measure at least up to 400MHz.
Chances are the Rigol DS2000A is the most accurate counter I own, though not the most sensitive.
If someone with access to a better specced lab counter could run a few tests of accuracy at higher frequencies, please post results.