In the original version of his book "The Great Terror," Robert Conquest gave the following estimates of those arrested, executed, and incarcerated during the height of the Purge:
Arrests, 1937-1938 - about 7 million
Executed - about 1 million
Died in camps - about 2 million
In prison, late 1938 - about 1 million
In camps, late 1938 - about 8 million
Conquest concluded that "not more than 10 percent of those then in camp survived." Updating his figures in the late 1980s based on recently-released archival sources, he increased the number of "arrests" to 8 million, but reduced the number in camps to "7 million, or even a little less." This would give a total death toll for the main Purge period of just under ten million people. About 98 percent of the dead (Gendercide Watch's calculation) were male.
The estimates are "only approximations," Conquest notes, and "anything like complete accuracy on the casualty figures is probably unattainable." But "it now seems that further examination of the data will not go far from the estimates we now have except, perhaps, to show them to be understated" and "in any case, the sheer magnitudes of the Stalin holocaust are now beyond doubt." He cites Joseph Berger's remark that the atrocities of Stalin's rule "left the Soviet Union in the condition of 'a country devastated by nuclear warfare.'" (All figures and quotes from Conquest, The Great Terror: A Reassessment, pp. 485-88.)
I've heard the figure of 27 million.
Stalin himself admitted to 10 million dying during collectivisation.
There are estimates that over 30 million people were sent to the Gulags and as many as 10million died in them.