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In the Time War, nearly all of the Daleks were destroyed, and the Time Lords disappeared. Other races were partially or fully wiped out by side effects of the fighting.
Is it ever revealed how many beings died during the Time War? I'm aware that many, many Time Lords "died" during the War, but most were able to regenerate, at least until they were out of regenerations. Therefore, I'm discarding those "deaths" where the beings survived.
As @UncleMikey says in his answer, it's impossible to get a serious figure for all the deaths from all the species involved (including as 'collateral damage') in all the years (centuries? millenia? all of time and space?) in the Last Great Time War. However, we can get rough approximations for the numbers of the main antagonists (Time Lords and Daleks) killed in the very last confrontation.
From the 50th Anniversary special, The Day of the Doctor:
WAR DOCTOR: Did you ever count?
11TH DOCTOR: Count what?
WAR DOCTOR: How many children there were on Gallifrey that day.
[...]
10TH DOCTOR: Two point four seven billion.
In the last act of the Time War, when the Doctor (apparently) wiped out both the Time Lords and the Daleks, 2.47 billion Gallifreyan children were lost.
Now, what proportion is this likely to be of the entire population?
For my analysis I took the UK as a sample country. (Well, Doctor Who is made there, after all.) According to this government report on the results of census records over the last 40 years, around 22% of the population were children (aged under 16) in 1981, compared with around 19% in 2006. I didn't find any figures from 1945, but it's reasonable to assume the percentage of children in the population would be considerably higher in wartime, as most of the people being killed will be military and therefore adults. So let's say children accounted for 25-30% of the Gallifreyan population at the end of the Last Great Time War. Combining this with our figure of 2.47 billion children gives a final answer of 8-10 billion Gallifreyans.
All I have to go on is this line from the War Doctor in The Day of the Doctor:
There's still a billion billion Daleks up there, attacking.
Obviously this could be hyperbole, but it seems to be the best answer we have for the number of Daleks in that almighty wipeout on the last day of the Time War. It does make sense for the Daleks to outnumber the Time Lords so massively. Time Lord technology is, as we all know, pretty advanced (so much so that even Daleks use it for some of their greatest endeavours), and if the Doctor is anything to go by, a single Time Lord is more than a match for a vast number of Daleks. But the Time Lords were facing annihilation at the end of the Time War; they must have been extremely heavily outnumbered by those exterminatory little buggers in the polycarbide cases.
There is no canonical or out-of-universe statement of the total number of casualties across the entirety of the Time War. We certainly know that entire species were wiped out or nearly so--the Zygons, the Nestene, the Gelth, to name a few--as collateral damage, but since we have no sense of their population figures, nor any comprehensive list of other races and beings destroyed, the question cannot really be answered.
Complicating the inability to answer further is the implication that the Time War rewrote events all the time--as you would imagine a Time War would. Some people who died, un-died (and then, possibly, died again). Some races that were lost were un-lost.
Since the events of the war were "time locked", it should be possible to calculate a final number, but no such calculation has ever been presented, either on-screen or in official statements by production staff.
Is it ever revealed how many beings died during the Time War?
No. There are only hints as to the incomprehensible scale.
It effected multiple civilizations across multiple galaxies. Neither side hesitate in actions that caused collateral damage.
"...you aren't finished yet! Some of the universe is still standing"
Pilot Cass to a "Time Lord" re the War - "The Night of the Doctor"
It effected multiple timelines as both races had access to time travel and would race back through time to alter future events to their advantage. This is the kind of war that featured horrors such as the "Could've Been King with his Army of Meanwhiles and Neverweres"
"At the heart of the war, millions were killed and brought back to life every second." (see "The End of Time")
The only weapon the Time Lords hesitated to use was the "Moment", a weapon that could judge them (and then wipe them out). (see "The Day of the Doctor")
The Time Lord's leader, Rassilion, attempted to win the war by creating a paradox so severe (The "Ultimate Sanction") it would destroy the entire space-time vortex (and the universe). The Time Lords planned to escape the destruction by transforming to become entities of consciousness alone. (see "The End of Time")
The Dalek's attempted (and succeeded in one time line, see "Turn Left", thanks to the 'Trickster' -
'Oh my God, Donna look, the stars are goin out' - Wilfred Mott
) to detonate a "Reality Bomb" to wipe out everything except themselves not only in their current universe but also in all parallel universes. (see "Journey's End")
So, depending on your temporal philosophy, if you think lives lost in other time-lines and parallel universes count as fatalities, the total fatalities from the Time War is in the order of "nearly everyone ever anywhere"
for more background see
