Statisticsof Wars, Oppressions and Atrocities of the Nineteenth Century(the1800s) is an excellent site that summarizes the different statistical sources:
As an approximation, dead from both military and and non-battlefield causes might be:
- UK a bit over 20,000
- France close to 100,000
- Turkey maybe 45,000
- Russia, 100,000+
Also, some authors have put the total death toll in the conflict at over one million.