pprox height 3.3cm.
The case is a .303 type. Specifically, with markings 1942, VII Z and D1. There are hundreds of different case types and variations, this is the Canadian version made by Defense Industries in Montreal.
Canada was initially reluctant to go to war but by 1943-45, the 3rd Canadian Division landed on Juno Beach in the Normandy landings and sustained heavy casualties. By the end of D-Day, the Canadians had penetrated deeper into France than either the British or the American troops at their landing sites. In the first month of the Normandy campaign, Canadian, British and Polish troops were opposed by some of the strongest and best trained German troops in the theatre, including the 1st SS Panzer Division Leibstandarte SS Adolf Hitler, the 12th SS Panzer Division Hitlerjugend and the Panzer-Lehr-Division.
The First Canadian Army took over the left flank of the Allied armies on their battle to Berlin after the D-Day landings and set out to clear the Channel Ports as well as eliminate the V-rocket launching sites.
Canadian forces in North-West Europe settled into the Nijmegen Salient and fought in North Western Germany.
This WW2 relic was likely worn by a Canadian Soldier in the above theatre of war. There is some speculation about its use, it was either used as contraband to allow soldiers to gamble and play in between battles (dice were not allowed), it could also have been a type of talisman or lucky charm, i.e. that life was 'a gamble', a 'game' and high risk, and soldiers would make such charms in a manner to deal with this risk or seek to control it. As the dice are often made from animal bones, these bullet dice were often called Kaiser Bill's Bones, when soldiers of WW1 were fighting Kaiser Wilhelm. 
Hazard/Craps ...An early game played with two dice, was mentioned in Geoffrey Chaucer's Canterbury Tales in the 14th century, and this particular relic likely was used to play this game.
These type of bullet dice were used in other wars, including WW1, American Civil War and Napoleonic Wars.
An extraordinary relic indeed. Having survived the horrors of war without being lost, it was likely worn at the end of a fob watch thereafter.