Unique: Your champion gains 32 health per stack, receiving 2 stacks for a kill and 1 stack for an assist. This effect can stack 20 times; you lose a third of your stacks if you die. At 20 stacks, your champion takes 15% less damage.
Even at 20 stacks Leviathan does not give the most health of any item. The Leviathan would give 820 HP compared to the Warmog's Armor base amount of 920.
15% damage reduction increases effective health, but not at a fixed amount. The effective health granted by the 15% reduction increases with more armor/magic resist, where 0 armor/magic resist grants 17.6% increase while 100 armor/magic resist grants 35.3% increase. Due to how the damage reduction scales, it is more efficient on champions with a high health ratings.
Not including base stats, this gives a fully stacked Leviathan an effective health of 965.
As a single purchase without including armor/magic resist, it would take a base health of 1733 for a fully stacked Leviathan to provide an effective health equal to a fully stacked Warmog's Armor (at 1270 health).
Almost all champions will have more than 1733 HP by level 18, meaning the EHP granted by a fully stacked Leviathan will almost always outstrip Warmog's Armor at end game.
The stacking buff granted by Leviathan when a kill or assist is scored is called "Leviathan Armor".
Giant's Belt costs less at 1110g, and provides more health up to 7 stacks.
If one has a Ruby Crystal and the upgrade cost of 800 gold, selling the Ruby Crystal grants a total of 1132 gold: enough to buy a Giant's Belt.
Unique passive: Your champion gains 37.5 health per stack, receiving 2 stacks for a kill or 1 stack for an assist. This effect can stack 20 times; you lose a third of your stacks if you die. At 20 stacks, your champion takes 15% less damage.