How does Locke’s interpretation of the social contract differ from Hobbes’s interpretation?

The differences are fundamental and relate to their respective understandings of what a social contract is for. Locke, like most social contract thinkers, looks upon the arrangement as a means of keeping governmental power in check. For Hobbes, on the other hand, a social contract is a way of keeping the innate greed and selfishness of human beings in check. Locke believes that the people should ultimately control the government; for Hobbes it is the other way around.
Another key difference lies in their respective views concerning natural rights. Locke believes human beings to be endowed with certain innate rights. Locke is no more sentimental than Hobbes when it comes to the purposes of government. It exists to protect our rights, the most important of which is the right to own property.
Hobbes believes that human beings are fundamentally selfish and always look out for themselves. Accordingly, we have no natural rights to speak of in the Lockean sense. In the barbarous state of nature, our natural right consist of grabbing whatever we can lay our hands on. This right is dangerous and needs to be given up when we enter into a contract with an all-powerful sovereign, who keeps all citizens under control.
For Locke, the government can only exercise its authority with the just consent of the governed. As we have seen, it exists purely and solely to protect our natural rights. However, if the government should fail to do so, then, under the right circumstances, we have the right to change it. It is not surprising that Locke's political thought was so influential on American revolutionaries, who put his ideas into practice in their war with the British.
Such a notion is completely unthinkable to Hobbes. He does concede that we do still retain the right to self-defense, however. However, beyond that, we have no right to overthrow the sovereign power. If we are foolish enough to challenge the sovereign, chaos, war, and bloodshed will ensue. Moreover, in the event of success, we would have to replace the old sovereign with a new one. If the new sovereign power were limited, then, according to Hobbes, it would not be truly sovereign. On the other hand, if the new sovereign does have absolute power, it is formally identical to the old sovereign. Overthrowing the old sovereign merely allowed for the possibility of anarchy and disorder.
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