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We evaluate the total probability of human extinction from naturally occurring processes. Such processes include risks that are well characterized such as asteroid impacts and supervolcanic eruptions, as well as risks that remain unknown. Using only the information that Homo sapiens has existed at least 200,000 years, we conclude that the probability that humanity goes extinct from natural causes in any given year is almost guaranteed to be less than one in 14,000, and likely to be less than one in 87,000. Using the longer track record of survival for our entire genus Homo produces even tighter bounds, with an annual probability of natural extinction likely below one in 870,000. These bounds are unlikely to be affected by possible survivorship bias in the data, and are consistent with mammalian extinction rates, typical hominin species lifespans, the frequency of well-characterized risks, and the frequency of mass extinctions. No similar guarantee can be made for risks that our ancestors did not face, such as anthropogenic climate change or nuclear/biological warfare.