A systematic analysis of the relationship between spontaneous fission and $\alpha$-decay half-lives is performed for actinides and superheavy nuclei in the ground state. The ratio of logarithmic half-lives exhibits regular trends with nuclear mass and charge numbers, showing almost constant behavior at fixed neutron excess. Based on these systematics, a new semiempirical formula is proposed that relates spontaneous fission half-lives to $\alpha$-decay half-lives and neutron excess. The formula contains only three fitted parameters and provides a unified description for nuclei of different parities without introducing separate hindrance factors. It reproduces experimental spontaneous fission half-lives with a mean absolute deviation of 0.94 orders of magnitude for the dataset of 78 nuclei. A detailed comparison of the predicted half-lives calculated using microscopic-macroscopic and self-consistent microscopic models, more complex empirical parametrizations, and the new formula is presented. The formula can be used to predict spontaneous fission half-lives and validate experimental data, and it provides a criterion to determine the dominant decay mode ($\alpha$ decay or spontaneous fission). The existence of a fundamental relationship between spontaneous fission and $\alpha$-decay processes is discussed.

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• Alpha decay
• Fission
• Lifetimes & widths
• Nuclear reactions