Structural and optical high-pressure study of FASnBr3 (FA = formamidinium) revealed a cubic to orthorhombic phase transition near 1.4 GPa accompanied by a huge band gap red-shift from 2.4 to 1.6 eV, which is followed by a blue-shift of ∼0.2 eV upon further pressure increase. DFT calculations indicate that the variation in band gap is related to changes in Sn-Br bond length alternation, with an equalization of such difference predicted at high pressure. Extending the calculations to analogous lead-free systems provides a unifying mechanistic picture of pressure-induced band gap tuning in tin halide perovskites, which is correlated to the variation of specific structural parameters. These results represent a solid guide to predict and modulate the pressure-response of metal halide perovskites based on the knowledge of their structural properties at ambient pressure. This journal is © The Royal Society of Chemistry.