The specifics of the simulated injection choices in the case of stratospheric aerosol injections (SAI) are part of the crucial context necessary for meaningfully discussing the impacts that a deployment of SAI would have on the planet. One of the main choices is the desired amount of cooling that the injections are aiming to achieve. Previous SAI simulations have usually either simulated a fixed amount of injection, resulting in a fixed amount of warming being offset, or have specified one target temperature, so that the amount of cooling is only dependent on the underlying trajectory of greenhouse gases. Here, we use three sets of SAI simulations achieving different amounts of global mean surface cooling while following a middle‐of‐the‐road greenhouse gas emission trajectory: one SAI scenario maintains temperatures at 1.5°C above preindustrial levels (PI), and two other scenarios which achieve additional cooling to 1.0°C and 0.5°C above PI. We demonstrate that various surface impacts scale proportionally with respect to the amount of cooling, such as global mean precipitation changes, changes to the Atlantic Meridional Overturning Circulation and to the Walker Cell. We also highlight the importance of the choice of the baseline period when comparing the SAI responses to one another and to the greenhouse gas emission pathway. This analysis leads to policy‐relevant discussions around the concept of a reference period altogether, and to what constitutes a relevant, or significant, change produced by SAI.