Abstract: Reconstructions of volcanic aerosol radiative forcing are required to understand past climate variability. Currently, reconstructions of pre‐20th century volcanic forcing are derived from sulfate concentrations measured in polar ice cores, mainly using a relationship between the average ice‐sheet sulfate deposition and stratospheric sulfate aerosol burden based on a single explosive eruption—the 1991 eruption of Mt. Pinatubo. Here we estimate volcanic radiative forcings and associated uncertainty ranges from ice‐core sulfate records of eight of the largest bipolar deposition signals in the last 2,500 years using statistical emulation of a perturbed parameter ensemble of aerosol‐climate model simulations of explosive eruptions. Extensive sampling of different combinations of eruption source parameters using the emulators reveals that a very wide range of eruptions in different seasons with different sulfur dioxide emissions, eruption latitudes, and emission altitudes produce ice‐sheet sulfate deposition consistent with ice‐core records. Consequently, we find a large range in the volcanic forcing that can be directly attributed to the unknown eruption source parameters. We estimate that the uncertainty in volcanic forcing caused by many plausible eruption realizations leads to uncertainties in the global mean surface cooling of around 1°C for the largest unidentified historical eruptions. Our emulators are available online (https://cemac.github.io/volcanic-forcing-deposition) where eruption realizations for given ice‐sheet sulfate depositions can be explored.