Radical formation in polycrystalline lithium formate monohydrate after irradiation with γ rays, protons and nitrogen ions at room temperature was studied by continuous-wave electron paramagnetic resonance (EPR) spectroscopy. The linear energy transfer (LET) of the various radiation beams was 0.2, 0.7–3.9 and 110–164 keV/µm for γ rays, protons and nitrogen ions, respectively. Doses between 5 and 20 Gy were given. The EPR reading (the area under the EPR absorption resonance) increased linearly with dose for all types of radiation. As the LET increased, the relative effectiveness (the EPR reading per dose relative to that for γ rays) decreased, while the EPR line width increased. Track structure theory and modeling of detector effectiveness predicted the dosimeter response observed after proton and nitrogen-ion irradiation. A semi-empirical line broadening model including dipolar spin-spin interactions was developed that explained the dependence of the line width on LET. The findings indicate that the local radical density in lithium formate is increased after high-LET irradiation.