We describe a universal linear relationship between the acquisition magnetic field, B, and thermoremanent magnetization M tr (T r ) measured at room temperature T r . The efficiency ɛ(T r ) of a remanent magnetization (REM) is the ratio of the natural remanent magnetization M nr (T r ) to the saturation remanence J sr (T r ) . We report a power law relationship with exponent related to J s (T r ) and unit slope indicating a linear relationship. Thus logɛ(T r ) of M tr (T r ) in equidimensional-shaped magnetic minerals of contrasting saturation magnetization J s (T r ) plots linearly with the logarithm of the applied magnetic field B along separate grain-size-independent straight lines with nearly unit slope and offsets related to J s (T r ). This empirical relationship is well suited for paleofield-intensity estimation, predicts strong magnetization of hematite and pyrrhotite in weak fields, and can be used as an assessment tool for observed remanence in planetary and meteoritic objects.