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 e(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 loge(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. D 2004 Elsevier B.V. All rights reserved.