Thermal fluctuation analysis is a new method of determining 'magnetic grain size' v and microscopic coercive force Hk in particles too small for direct domain observations. When it is used with single-physical grain volume and Hk is usually closely related to grain shape. For multidomain particles, v corresponds to one Barkhausen jump of a domain wall, and Hk describes the opposition to wall motion. The technique require three steps: (1) measurement of coercive force Hc and saturation magnetization over a broad temperature range, (2) separation of the contributions of Hk and the 'fluctuation field' Hq to Hv, in a manner suggested by the N¿el (1949) theory, and (3) calculation of average values of v and room temperature Hk from Hq(T) and Hk(T). Thermal fluctuation analysis is the only simple means of calculating average v and Hk separately. If thermal fluctuations are important, as is always the case for the fine particles or small wall displacements involved in low-field thermoremanence or viscous remanence, thermal and alternating field demagnetization do not resolve v and Hk unambiguously, because observed coercivities and blocking temperatures TB depend on both v and Hk. The method is tested by applying it to single-domain materials of known grain size. Fluctuation analysis is then used to infer the possible domain structure of 500- to 2200-¿ magnetite particles and to point up a deficiency in the Stacey and Banerjee (1974) procedure for detecting ordering or lattice defects impeding domain wall motion. Potential broader applications include determining mean grain sizes of single, and under favorable conditions, double populations of magnetic carriers in rocks, defining average elongation for single-domain particles in rocks and synthetic dispersions (e.g., magnetic recording tapes), and deducing the mechanism of anisotropy (shape, crystalline or magnetoelastic) or of opposition to wall motion (strain, inclusion or magnetostatic). The main limitations to the method are that the averages of v and Hk become nonstationary if Hc measurements are made within the TB range and that step 2 (separation of HB(T) and Hq(T) is difficult unless Hk is predominantly due to a single anisotropy or wall opposition mechanism.