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We present a galaxy classification system for 238 (E1.Sdm) CALIFA (Calar Alto Legacy Integral Field Area) galaxies based on the shapes and amplitudes of their circular velocity curves (CVCs). We infer the CVCs from the de-projected surface brightness of the galaxies, after scaling by a constant mass-to-light ratio based on stellar dynamics - solving axisymmetric Jeans equations via fitting the second velocity moment Vrms = √V² + σ² of the stellar kinematics. We use principal component analysis (PCA) applied to the CVC shapes to find characteristic features and use a k-means classifier to separate circular curves into classes. This objective classification method identifies four different classes, which we name slow-rising (SR), flat (FL), round-peaked (RP) and sharp-peaked (SP) circular curves. SR are typical for low-mass, late-type (Sb.Sdm), young, faint, metal-poor and disc-dominated galaxies. SP are typical for high-mass, early-type (E1-E7), old, bright, metal-rich and bulge-dominated galaxies. FL and RP appear presented by galaxies with intermediate mass, age, luminosity, metallicity, bulge-to-disc ratio and morphologies (E4-S0a, Sa-Sbc). The discrepancy mass factor, fd = 1 - M*/Mdyn, have the largest value for SR and SP classes (~ 74 per cent and ~ 71 per cent, respectively) in contrast to the FL and RP classes (with ~ 59 per cent and ~ 61 per cent, respectively). Circular curve classification presents an alternative to typical morphological classification and appears more tightly linked to galaxy evolution. [ABSTRACT FROM AUTHOR]