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Reversible logic is used increasingly to design digital circuits with lower power consumption. The parity preserving (PP) property contributes to detect permanent and transient faults in reversible circuits by comparing the input and output parity. Multiplication is also considered one of the primary operations in both digital and analog circuits due to its wide applications in digital signal processing and computer arithmetic operations. Accordingly, Vedic mathematics, as a set of techniques sutras, has become popular and is extensively used to solve mathematical problems more efficiently and faster. This work proposes three PP reversible blocks, N1, N2, and N3, which are used to develop a novel effective 2‐bit PP reversible Vedic multiplier and 4‐bit ripples carry adders (RCAs). Moreover, 2‐bit Vedic multiplier and RCA are used to develop the 4‐bit PP reversible Vedic multiplier. The proposed designs outperform the most relevant state‐of‐the‐art structures in terms of garbage output (GO), constant input (CI), gate count (GC), and quantum cost (QC). Average savings of 22.37%, 35.44%, 35.44%, and 34.76%, and 17.76%, 26.60%, 24.52%, and 27.27% respectively, are observed for two‐bit and four‐bit PP reversible Vedic multipliers in terms of QC, GO, CI and GC as compared to previous works. [ABSTRACT FROM AUTHOR]