This work focuses on the efficient computation of p-variation. For $p > 1,$ this semi-norm is associated with fractional regularity $s = 1/p < 1$ and the fractional $BV$ space $BV^s.$ It is wellknown in probability theory and has recently gained significance in the context of hyperbolic partial differential equations. The primary motivation of this paper is to calculate p-variation efficiently for numerical schemes of hyperbolic conservation laws. The p-variation is a nonlocal semi-norm. Initially, based on its definition, the cost of computing the p-variation for a piece-wise constant function with N data points appears to be exponential with respect to N. However, We introduce new algorithms featuring polynomial costs, after the recent one provided by Vygantas Butkus and Rimas Norvaisa.