This paper presents a simple method for generating finite difference formulas on arbitrarily spaced grids. The method uses recursion relations to compute weights for approximating derivatives of any order on one-dimensional grids with arbitrary spacing. The weights are calculated for any order of derivative and any order of accuracy. The method is particularly useful for dynamically changing grids, as it requires only four arithmetic operations per weight. The algorithm is described in detail, including the notation and steps for computing the weights. The derivation of the algorithm is based on Lagrange interpolation and the properties of polynomials. The paper also includes tables of weights for special cases, such as centered and one-sided approximations on equidistant grids. These tables are provided for derivatives up to the fourth order and for different grid spacings. The weights for these cases are given, with the note that they should be divided by the grid spacing raised to the power of the derivative order for non-unit spacings. The paper acknowledges the helpful comments of the referee in generalizing and simplifying the algorithm.This paper presents a simple method for generating finite difference formulas on arbitrarily spaced grids. The method uses recursion relations to compute weights for approximating derivatives of any order on one-dimensional grids with arbitrary spacing. The weights are calculated for any order of derivative and any order of accuracy. The method is particularly useful for dynamically changing grids, as it requires only four arithmetic operations per weight. The algorithm is described in detail, including the notation and steps for computing the weights. The derivation of the algorithm is based on Lagrange interpolation and the properties of polynomials. The paper also includes tables of weights for special cases, such as centered and one-sided approximations on equidistant grids. These tables are provided for derivatives up to the fourth order and for different grid spacings. The weights for these cases are given, with the note that they should be divided by the grid spacing raised to the power of the derivative order for non-unit spacings. The paper acknowledges the helpful comments of the referee in generalizing and simplifying the algorithm.