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A new method to calculate the lattice contribution to electric field gradients at a nuclear site in tetragonal crystals is developed. The crystal is regarded as an assembly of positive ions at lattice points embedded in a uniform background of negative charge (point charge model). The method uses Euler-Maclaurin formula and makes the plane-wise summation in the direct crystal space unlike most of the previous methods utilising Fourier transform to reciprocal space. The numerical values obtained using the above approach agree well with previous results.