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The precise calculations of the Wigner's d-matrix are important in variousresearch fields. Due to the presence of large numbers, direct calculations ofthe matrix using the Wigner's formula suffer from loss of precision. We presenta simple method to avoid this problem by expanding the d-matrix into a complexFourier series and calculate the Fourier coefficients by exactly diagonalizingthe angular-momentum operator $J_{y}$ in the eigenbasis of $J_{z}$. This methodallows us to compute the d-matrix and its various derivatives for spins up to afew thousand. The precision of the d-matrix from our method is about $10^{-14}$for spins up to $100$.

High-precision evaluation of Wigner's d-matrix by exact diagonalization