AngPow computes the auto (z1 = z2) and cross (z1 ≠ z2) angular power spectra between redshift bins (i.e. Cℓ(z1,z2)). The developed algorithm is based on developments on the Chebyshev polynomial basis and on the Clenshaw-Curtis quadrature method. AngPow is flexible and can handle any user-defined power spectra, transfer functions, bias functions, and redshift selection windows. The code is fast enough to be embedded inside programs exploring large cosmological parameter spaces through the Cℓ(z1,z2) comparison with data.