In this paper, we introduce a very fast method to compute the current distribution in helically wound thin conductors when one or many of them are arranged in a symmetrical manner to form a single-layer power cable. The method relies on two different approaches to find the magnetic vector potential due to helically wound current sheets. By invoking relevant symmetry arguments associated with the geometry of the problem and neglecting the thickness of the tape conductors, we show that this 3-D problem can be reduced to a computationally small 1-D problem whose domain lies along the half-width of any of the constituting conductor. As a consequence, the proposed method is very efficient in terms of computational time, and it is more accurate than many previous 2-D methods that cannot take into account the twist pitch. Since the nonlinear resistivity of the superconducting material can easily be treated with this method, it can be used to find current and field distributions, as well as ac losses in high-temperature superconductor coils and cables made of coated tapes. To verify the validity of the proposed method, we performed experimental measurements of ac losses in two configurations of solenoid-type cables made of a sample of YBCO-coated conductor tape. Excellent agreement was observed between the experimental data and the simulation results.