Magnetization loss on a twisted superconducting (SC) tape in a ramped magnetic field is theoretically investigated through the use of a power law for the electric field--current density characteristics and a sheet current approximation. First, the Maxwell equation in a helicoidal coordinate system is derived to model a twisted SC tape, taking account of the response to the perpendicular field component in the steady state. We show that a loosely twisted tape can be viewed as the sum of a portion of tilted flat tapes of infinite length by examining the perpendicular field distribution on a twisted tape. The analytic formulae for both magnetization and loss power in the tilted flat tape approximation are verified based on the analytic solution of the reduced Maxwell equation in the loosely twisted tape limit of $L_{rm p}rightarrow infty$ with the twist pitch length $L_{rm p}$. These analytic formulae show that both magnetization and loss power decrease by a factor of $B(1+1/2n,1/2)/pi$ (where $B$ is the beta function) for an arbitrary power of SC nonlinear resistivity $n$, compared with those in a flat tape of infinite length. Finally, the effect of the field-angle dependence of the critical current density $J_{rm c}$ on the loss power is investigated, and we demonstrate that it is possible to obtain an approximate estimate of the loss power value via $J_{rm c}$ in an applied magnetic field perpendicular to the tape surface (i.e., parallel to the $c$ axis).
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