Quantum-dot cellular automata (QCA) is a highly attractive alternative to CMOS for future digital circuit design, relying on its high-performance and low-power-consumption features. This paper analyzes and compares previously published five-input majority gates. These designs do not perform well in terms of physical properties, especially concerting power consumption. Therefore, an ultra-low-power five-input majority gate in one layer is proposed, which uses a minimum number of cells and smaller area, and achieves the expected highly polarized output compared with previous designs. In order to evaluate its practicability, a new one-bit coplanar full-adder is proposed. The analysis results show that this full-adder performs well compared with existing multilayer and single-layer designs. The number of cells of the proposed design is reduced by 7.14% to get the same area and clock delay compared with the best coplanar full-adder. In addition, its power dissipation is also reduced by 9.28% at 0.5[Formula: see text], 11.09% at 1[Formula: see text] and 12.66% at 1.5[Formula: see text] in terms of average energy dissipation compared with the best single-layer design. QCADesigner tool is used to verify the simulation results of the proposed designs and QCAPro tool is used to evaluate the power dissipation of all considered designs.