Quantum-dot cellular automata (QCA), which is a burgeoning technique at nanoscale region to take the important place of complementary metal-oxide-semiconductor technology, has been studied for several years. The recent primary research emphasis is mainly focusing on circuit design, for instance, full adders (FAs) and multiplexers. The authors will present a new five-input majority gate to construct FAs. Three QCA normalised FAs based on different logical expressions are then selected and designed, denoted as NFA1-NFA3, respectively. To conveniently compare with existing adders, three simplified FAs are also designed, named SFA1-SFA3. Analysis results indicate that SFA3 presents better performance in some extent. © 2017 Institution of Engineering and Technology. All rights reserved.