The tunability of the longitudinal localized surface plasmon resonances (LSPRs) of metallic nanoarcs is demonstrated with key relationships identified between geometric parameters of the arcs and their resonances in the infrared. The wavelength of the LSPRs is tuned by the mid-arc length of the nanoarc. The ratio between the attenuation of the fundamental and second order LSPRs is governed by the nanoarc central angle. Beneficial for plasmonic enhancement of harmonic generation, these two resonances can be tuned independently to obtain octave intervals through the design of a non-uniform arc-width profile. Because the character of the fundamental LSPR mode in nanoarcs combines an electric and a magnetic dipole, plasmonic nanoarcs with tunable resonances can serve as versatile building blocks for chiroptical and nonlinear optical devices.