Abstract The separate effects of flame stretch and flame curvature are investigated in the present study considering a stationary spherical flame configuration that experiences no stretch but has a finite curvature. A theoretical expression for the flame displacement speed, derived from asymptotic analysis, is compared with numerical simulations exhibiting very good agreement between the two. The notion of the curvature Markstein length is introduced, a coefficient which is independent from diffusion and chemical reaction effects, in contrast to the Markstein length associated with total flame stretch. It is shown that its value depends strongly on the iso-surface chosen to define the flame, exhibiting large variations in the preheat zone and more insensitive behavior close to the burned side.