There is no universal pixel value for a button corner. Start with the visual language of the interface: compact tools may use subtle rounding, while friendly or touch-first controls may be softer. Then choose a small set of radius tokens and reuse them across buttons with the same role.
Check the button at its real height. An extremely large radius creates a pill; a radius greater than half the height will not make it rounder. Compare default, hover, focus, and disabled states so the silhouette remains consistent. A border-radius generator can help preview options.
Consistency and accessible focus treatment matter more than the exact radius.
Akousa