Is there a standard button size?

What size buttons do I need?

Generally your buttonhole should be 1/8" bigger than the widest part of the button unless the button is domed. If your initial button was a flat 15mm, a domed 15mm button is probably too big for the same buttonhole. Standard Sizes: Sleeve buttons are usually between 11-13mm.

See https://support.google.com/accessibility/android/answer/7101858?hl=en which says that a touch target should — at minimum — be 48x48dp

Outdated (see comments below): Android Design Guidelines specifically call out 48dp as the recommended minimum size for any touchable object. See "48dp Rhythm": http://developer.android.com/design/style/metrics-grids.html

You may find this helpful: http://www.lukew.com/ff/entry.asp?1085. About 8mm (50 dips) should be OK.

Just take a look at the Android Design Guidelines for Buttons:

Material Design Guideline for Button size and padding