You Do Need power plug adapter while traveling from Christmas Island to São Tomé and Príncipe.

Here is Why You Need An Adapter

The outlet and plug type used in São Tomé and Príncipe are C and F and in Christmas Island is I. This is how they look like.

In Christmas Island, outlets of type I are in use.

Type I

In São Tomé and Príncipe, outlets of type C and F are in use.

Type C

Type F

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