You Do Need power plug adapter while traveling from South Africa to Denmark.

Here is Why You Need An Adapter

The outlet and plug type used in Denmark are C, E, F and K and in South Africa are C, M and N. This is how they look like.

South Africa

In South Africa, outlets of type C, M and N are in use.

Type C

Type M

Type N

Denmark

In Denmark, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K