Yes it is, because both of them are just the distance around the circle, the equation forthe circumference is pi x Diameter.
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Perimeter is the distance around something. In the case of a circle (or other curved figures), this is simply called the perimeter, so I would say perimeter is the same as circumference. Except that it is uncommon to call the circumference of a circle the "perimeter".
The circumference of a circle represents its perimeter and the distance around it.
A circumference is the perimeter of a circle
Circumference ("perimeter") of a circle = (pi) x (diameter of the circle)
circumference