Circumference, perimeter, periphery, circuit, compass are comparable because all in their basic senses denote a continuous line enclosing an area or space. They differ, however, in the extent to which they retain this meaning and in the number and character of their acquired implications and connotations.
Precisely, circumference designates either the line that describes a circle or an ellipse or the length of such a line; in extended use it is applied to something felt as having a center (see CENTER).
Perimeter is more comprehensive than circumference; it includes not only the line that bounds any circular figure or area, but also the broken line that encloses any polygon ; moreover it may designate the whole outer boundary of a body, especially a more or less spherical body.
Periphery is sometimes interchangeable with perimeter but it is more frequently used in an extended sense. More often than any other word in this group it is referred to the actual edge or border or boundaries of something concrete. Occasionally it suggests limits which cannot be exceeded.
Circuit has become so tied up with the idea of a journey round the periphery of something that the two ideas are fused.
On the other hand, compass usually refers to the area or space within an enclosing line or the ground that figuratively might be covered by the leg of a compass describing such a line.