Blender has a measure tool, but it only lets you draw straight lines. I also (speaking personally) find it really fiddly and annoying.
In Blender 2.8, one of the overlays you can display is the length of an edge (find it in the overlays menu). This would display the length of each edge you have selected in edit mode in edge select. It’s in Blender 2.79 too, in the n-panel (if memory serves). Again though, you are talking about straight lines, and you have to add them up yourself.
If you were looking for something like a circumference, you would really need to draw a curve. I think you would have to use scripting. If you drew your curve (maybe using surface snapping) so that it was the circumference you wanted, you can then use bpy.data.curves[‘BezierCircle’].splines[0].calc_length() in the terminal to get the length of that curve (or, to be more specific, the first (and presumably only) spline in that curve object). Obviously change BezierCircle if your object has a different name.
Hope that helps.
