Core jam indicators for use with coring tools include a plug coupled with an inner barrel and configured to selectively close the entrance of the inner barrel. The plug has at least one fluid port extending through a wall of the plug between an interior and an exterior of the plug. The mandrel at least partially covers the at least one fluid port of the plug in an activated position and the at least one fluid port is at least partially uncovered by the mandrel in a deactivated position. The mandrel is coupled to the inner barrel. A piston force acting on the mandrel resulting from a pressure difference above and below the mandrel acts over an area smaller than a maximum transverse cross-sectional area of the inner barrel. Coring tools include such core jam indicators. Components are provided and assembled to form such core jam indicators.