A sheet measuring apparatus includes a first rotating member that includes a first peripheral surface portion that contacts a transported sheet; a second rotating member that includes a second peripheral surface portion made of a material different from that of the first peripheral surface portion, the second peripheral surface contacting the first peripheral surface portion and not contacting the sheet; a first rotation amount detecting unit that detects a first rotation amount that is a rotation amount of the first rotating member; a second rotation amount detecting unit that detects a second rotation amount that is a rotation amount of the second rotating member, the second rotation amount being used for a calculation related to the transported sheet; and a fault detecting unit that detects a fault that has occurred in the first rotating member on the basis of the first rotation amount and the second rotation amount.