The generalised added-mass coefficients of a torus in translatory and rotational motion in an inviscid incompressible fluid are obtained via an exact solution of Laplace's equation in toroidal coordinates. Of the six possible independent coefficients three are found to have nonzero, finite and separate values, due to symmetry. These are translation in, and perpendicular to the ring plane and rotation around a diameter. For translation normal to the ring plane, the added mass is somewhat larger than the mass of the torus of equal density. This coefficient tends to the torus mass for slender tori (large ratio of ring to core diameters). For translation in the ring plane the added mass tends to one half the torus mass, and for rotation the added inertia is approximately the torus moment of inertia for such slender tori. Simple relations for the added-mass coefficients as a function of the diameter ratio for general tori are also presented.