Combining quantum and Bayesian principles leads to optimality in metrology, but exact solutions can be hard to find. This work mitigates this problem with a novel class of exactly solvable optimisation equations. For any quantity isomorphic to a location parameter, rules to devise optimal measurements are given in closed form. These are valid for any parameter range, prior information, or state, and the associated estimators apply to finite samples. This framework unifies the metrology of locations, scales, and other parameter types such as relative weights, for which hyperbolic errors are required. But the central advantage lies on its simplifying power: searching for good strategies amounts to identifying which symmetry leaves a state of maximum ignorance invariant, irrespective of error bounds. This reduces the number of calculations needed in practice and enables the rigorous application of quantum metrology to fundamental physics, where symmetries play a key role.