A realisation of a graph in the plane as a bar-joint framework is rigid if there are finitely many other realisations, up to isometries, with the same edge lengths. Each of these finitely-many realisations can be seen as a solution to a system of quadratic equations prescribing the distances between pairs of points. For generic realisations, the size of the solution set depends only on the underlying graph so long as we allow for complex solutions. The realisation number of the graph is the cardinality of this solution set. In this talk, we will provide a characterisation of the realisation number of a minimally rigid graph as a tropical intersection product. Explicitly, our characterisation uses tropical geometry to express the realisation number as an intersection of Bergman fans of the cycle matroid. As a consequence, we derive a combinatorial upper bound on the realisation number involving the Tutte polynomial. Moreover, we provide computational evidence that our upper bound is usually an improvement on the mixed volume bound. This is joint work with Oliver Clarke, Sean Dewar, Daniel Green-Tripp, James Maxwell, Tony Nixon and Yue Ren.