  In an effective theory of gravity, thermodynamic quantities of black holes
receive corrections from the infinite series of higher derivative terms. At the
next to leading order, these can be obtained by using only the leading order
solution. In this paper, we push forward this property to the next to next to
leading order. We propose a formula which yields the Euclidean action of
asymptotically flat black holes at the next to next to leading order using only
the solution up to and including the next to leading order. Other conserved
quantities are derived from the Euclidean action via standard thermodynamic
relation. We verify our formula in examples of $D$-dimensional pure gravity and
Einstein-Maxwell theory extended by 4- and 6-derivative terms. Based on our
formula, we also prove that for asymptotically flat black holes, the physical
quantities are invariant under field redefinitions.
