  Let $X$ and $X'$ be nonsingular projective $3$-folds related by a flop of a
disjoint union of $(-2)$-curves. We prove a flop formula relating the
Donaldson-Thomas invariants of $X$ to those of $X'$, which implies some simple
relations among BPS state counts. As an application, we show that if $X$
satisfies the GW/DT correspondence for primary insertions and descendants of
the point class, then so does $X'$. We also propose a conjectural flop formula
for general flops.
