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Given a big divisor $D$ on a normal complex projective variety $X$, we showthat the restricted volume of $D$ along a very general complete-intersectioncurve $C\subset X$ can be read off from the Okounkov body of $D$ with respectto an admissible flag containing $C$. From this we deduce that if two bigdivisors $D_1$ and $D_2$ on $X$ have the same Okounkov body with respect toevery admissible flag, then $D_1$ and $D_2$ are numerically equivalent.

Okounkov bodies and restricted volumes along very general curves