If
A
0
{A_0}
and
A
1
{A_1}
are a compatible couple of Banach spaces, one of which is uniformly convex, then the complex interpolation spaces
[
A
0
,
A
1
]
θ
{[{A_0},{A_1}]_\theta }
are also uniformly convex for
0
>
θ
>
1
0 > \theta > 1
. Estimates are given for the moduli of convexity and smoothness of
[
A
0
,
A
1
]
θ
{[{A_0},{A_1}]_\theta }
in terms of these moduli for
A
0
{A_0}
and
A
1
{A_1}
. In general, up to equivalence of moduli these estimates are best possible.