Assume
G
\mathbf {G}
is a connected reductive algebraic group defined over an algebraic closure
K
=
F
¯
p
\mathbb {K} = \overline {\mathbb {F}}_p
of the finite field of prime order
p
>
0
p>0
. Furthermore, assume that
F
:
G
→
G
F : \mathbf {G} \to \mathbf {G}
is a Frobenius endomorphism of
G
\mathbf {G}
. In this article we give a formula for the value of any
F
F
-stable character sheaf of
G
\mathbf {G}
at a unipotent element. This formula is expressed in terms of class functions of
G
F
\mathbf {G}^F
which are supported on a single unipotent class of
G
\mathbf {G}
. In general these functions are not determined, however, we give an expression for these functions under the assumption that
Z
(
G
)
Z(\mathbf {G})
is connected,
G
/
Z
(
G
)
\mathbf {G}/Z(\mathbf {G})
is simple and
p
p
is a good prime for
G
\mathbf {G}
. In this case our formula is completely explicit.