In this article, we work with certain families of ideals called
p
p
-families in rings of prime characteristic. This family of ideals is present in the theories of tight closure, Hilbert-Kunz multiplicity, and
F
F
-signature. For each
p
p
-family of ideals, we attach an Euclidean object called
p
p
-body, which is analogous to the Newton Okounkov body associated with a graded family of ideals. Using the combinatorial properties of
p
p
-bodies and algebraic properties of the Hilbert-Kunz multiplicity, we establish a Volume = Multiplicity formula for
p
p
-families of
m
R
\mathfrak {m}_{R}
-primary ideals in a Noetherian local ring
R
R
.