At closest it is 7.5 billion km and at farthest it is 4.28 billion km.

in the solar system travel in elliptical orbits rather than perfect circles, and so the distance between them is constantly changing. At its most distant, when the two bodies (Earth and Pluto) are on the opposite sides of from one another, Pluto lies 7.5 billion km from Earth. They are at their closest when the two are on same side of Sun and distance is only 4.28 billion km.