This transformation plots all resistances onto the diameter of a circle centered on Zo (the characteristic impedance), with a short circuit (0 ohms) on the left and an open circuit ("infinity") on the right. Pure reactances are plotted onto the circumference of the circle, with reactance increasing from zero towards infinite as you move away from the short circuit impedance point towards the open circuit impedance point. The top half of the circle represents increasing inductances and the bottom half increasing capacitances. Impedances having the same value of resistance will fall on circles contained within the unit circle and tangent with the open circuit impedance point. Impedances having the same value of reactance will fall along circular arcs passing through the open circuit impedance point.

Reflection coefficients may be plotted on the Smith Chart in standard polar format: the magnitude of the reflection coefficient (a number between 0 and 1) is the distance out from the center of the chart; the angle of the reflection coefficient indicates the amount of rotation around the chart. 0 degrees corresponds to the open circuit impedance; positive phase angles move across the top (inductive portion) of the chart to 180 degrees at the short circuit impedance point; negative phase angles move across the bottom (capacitive portion) of the chart to -180 degrees at the short circuit impedance point.

The mathematical relationship between reflection coefficient and impedance is

Z/Zo = (1 + ) / (1 - ) or = (Z - Zo) / (Z + Zo)