In physics and electrical engineering the reflection coefficient is a parameter that describes how much of a wave is reflected by an impedance discontinuity in the transmission medium. It is equal to the ratio of the amplitude of the reflected wave to the incident wave, with each expressed as phasors. For example, it is used in optics to calculate the amount of light that is reflected from a surface with a different index of refraction, such as a glass surface, or in an electrical transmission line to calculate how much of the electromagnetic wave is reflected by an impedance discontinuity. The reflection coefficient is closely related to the transmission coefficient. The reflectance of a system is also sometimes called a reflection coefficient.

Different disciplines have different applications for the term.

In telecommunications and transmission line theory, the reflection coefficient is the ratio of the complex amplitude of the reflected wave to that of the incident wave. The voltage and current at any point along a transmission line can always be resolved into forward and reflected traveling waves given a specified reference impedance Z₀. The reference impedance used is typically the characteristic impedance of a transmission line that's involved, but one can speak of reflection coefficient without any actual transmission line being present. In terms of the forward and reflected waves determined by the voltage and current, the reflection coefficient is defined as the complex ratio of the voltage of the reflected wave (${\displaystyle V^{-}}$) to that of the incident wave (${\displaystyle V^{+}}$). This is typically represented with a ${\displaystyle \Gamma }$ (capital gamma) and can be written as:

It can also be defined using the currents associated with the reflected and forward waves, but introducing a minus sign to account for the opposite orientations of the two currents:

The reflection coefficient may also be established using other field or circuit pairs of quantities whose product defines power resolvable into a forward and reverse wave. With electromagnetic plane waves, one uses the ratio of the electric fields of the reflected to that of the incident wave (or magnetic fields, again with a minus sign); the ratio of each wave's electric field E to its magnetic field H is the medium's characteristic impedance, ${\displaystyle Z_{0}}$, (equal to the impedance of free space if the medium is a vacuum).

In the accompanying figure, a signal source with internal impedance ${\displaystyle Z_{S}}$ possibly followed by a transmission line of characteristic impedance ${\displaystyle Z_{S}}$ is represented by its Thévenin equivalent, driving the load ${\displaystyle Z_{L}}$. For a real (resistive) source impedance ${\displaystyle Z_{S}}$, if we define ${\displaystyle \Gamma }$ using the reference impedance ${\displaystyle Z_{0}=Z_{S}}$ then the source's maximum power is delivered to a load ${\displaystyle Z_{L}=Z_{0}}$, in which case ${\displaystyle \Gamma =0}$ implying no reflected power. More generally, the squared-magnitude of the reflection coefficient ${\displaystyle |\Gamma |^{2}}$ denotes the proportion of that power that is reflected back to the source, with the power actually delivered toward the load being ${\displaystyle 1-|\Gamma |^{2}}$.

Anywhere along an intervening (lossless) transmission line of characteristic impedance ${\displaystyle Z_{0}}$, the magnitude of the reflection coefficient ${\displaystyle |\Gamma |}$ will remain the same (the powers of the forward and reflected waves stay the same) but with a different phase. In the case of a short circuited load (${\displaystyle Z_{L}=0}$), one finds ${\displaystyle \Gamma =-1}$ at the load. This implies the reflected wave having a 180° phase shift (phase reversal) with the voltages of the two waves being opposite at that point and adding to zero (as a short circuit demands).

The reflection coefficient is determined by the load impedance at the end of the transmission line, as well as the characteristic impedance of the line. A load impedance of ${\displaystyle Z_{L}}$ terminating a line with a characteristic impedance of ${\displaystyle Z_{0}\,}$ will have a reflection coefficient of