Radiation resistance is that part of an antenna's feedpoint electrical resistance caused by the emission of radio waves from the antenna. A radio transmitter applies a radio frequency alternating current to an antenna, which radiates the energy of the current as radio waves. Because the antenna is absorbing the energy it is radiating from the transmitter, the antenna's input terminals present a resistance to the current from the transmitter.

Radiation resistance is an effective resistance, due to the power carried away from the antenna as radio waves. Unlike conventional ohmic resistance, radiation resistance is not an opposition to current (resistivity) of the imperfect conducting materials the antenna is made of. The radiation resistance (${\displaystyle \ R_{\mathsf {rad}}\ }$) is conventionally defined as the value of electrical resistance that would dissipate the same amount of power as heat, as is dissipated by the radio waves emitted from the antenna. From Joule's law, it is equal to the total power ${\displaystyle \ P_{\mathsf {rad}}\ }$ radiated as radio waves by the antenna, divided by the square of the RMS current ${\displaystyle \ I_{\mathsf {RMS}}\ }$ into the antenna terminals: ${\displaystyle \ R_{\mathsf {rad}}=P_{\mathsf {rad}}/I_{\mathsf {RMS}}^{2}~.}$

The feedpoint and radiation resistances are determined by the geometry of the antenna, the operating frequency, and the antenna location (particularly with respect to the ground). The relation between the feedpoint resistance (${\displaystyle \ R_{\mathsf {in}}\ }$) and the radiation resistance (${\displaystyle \ R_{\mathsf {rad}}\ }$) depends on the position on the antenna at which the feedline is attached. The relation between feedpoint resistance and radiation resistance is particularly simple when the feedpoint is placed (as usual) at the antenna's minimum possible voltage / maximum possible current point; in that case, the total feedpoint resistance ${\displaystyle \ R_{\mathsf {in}}\ }$ at the antenna's terminals is equal to the sum of the radiation resistance plus the loss resistance ${\displaystyle \ R_{\mathsf {loss}}\ }$ due to "Ohmic" losses in the antenna and the nearby soil: ${\displaystyle \ R_{\mathsf {in}}=R_{\mathsf {rad}}+R_{\mathsf {loss}}\ .}$ When the antenna is fed at some other point, the formula requires a correction factor discussed below. In a receiving antenna the radiation resistance represents the source resistance of the antenna, and the portion of the received radio power consumed by the radiation resistance represents radio waves re-radiated (scattered) by the antenna.

Electromagnetic waves are radiated by electric charges when they are accelerated. In a transmitting antenna, radio waves are generated by time varying electric currents, consisting of electrons accelerating as they flow back and forth in the metal antenna, driven by the electric field due to the oscillating voltage applied to the antenna by the radio transmitter. An electromagnetic wave carries momentum away from the electron which emitted it. The cause of radiation resistance is the radiation reaction, the recoil force on the electron when it emits a radio wave photon, which reduces its momentum. This is called the Abraham–Lorentz force. The recoil force is in a direction opposite to the electric field in the antenna accelerating the electron, reducing the average velocity of the electrons for a given driving voltage, so it acts as a resistance opposing the current.

The radiation resistance is only part of the feedpoint resistance at the antenna terminals. An antenna has other energy losses which appear as additional resistance at the antenna terminals; ohmic resistance of the metal antenna elements, ground losses from currents induced in the ground, and dielectric losses in insulating materials. When the feedpoint is (as usual) at a voltage minimum and current maximum, the total feedpoint resistance ${\displaystyle \ R_{\mathsf {in}}\ }$ is equal to the sum of the radiation resistance ${\displaystyle \ R_{\mathsf {rad}}\ }$ and loss resistance ${\displaystyle \ R_{\mathsf {loss}}\ }$

The power ${\displaystyle P_{\mathsf {in}}}$ fed to the antenna is split proportionally between these two resistances.

where

The power ${\displaystyle \ P_{\mathsf {rad}}\ }$ consumed by radiation resistance is converted to radio waves, the desired function of the antenna, while the power ${\displaystyle \ P_{\mathsf {loss}}\ }$ consumed by loss resistance is converted to heat, representing a waste of transmitter power. So for minimum power loss it is desirable that the radiation resistance be much greater than the loss resistance. The ratio of the radiation resistance to the total feedpoint resistance is equal to the efficiency (${\displaystyle \eta }$) of the antenna.