The effective temperature of a body such as a star or planet is the
temperature
Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
of a
black body that would emit the same total amount of
electromagnetic radiation
In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...
.
Effective temperature is often used as an estimate of a body's surface temperature when the body's
emissivity curve (as a function of
wavelength
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats.
In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
) is not known.
When the star's or planet's net
emissivity in the relevant wavelength band is less than unity (less than that of a
black body), the actual temperature of the body will be higher than the effective temperature. The net emissivity may be low due to surface or atmospheric properties, such as the
greenhouse effect.
Star

The effective temperature of a
star
A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...
is the temperature of a
black body with the same luminosity per ''surface area'' () as the star and is defined according to the
Stefan–Boltzmann law . Notice that the total (
bolometric) luminosity of a star is then , where is the
stellar radius. The definition of the stellar radius is obviously not straightforward. More rigorously the effective temperature corresponds to the temperature at the radius that is defined by a certain value of the
Rosseland optical depth (usually 1) within the
stellar atmosphere.
The effective temperature and the bolometric luminosity are the two fundamental physical parameters needed to place a star on the
Hertzsprung–Russell diagram. Both effective temperature and bolometric luminosity depend on the chemical composition of a star.
The effective temperature of the Sun is around .
The nominal value defined by the
International Astronomical Union
The International Astronomical Union (IAU; , UAI) is an international non-governmental organization (INGO) with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach, education, and developmen ...
for use as a unit of measure of temperature is .
Stars have a decreasing temperature gradient, going from their central core up to the atmosphere. The "core temperature" of the Sun—the temperature at the centre of the Sun where nuclear reactions take place—is estimated to be 15,000,000 K.
The
color index of a star indicates its temperature from the very cool—by stellar standards—red M stars that radiate heavily in the
infrared
Infrared (IR; sometimes called infrared light) is electromagnetic radiation (EMR) with wavelengths longer than that of visible light but shorter than microwaves. The infrared spectral band begins with the waves that are just longer than those ...
to the very hot blue O stars that radiate largely in the
ultraviolet
Ultraviolet radiation, also known as simply UV, is electromagnetic radiation of wavelengths of 10–400 nanometers, shorter than that of visible light, but longer than X-rays. UV radiation is present in sunlight and constitutes about 10% of ...
. Various colour-effective temperature relations exist in the literature. Their relations also have smaller dependencies on other stellar parameters, such as the stellar metallicity and surface gravity. The effective temperature of a star indicates the amount of heat that the star radiates per unit of surface area. From the hottest surfaces to the coolest is the sequence of
stellar classifications known as O, B, A, F, G, K, M.
A red star could be a tiny
red dwarf
A red dwarf is the smallest kind of star on the main sequence. Red dwarfs are by far the most common type of fusing star in the Milky Way, at least in the neighborhood of the Sun. However, due to their low luminosity, individual red dwarfs are ...
, a star of feeble energy production and a small surface or a bloated giant or even
supergiant star such as
Antares or
Betelgeuse, either of which generates far greater energy but passes it through a surface so large that the star radiates little per unit of surface area. A star near the middle of the spectrum, such as the modest
Sun or the giant
Capella radiates more energy per unit of surface area than the feeble red dwarf stars or the bloated supergiants, but much less than such a white or blue star as
Vega or
Rigel.
Planet
Blackbody temperature
To find the effective (blackbody) temperature of a
planet
A planet is a large, Hydrostatic equilibrium, rounded Astronomical object, astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets b ...
, it can be calculated by equating the power received by the planet to the known power emitted by a blackbody of temperature .
Take the case of a planet at a distance from the star, of
luminosity
Luminosity is an absolute measure of radiated electromagnetic radiation, electromagnetic energy per unit time, and is synonymous with the radiant power emitted by a light-emitting object. In astronomy, luminosity is the total amount of electroma ...
.
Assuming the star radiates isotropically and that the planet is a long way from the star, the power absorbed by the planet is given by treating the planet as a disc of radius , which intercepts some of the power which is spread over the surface of a sphere of radius (the distance of the planet from the star). The calculation assumes the planet reflects some of the incoming radiation by incorporating a parameter called the
albedo (a). An albedo of 1 means that all the radiation is reflected, an albedo of 0 means all of it is absorbed. The expression for absorbed power is then:
:
The next assumption we can make is that the entire planet is at the same temperature , and that the planet radiates as a blackbody. The
Stefan–Boltzmann law gives an expression for the power radiated by the planet:
:
Equating these two expressions and rearranging gives an expression for the effective temperature:
: