It may be shown by the electromagnetic theory, by the quantum theory, or by thermodynamics, making no assumptions as to the nature of the radiation, that the pressure against a surface exposed in a space traversed by radiation uniformly in all directions is equal to 1/3 the total radiant energy per unit volume within that sphere. For black body radiation, in equilibrium with the exposed surface, the energy density is, in accordance with the Stefan-Boltzmann law, equal to 4σT4/c; in which σ is the Stefan-Boltzmann constant, c is the speed of light, and T is the absolute temperature of the space. One third of this energy is equal to 2.523×10-15T4 (erg/cm3), which is therefore equal to the pressure in bars. For example, at the boiling[?] point of water (T = 373.2°C), the pressure only amounts to 0.00005 dyne/cm2, or about 3 pounds per square mile. Such feeble pressures are, nevertheless, able to produce marked effects upon minute particles like gas ions and electrons, and are important in the theory of electron emission from the Sun, of cometary material, etc. (see also: Yarkovsky effect).
Sources for the above information include the van Nostrand Scientific Encyclopedia (3rd edition)
In stellar interiors the temperatures are very high. Stellar models predict a temperature of 1.5×107 Kelvin in the center of the Sun and at the cores of supergiant stars the temperature may exceed 109 Kelvin. As the radiation pressure scales to the fourth power of the temperature, it becomes important in these high temperatures. In the Sun, radiation pressure is still quite small when compared to the gas pressure. In heaviest stars radiation pressure is the dominant pressure component.
In acoustics, radiation pressure is the unidirectional pressure force exerted at an interface between two media due to the passage of a sound wave.