In black hole thermodynamics, entropy is proportional to the event horizon’s area.
The relationship is expressed by the Bekenstein–Hawking formula, which states that black hole entropy equals the horizon area multiplied by the Boltzmann constant and divided by four times the square of the Planck length. In natural units, where the relevant constants are set to one, the formula is simply S = A/4.
Jacob Bekenstein proposed in 1972 that a black hole should possess entropy related to its horizon area. Stephen Hawking’s 1974 prediction that black holes emit thermal radiation supplied the missing physical foundation and fixed the proportionality constant. This linked general relativity, quantum theory, and thermodynamics.
The result is surprising because ordinary systems usually have entropy associated with volume or the number of particles, whereas a black hole’s maximum information content scales with its boundary area. The area also obeys a classical second-law analogue: under suitable conditions, a black hole’s horizon area cannot decrease. Entropy is therefore not the same as temperature, luminosity, or pressure, although it is connected to temperature through black hole thermodynamics.