The name of the equation used to calculate the energy of a photon is E = hf, where E denotes energy, h is Planck's constant (approximately 6.626 x 10^-34 Js), and f represents the frequency of the photon. This fundamental equation in quantum mechanics demonstrates the direct relationship between the energy of photons and their frequency. Higher frequency photons, like gamma rays, carry more energy than lower frequency photons, such as radio waves.