Hydrogen Energy Levels Calculator

About this calculator

The hydrogen energy levels calculator computes the energy of a hydrogen atom's electron in orbital n using the Bohr model formula Eₙ = −13.6 eV / n², where n is the principal quantum number (1, 2, 3, …). The negative sign reflects that the electron is bound to the nucleus; n = 1 is the ground state at −13.6 eV, and as n increases the levels get closer together and approach zero, the point at which the electron is no longer bound (ionization).

The energy difference between two levels, ΔE = 13.6 eV × (1/n₁² − 1/n₂²), predicts the exact wavelengths of hydrogen's spectral lines — the Lyman series (transitions to n = 1, ultraviolet), Balmer series (to n = 2, visible light), and Paschen series (to n = 3, infrared) all follow directly from this formula. Physics and chemistry students, and anyone studying atomic spectroscopy use this calculator to find a given level's energy in electronvolts or joules and check it against the Bohr model before moving on to the full quantum-mechanical treatment.