Time-of-flight mass spectrometry (TOFMS) is a method of mass spectrometry in which an ion's mass-to-charge ratio is determined by a time of flight measurement. Ions are accelerated by an electric field of known strength. This acceleration results in an ion having the same kinetic energy as any other ion that has the same charge. The velocity of the ion depends on the mass-to-charge ratio (heavier ions of the same charge reach lower speeds, although ions with higher charge will also increase in velocity). The time that it subsequently takes for the ion to reach a detector at a known distance is measured. This time will depend on the velocity of the ion, and therefore is a measure of its mass-to-charge ratio. From this ratio and known experimental parameters, one can identify the ion. Theory The potential energy of a charged particle in an electric field is related to the charge of the particle and to the strength of the electric field: where Ep is potential energy, q is the charge of the particle, and U is the electric potential difference (also known as voltage). When the charged particle is accelerated into time-of-flight tube (TOF tube or flight tube) by the voltage U, its potential energy is converted to kinetic energy. The kinetic energy of any mass is: In effect, the potential energy is converted to kinetic energy, meaning that equations () and () are equal The velocity of the charged particle after acceleration will not change since it moves in a field-free time-of-flight tube. The velocity of the particle can be determined in a time-of-flight tube since the length of the path (d) of the flight of the ion is known and the time of the flight of the ion (t) can be measured using a transient digitizer or time to digital converter. Thus, and we substitute the value of v in () into (). Rearranging () so that the flight time is expressed by everything else: Taking the square root yields the time, These factors for the time of flight have been grouped purposely. contains constants that in principle do not change when a set of ions are analyzed in a single pulse of acceleration. () can thus be given as: where k is a proportionality constant representing factors related to the instrument settings and characteristics. () reveals more clearly that the time of flight of the ion varies