Number of Elementary Charges (N = Q/e)

Charge is not continuous. Every free particle ever observed carries a whole-number multiple of $e = 1.602176634 \times 10^{-19}$ C, so any charge you measure is really a count, and $N = Q/e$ is the conversion from the coulomb — a human bookkeeping unit — to the number of things. One coulomb is $6.241509 \times 10^{18}$ elementary charges, which puts the coulomb in perspective: it is an enormous quantity of charge, and the reason ordinary static electricity is measured in nanocoulombs.

Everyday currents are torrents on this scale. A 20 mA LED passes $0.02/1.602 \times 10^{-19} \approx 1.2 \times 10^{17}$ electrons every second. Charge a 100 µF capacitor to 12 V and the 1.2 mC on its plate is $7.5 \times 10^{15}$ electrons moved from one plate to the other. In the other direction, the smallest charge a good electrometer can resolve is a few hundred electrons, and a single-electron transistor counts them one at a time.

Robert Millikan pinned this number down between 1909 and 1913 by balancing charged oil drops against gravity in a known field, and the quantisation was the point of the experiment — the charges on his drops came out as multiples of one indivisible amount. His value was about 0.6% low because he used a slightly wrong viscosity for air, and the subsequent literature crept toward the true figure in timid steps rather than correcting it outright, an episode Feynman used in 1974 as a standing warning about experimenter bias. On 20 May 2019 the measuring stopped: the revised SI fixed $e$ at exactly $1.602176634 \times 10^{-19}$ C and defined the ampere from it, so there are no further digits to find.

Two honest cautions. $N$ is a whole number by nature, so a fractional answer is a statement about the precision of $Q$, not about a fraction of an electron — round it, and if the figure runs to $10^{18}$, quote it in scientific notation and stop pretending the last digits are a count. And "elementary charge" means the charge of a free particle: quarks carry thirds of it, but no experiment has ever isolated one, so nothing you can weigh or wire up violates the rule. Finally, remember which sign you have. An electron carries $-e$ and a proton $+e$; this page counts magnitudes, and it is your job to say which kind of charge $N$ of them are.