Fundamentals in Measurement: Looking Out for Number 1

Abstract

The International System of Units (SI) [1] was inaugurated in 1960, following years of discussions interrupted by world wars. At that time, a consensus did not yet exist on whether the SI unit of plane angle, the radian (symbol: rad), should be treated as a base unit with its own dimension A, independent of all other base dimensions, or as a unit derived from the meter (m). Provisionally, either interpretation could be used as needed. Thirty-five years later, it was finally decided that the radian should be defined as a derived unit equal to 1. Mathematically, then, $1\ \text{rad} =1\ \mathrm{m}/\mathrm{m}=1$. Reference [1] notes that some ambiguities have arisen from this choice. For instance, a general rule that “the unit symbol 1 or unit name ‘one’ are not explicitly shown” can be problematic. Therefore, rad can be used for clarity when helpful, i.e., rad can be written explicitly with the understanding that 1 rad = 1.