<P> The concept of radian measure, as opposed to the degree of an angle, is normally credited to Roger Cotes in 1714 . He described the radian in everything but name, and he recognized its naturalness as a unit of angular measure . The idea of measuring angles by the length of the arc was already in use by other mathematicians . For example, al - Kashi (c. 1400) used so - called diameter parts as units where one diameter part was 1 / 60 radian and they also used sexagesimal subunits of the diameter part . </P> <P> The term radian first appeared in print on 5 June 1873, in examination questions set by James Thomson (brother of Lord Kelvin) at Queen's College, Belfast . He had used the term as early as 1871, while in 1869, Thomas Muir, then of the University of St Andrews, vacillated between the terms rad, radial, and radian . In 1874, after a consultation with James Thomson, Muir adopted radian . </P> <Table> Conversion of common angles <Tr> <Th> Turns </Th> <Th> Radians </Th> <Th> Degrees </Th> <Th> Gradians (Gons) </Th> </Tr> <Tr> <Td> 0 </Td> <Td> 0 </Td> <Td> 0 ° </Td> <Td> 0 </Td> </Tr> <Tr> <Td> 1 / 24 </Td> <Td> π / 12 </Td> <Td> 15 ° </Td> <Td> 16 2 / 3 </Td> </Tr> <Tr> <Td> 1 / 12 </Td> <Td> π / 6 </Td> <Td> 30 ° </Td> <Td> 33 1 / 3 </Td> </Tr> <Tr> <Td> 1 / 10 </Td> <Td> π / 5 </Td> <Td> 36 ° </Td> <Td> 40 </Td> </Tr> <Tr> <Td> 1 / 8 </Td> <Td> π / 4 </Td> <Td> 45 ° </Td> <Td> 50 </Td> </Tr> <Tr> <Td> 1 / 2π </Td> <Td> </Td> <Td> c . 57.3 ° </Td> <Td> c . 63.7 </Td> </Tr> <Tr> <Td> 1 / 6 </Td> <Td> π / 3 </Td> <Td> 60 ° </Td> <Td> 66 2 / 3 </Td> </Tr> <Tr> <Td> 1 / 5 </Td> <Td> 2π / 5 </Td> <Td> 72 ° </Td> <Td> 80 </Td> </Tr> <Tr> <Td> 1 / 4 </Td> <Td> π / 2 </Td> <Td> 90 ° </Td> <Td> 100 </Td> </Tr> <Tr> <Td> 1 / 3 </Td> <Td> 2π / 3 </Td> <Td> 120 ° </Td> <Td> 133 1 / 3 </Td> </Tr> <Tr> <Td> 2 / 5 </Td> <Td> 4π / 5 </Td> <Td> 144 ° </Td> <Td> 160 </Td> </Tr> <Tr> <Td> 1 / 2 </Td> <Td> π </Td> <Td> 180 ° </Td> <Td> 200 </Td> </Tr> <Tr> <Td> 3 / 4 </Td> <Td> 3π / 2 </Td> <Td> 270 ° </Td> <Td> 300 </Td> </Tr> <Tr> <Td> </Td> <Td> 2π </Td> <Td> 360 ° </Td> <Td> 400 </Td> </Tr> </Table> <Tr> <Th> Turns </Th> <Th> Radians </Th> <Th> Degrees </Th> <Th> Gradians (Gons) </Th> </Tr>

What is 1 radian in terms of pi