Skill 10 of 13
In Progress

Direction & angle

Technical skill ●●○○○

The helicopter pilot yells directions over the radio to guide street police: ‘To your right!’ ‘Head east-north-east!’ and ‘At your six (o’clock)!’ He cannot point out the direction physically, so he is “pointing” it out verbally.

What do all these ways of communicating a direction have in common? They are all about splitting a full round into smaller bits.

  • We could split it into four bits – quarters – and say ‘one quarter’, ‘two quarters’ and ‘three quarters clockwise’,
  • into 12 bits such as on a clock or
  • or into 16 bits such as on a simple compass with its ‘east’, ‘north-west’, ‘south-south-west’ etc.1

The more bits we split into, the more precisely can a direction be pointed out.

So why not even more, for example 360 bits? That is in fact the general choice that was made back in the past2 and is still in use today.

Let us invent a name for those 360 bits; why not the term degrees? We can give them a simple little lifted circle ^\circ as a unit symbol,3 and the turn itself is something we can call an angle and give a symbol, say the letter theta \theta from the Greek alphabet.

Then ‘three o’clock’ and ‘a quarter of a round’ are the same as ‘an angle of 90 degrees’, in short:


85 degrees would be a slightly smaller angle than a quarter of a round, while 1 degree is a very, very small turn, only one three-hundred-and-sixtieth of a full round. 360 degrees would be a full round, and 361 degrees would be the same direction as 1 degree, just one round ahead.

Angles in degrees
$1^\circ$One three-hundred-and-sixtieth of a round
$45^\circ$Half of a quarter round
$90^\circ$A quarter of a round
$180^\circ$Half a round
$270^\circ$Three quarters of a round
$360^\circ$A full round


  1. What is the origin of the fact that a circle has 360 degrees? Why not 720 or 270?’ (web page, answer to forum post),, (accessed May 7th, 2019)
  2. Origin of 360 degrees?’ (web page, answer to forum post), History of Science and Mathematics Stack Exchange, 2015, (accessed May 7th, 2019)