The two ways to measure a full circle
A full rotation can be expressed in two units: degrees and radians. Both describe the same physical reality — they're just different scales.
| Degrees | 360° for a full circle. Intuitive for most people; used in navigation and everyday life. |
| Radians | 2π (≈6.283) for a full circle. Natural for mathematics — the unit where derivatives of sine and cosine come out cleanly. |
| Conversion | Degrees × (π ÷ 180) = Radians |
| Conversion | Radians × (180 ÷ π) = Degrees |
Math convention vs navigation convention
This is the most important distinction when moving between pure math and applied navigation:
| Math convention | Angles measured counter-clockwise from the positive x-axis (pointing right). 0° = East, 90° = North, 180° = West, 270° = South. |
| Navigation convention | Angles (called bearings or headings) measured clockwise from North. 0° = North, 90° = East, 180° = South, 270° = West. |
Converting between conventions: To convert a math angle (counter-clockwise from East) to a navigation bearing (clockwise from North): subtract the math angle from 90°, then add 360° if the result is negative. This adjustment accounts for both the different reference direction (East vs North) and the reversed rotation direction.
Cardinal directions as bearings
| North | 0° / 360° |
| East | 090° |
| South | 180° |
| West | 270° |
Heading, track, and course in aviation
In aviation, three related but distinct terms all describe direction:
- Heading — the direction the aircraft's nose points (magnetic or true)
- Track — the actual path the aircraft traces over the ground (affected by wind)
- Course — the intended path from departure to destination
Crosswind creates the difference between heading and track. A pilot flying a heading of 090° (due East) in a 20-knot southerly crosswind will actually track slightly north of east — the aircraft must angle into the wind to hold the desired course.