# Angle Measurement

Following are the rules and formulae for angle measurements:

1. Angle measurements greater than zero represent counter-clockwise measurements/rotation. Angle measurements lesser than zero represent clockwise measurements/rotation.
2. Angle measurements/Rotations are modular 360 arithmatic. This means the angular calculations wrap around to zero after reaching $$\pm 359$$°. For e.g. a measurement/rotation of $$\pm 727$$° is actually a measurement of $$\pm 7$$°.
3. Every counter-clockwise measurement/rotation has a corresponding clockwise measurement/rotation and vice versa. The following table illustrates this formula with examples:
 Measurement/Rotation Type Corresponding measurement/rotation given by Example Counter-Clockwise of/by $$\theta$$ Clockwise of/by $$(\theta \bmod 360) - 360$$ If Counter-Clockwise = 732° $$\Rightarrow$$ Actual Counter-Clockwise=$$(732 \bmod 360)$$=12° $$\Rightarrow$$ Clockwise = 12° - 360° = -348° Clockwise of/by $$\theta$$ Counter-Clockwise of/by $$(\theta \bmod 360) + 360$$ If Clockwise = -732° $$\Rightarrow$$ Actual Clockwise=$$(-732 \bmod 360)$$=-12° $$\Rightarrow$$ Counter-Clockwise = -12° + 360° = 348°