Guide to Game Development/Theory/Mathematics/Trigonometry/Degrees Vs Radians Vs Gradians

Degrees, radians and gradians are all different ways of measuring angles, and there isn't a standard, they all have their uses and so all of them are used.

Degrees
Degrees are denoted by the symbol: °.

Degrees measure angles where a right-angle is 90°, this means that a line has an angle of 180° and that a circle has an angle of 360°.

Radians
Radians can be denoted by the symbol: r, but often no symbol is used.

The greek letter pi (π) has been used as a constant of the ratio of a circle's circumference to its diameter. $$\pi \approx 3.1415926536$$.

Radians measure angles where a right-angle is $$\frac{\pi}{2}$$, this means that a line has an angle of $$\pi$$ and that a circle has an angle of $$2\pi$$.

As $$2\pi$$ is a bit of a weird number for a full circle, the greek letter tau (τ) is often used to mean $$2\pi$$. $$\tau \approx 6.2831853072$$. The benefit of using this new constant is that now a right angle (a quarter of a circle) is $$\frac{\tau}{4}$$, half of the circle is $$\frac{\tau}{2}$$, three-quarters of a circle is $$\frac{3\tau}{4}$$ and a full circle is $$\tau$$. As this isn't the standard, throughout this book π will be used instead.

Gradians
Gradians are denoted by the symbol: g.

Gradians are only used in continental Europe.

Gradians measure angles where a right-angle is 100g, this means that a line has an angle of 200g and that a circle has an angle of 400g.