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
[edit | edit source]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
[edit | edit source]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. .
Radians measure angles where a right-angle is , this means that a line has an angle of and that a circle has an angle of .
As is a bit of a weird number for a full circle, the greek letter tau (τ) is often used to mean ^{[1]}. . The benefit of using this new constant is that now a right angle (a quarter of a circle) is , half of the circle is , three-quarters of a circle is and a full circle is . As this isn't the standard, throughout this book π will be used instead.
Gradians
[edit | edit source]Gradians are denoted by the symbol: ^{g}.
Gradians are only used in continental Europe^{[2]}.
Gradians measure angles where a right-angle is 100^{g}, this means that a line has an angle of 200^{g} and that a circle has an angle of 400^{g}.
Converting between them
[edit | edit source]Degrees | Radians | Gradians |
---|---|---|
1° | 1.111...^{g} | |
30° | 33.333...^{g} | |
45° | 50^{g} | |
60° | 66.666...^{g} | |
90° | 100^{g} | |
180° | 200^{g} | |
270° | 300^{g} | |
360° | 400^{g} |