Convert an angle between degrees and radians, and see the result expressed as a multiple of π.
Degrees and radians are two different ways of measuring angles. The relationship between them is:
A full circle is 360°, which equals 2π radians. That's why many textbook answers are expressed as fractions of π — for example, 90° is the same as 0.5 × π radians, and 180° is the same as π radians.
Radians tie the angle directly to the length of the circular arc and radius, which makes formulas in calculus and trigonometry simpler and more consistent. Many formulas for differentiating and integrating trigonometric functions assume radians.
A full circle is 360°, which equals 2π radians (about 6.2832 radians).
π is the ratio between a circle's circumference and diameter, about 3.14159. In angle conversion, π is used to link degrees (where a full circle is 360) with radians (where a full circle is 2π).