Degrees to Radians Converter
Degrees to Radians Converter
Degrees and radians are two ways to measure angles. Radians are based on the radius of a circle — one radian is the angle where the arc length equals the radius.
Conversion Formula
Since a full circle is 360° = 2π radians, dividing both sides by 360 gives 1° = π/180 radians. Multiply any degree value by π/180 to convert.
Step-by-Step Examples
90° = 1.5707963268 rad
90° = π/2 radians, a quarter turn.
45° = 0.7853981634 rad
45° = π/4 radians, an eighth turn.
Frequently Asked Questions
How do you convert degrees to radians?
Multiply the degree value by π/180. For example, 90° × π/180 = π/2 ≈ 1.5708 radians.
Why do we use radians instead of degrees?
Radians simplify many mathematical formulas. In calculus, the derivative of sin(x) is cos(x) only when x is in radians.
What is π radians in degrees?
π radians equals exactly 180 degrees. This is the fundamental relationship between the two units.
How many radians is a full circle?
A full circle is 2π radians, which equals approximately 6.2832 radians.
What is 1 degree in radians?
1 degree equals π/180 ≈ 0.01745 radians.