Degrees to Radians Converter
Convert angles between degrees and radians.
Two ways to measure an angle
Angles can be measured in degrees, the familiar system where a full circle is 360, or in radians, the system built into higher mathematics. This converts between them, a constant need once you work with trigonometry and calculus.
Enter an angle in either unit to convert it.
Why radians exist
Degrees are convenient and intuitive, but the 360 is essentially arbitrary, a historical choice. Radians are defined more naturally: one radian is the angle where the arc length equals the radius, so a full circle is two pi radians. This seems less tidy but makes the mathematics far cleaner — many formulas in calculus and physics are simple in radians and cluttered with conversion factors in degrees, which is why higher maths uses radians almost exclusively. The practical upshot is the classic pitfall: a calculator or formula expecting radians will give wrong answers if fed degrees, and vice versa, so knowing which a context wants, and converting correctly, prevents a whole category of errors in trigonometry and beyond.
Common questions
What is a radian?
The angle where the arc length equals the radius, making a full circle two pi radians — a more natural unit for higher mathematics than the arbitrary 360 degrees.
Why does higher maths use radians?
Because formulas in calculus and physics are far simpler in radians, without the conversion factors that degrees introduce.
Is anything uploaded?
No. The conversion happens in your browser.