Degrees to Radians Converter

Degrees and radians are two ways to measure the same angular quantity. A complete turn contains 360 degrees or two pi radians, so 180 degrees equals pi radians. This exact relationship gives the conversion formula: multiply degrees by pi and divide by 180. The reverse conversion multiplies radians by 180 and divides by pi. Unlike degrees, radians are dimensionless because they describe the ratio between an arc length and the radius of its circle. Radians are the standard angular unit in advanced mathematics and science. Trigonometric derivatives, integrals, Taylor series, rotational motion equations, and many programming language functions assume angles are expressed in radians. For example, the sine of 90 degrees is calculated as the sine of pi divided by two radians. Passing 90 directly to a software sine function usually means 90 radians, which produces a very different result. Converting explicitly prevents this common error. The degree system remains useful because its subdivisions are intuitive and historically established. A right angle is 90 degrees, a straight angle is 180 degrees, and a full rotation is 360 degrees. Radians reveal the underlying circle geometry more naturally: those same angles are pi divided by two, pi, and two pi radians. Familiar benchmark values make it easy to estimate whether a calculated decimal is reasonable. Approximately 57.2958 degrees equals one radian. This calculator uses the JavaScript value of pi and lets you choose the displayed precision. Selecting more decimal places does not change the mathematical conversion; it changes only how the answer is rounded for display. Keep additional digits during intermediate scientific or engineering calculations, then round the final result to match the precision of the input data. A rounded decimal is an approximation because pi is irrational and has infinitely many nonrepeating digits. Positive angles conventionally rotate counterclockwise and negative angles rotate clockwise, although a specific application may define orientation differently. Values larger than 360 degrees are valid and represent multiple turns. The converter accepts positive, negative, fractional, and multi-turn angles without normalizing them, so 720 degrees correctly returns four pi radians as a decimal. Use the tool for homework checks, animation transforms, robotics, navigation, signal processing, physics formulas, and any calculation that requires dependable degree-to-radian conversion.