Degrees to Radians Calculator

This converter changes any angle measured in degrees into its equivalent in radians. Degrees and radians are two different units for measuring the same thing, the size of an angle, and understanding both is essential once you move beyond basic geometry into calculus, trigonometry, and physics. The degree is a historical unit that divides a full circle into 360 equal parts. The radian is the mathematically natural unit: one radian is the angle you get when you lay the radius of a circle along its circumference, and a full circle spans exactly two pi radians. The conversion formula is straightforward: multiply the degree value by pi divided by 180. So 90 degrees equals 90 times pi over 180, which simplifies to pi over 2, or approximately 1.5708 radians. Knowing the fraction-of-pi form is often more useful than the decimal because it makes patterns like 30 degrees equals pi over 6 and 45 degrees equals pi over 4 much clearer. This calculator returns both the exact fraction-of-pi representation (where possible) and the decimal approximation to five significant figures. It also shows the angle in gradians, the third common angular unit used in surveying, where a full circle is 400 gradians. Enter any degree value, positive or negative, integer or decimal, and all three conversions update instantly. Common reference angles such as 30, 45, 60, 90, 180, and 360 degrees are shown in the worked example. This tool is designed for students, engineers, and programmers who work with trigonometric functions that expect radian inputs. Results are for reference only.

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