Degrees to Radians Converter

Trig functions in JavaScript, Python, C and most spreadsheets expect radians. Pass them degrees and you get a wrong answer with no warning: Math.sin(30) returns −0.988, not 0.5. Convert first.

This page is ideal for checking what a value should be, but the 4–5 digits it displays are rounded. Using its 0.5236 for 30° gives sin(0.5236) = 0.5000011, which is close but not exact. In code, convert inside the expression with degrees * Math.PI / 180 and use the converter to sanity-check the result.

Textbooks and exams usually want radians written with π, such as π/4, rather than a decimal. The converter gives decimals, so get the exact form by dividing the angle by 180 and simplifying the fraction:

Use the decimal column to check your simplified fraction. Note that 720° stays 12.5664 rad: the converter does not reduce angles to a single turn, which is what you want when counting rotations.

Radians make arc length a single multiplication: arc = radius × angle in radians. One degree is 0.017453 rad, so on a 1 m radius a 1° sweep traces 17.45 mm of arc, and 5° traces about 87.3 mm. This is handy for curved cuts, wheel and pulley layouts, and how far the end of a long arm moves when it turns.

For small angles the tangent is nearly the same as the angle in radians. At 5°, the angle is 0.087266 rad and its tangent is 0.08749, only 0.25% apart. That is why a slope of a few degrees can be estimated as rise ÷ run without a trig table.

Multiply by 0.01745, which is 0.019% low, or divide by 57.3, which is 0.007% low. For 30°, the first gives 0.5235 and the second 0.52356, against the converter's 0.5236.