Degrees to Radians Converter
Converts in both directions and keeps the answer exact. 135° comes out as 3π/4, not as 2.3562, because the exact form is what the next step usually needs.
How it works
How the Degrees to Radians Calculator works
the part a result on its own leaves out
Why the factor is π/180
A half turn is 180° and also π radians, so the two measures of the same angle give the ratio π/180. Every conversion is that one multiplication.
Why radians exist at all
A radian measures an angle by the arc it cuts on a unit circle, which makes the calculus come out clean: the derivative of sin x is cos x only when x is in radians. In degrees an awkward constant appears.
Common mistakes
Common mistakes with degrees and radians
the errors that actually show up, not every possible slip
Leaving the calculator in the wrong mode
sin(30) is 0.5 in degree mode and −0.988 in radian mode. Both are correct answers to different questions, which is what makes this error so easy to miss.
Rounding π away too early
3π/4 is exact. Writing 2.36 loses precision that compounds if the angle feeds into another calculation.
Multiplying by 180/π in the wrong direction
Degrees to radians uses π/180. The inverse, 180/π, goes the other way — a factor of about 3283 apart if swapped.
Questions
Asked often enough to answer here
answers that change how you work
How many radians in a full turn?
2π, roughly 6.283. That is one circumference of a unit circle, which is exactly where the definition comes from.
Why keep the answer as a fraction of π?
Because it is exact and it shows the structure — π/6, π/4, π/3 and π/2 are the standard angles, and recognising them is faster than reading decimals.
Does it handle negative angles?
Yes. A negative angle just turns the other way, and the conversion is the same multiplication.
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