Angle Converter
Converts angles between degrees, radians, gradians and full turns. A full circle is 360°, 2π radians, 400 gradians, or exactly 1 turn — enter any one representation and read the others.
How to use
- Enter the angle in the unit you have.
- Read the conversions — π-multiples of radians shown numerically.
- For trigonometry in code, check whether your library expects radians (most do).
- Gradians appear mainly on surveying gear and calculator GRAD mode.
When you actually need this
- Converting between the degrees of drawings and the radians a math library expects.
- Interpreting a slope given in degrees as a fraction of a turn.
- Checking why sin(30) returned nonsense — the code took 30 radians, not 30 degrees.
- Reading surveying angles quoted in gradians.
Why mathematics prefers the radian
The radian is the angle whose arc equals the radius, making a full turn 2π — and with angles measured this way, the calculus comes out clean: sin x ≈ x for small x, and the derivative of sine is cosine with no correction factor. In degrees those formulas sprout π/180 constants. That is why every mainstream programming language's sin and cos take radians, and passing degrees is among the commonest trig bugs — sin(30) is −0.988, not 0.5. The 360 of degrees is Babylonian bookkeeping that survived because it divides evenly by so many numbers; the gradian's 400 made right angles a clean 100 but never spread past surveying.
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FAQ
How precise are the conversion factors in Angle Converter?
The factors are the internationally defined exact values — one inch is exactly 25.4 millimetres, one pound is exactly 0.45359237 kilograms, and so on. Results are computed at full floating-point precision and only rounded for display.
Can I convert between metric and imperial units in both directions?
Yes. Enter a value in any field and every other unit updates at once, so the conversion works in either direction without switching modes or pressing a button.
Why does the last decimal place sometimes look off?
Because many conversions are irrational in decimal form and browsers use binary floating point, the final digit can differ by a tiny amount. The displayed value is rounded sensibly for everyday use; for laboratory or engineering work, carry the unrounded figure through your own calculation.