Angle converter
Convert between degrees, radians, gradians, arcminutes, arcseconds and turns, then watch a protractor arm swing round to show exactly how wide that angle is.
That's about the same as a right angle. That is 0.25 of a full turn.
What it means
How wide is that?
The road gradient shown is the tangent of the angle, the way highway signs measure steepness.
Every unit
Your angle in every unit
Learn
Three things worth knowing
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π radians is half a turn
180° = π rad, so 1 rad is about 57.3°. To go from degrees to radians, multiply by π and divide by 180.
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Why 360 degrees
Babylonian astronomers counted in sixties and reckoned a year at about 360 days, so the Sun moved roughly one degree a day. 360 also divides neatly 24 different ways.
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Degrees or radians on the calculator
sin(90) is 1 in degree mode but 0.894 in radian mode. Programming languages almost always expect radians, which is where the bug usually hides.
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Popular angle conversions
Background
About angle units
A full turn is 360 degrees, 2π radians or 400 gradians. Degrees suit everyday work, radians suit mathematics because they make the formulas come out clean, and gradians make a right angle exactly 100.
Astronomers split degrees further: 60 arcminutes each, and 60 arcseconds inside those.