📐 Angle Converter

Convert angle units — degrees, radians, gradians (gon), arcminutes, arcseconds, milliradians, full turns and compass points. π radians = 180°; 400 gon = 360°.

From

1 ° = 0.01745329252 rad

Precision

1 degrees = 0.017453293 radians

1 × 0.0174533 = 0.017453293

1 ° equals 0.0174533 rad, so multiplying by 0.0174533 converts the value. The result describes the exact same quantity — only the measuring stick changes.

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Popular angle conversions

All angle units

Unit	Symbol	Definition
Degree	°	The everyday angle unit — 360 degrees make a full circle, so a right angle is 90° and a straight line 180°. Divided into 60 arcminutes each of 60 arcseconds.
Radian	rad	The SI angle unit — the angle subtended when the arc length equals the radius. A full circle is 2π radians, so 1 rad ≈ 57.2958°. Used throughout mathematics and physics.
Gradian	gon	Also called the gon or grad — 400 gradians make a full circle, so a right angle is exactly 100 gon. Used in surveying and some European engineering.
Arcminute	′	One-sixtieth of a degree (also "minute of arc"). Used in astronomy, navigation and optics — the Moon spans about 30 arcminutes in the sky.
Arcsecond	″	One-sixtieth of an arcminute, or 1/3600 of a degree. Astronomers measure star positions and telescope resolution in arcseconds; a parsec is defined by one arcsecond of parallax.
Milliradian	mrad	A thousandth of a radian, about 0.0573°. Used in optics, ballistics and rifle scopes ("mils"), where 1 mrad subtends roughly 10 cm at 100 m.
Turn	tr	One full revolution — 360°, 2π radians or 400 gon. Also called a revolution or cycle; rotational counts and phase are often given in turns.
Compass point	pt	A traditional navigation unit — the compass rose has 32 points of 11.25° each (N, NNE, NE…). Largely historical but still seen in wind and bearing descriptions.