Angle Converter (Degrees, Radians)

Angle Converter converts angles between degrees, radians, gradians (gons), turns, arcminutes, arcseconds and milliradians, and lists the angle in all of them at once. Degrees are what most people use; radians are what mathematics, physics and every programming language’s sin and cos functions expect; gradians divide a right angle into 100 and appear on surveying instruments and calculators; arcminutes and arcseconds measure small angles in astronomy, navigation and map coordinates; milliradians are used in optics and long-range sighting. Because a radian is 180/π degrees, the conversion needs π, and the converter uses it to 20 significant figures rather than 3.14 or 22/7, in decimal arithmetic, so 180° comes out as π to the full precision shown.

1. Type the angle; negative angles are fine.
2. Choose its unit and the unit you want, or press a common conversion.
3. Read the answer and the angle in every other unit.

• Degrees–minutes–seconds written together (12° 30′ 15″) must be entered in parts, or as decimal degrees: 12.504167°.
• Angles are not reduced to one turn: 450° stays 450°, which is 1.25 turns.
• The NATO mil (6,400 to a turn) and other military mils differ from the milliradian here (about 6,283 to a turn) and are not included.
• π is held to 20 significant figures; answers are shown to 10.
• Conversions run in your browser; nothing is sent.

Multiply by π and divide by 180. 90° is π/2 ≈ 1.5708 rad; 30° is about 0.5236 rad.

About 57.2958°. It is the angle at which the arc is as long as the radius.

A four-hundredth of a turn, so a right angle is 100 gradians. Calculators show it as GRAD or gon.

It is probably in radians mode while you typed degrees, or the reverse. sin(30) is 0.5 in degrees but −0.988 in radians.

A 3,600th of a degree — about the width of a one-rupee coin seen from four kilometres away. On the Earth’s surface, one arcsecond of latitude is about 31 metres.