Angle Unit Converter

Convert between units of angle.

Supported Units

• Degree (°): The degree is the most commonly used unit of angle, with one full rotation divided into 360 degrees. This system is believed to originate from ancient Babylonian astronomy, where a year of roughly 360 days suggested dividing a circle into 360 parts. Degrees are used everywhere in daily life: compass bearings, slopes, architecture, and geometry. A right angle is 90 degrees, a straight angle is 180 degrees, and a full rotation is 360 degrees.
• Radian (rad): The radian is the SI unit of angle, defined as the angle subtended by an arc equal in length to the radius of the circle. One radian is approximately 57.296 degrees, and a full circle is 2 pi radians. Radians are the standard angular unit in mathematics, physics, and engineering because calculus formulas (such as the derivative of sine being cosine) require radian measure. Programming language math libraries also use radians by default.
• Gradian (gon): The gradian, also called the gon, was introduced during the French Revolution alongside the metric system. It divides a right angle into 100 gradians, making a full circle 400 gradians. This unit is primarily used in surveying, especially in France and Germany, where survey instruments may be graduated in gradians. The advantage is that a right angle is exactly 100, simplifying slope calculations. One gradian equals 0.9 degrees.
• Turn (turn): The turn represents one complete rotation, equal to 360 degrees, 2 pi radians, or 400 gradians. It is the most intuitive angular unit in everyday language: a "half turn" is 180 degrees, and a "quarter turn" is 90 degrees. In sports, figure skating jumps are described in turns (a triple axel is 3.5 turns), and skateboard tricks use 360 for one full rotation. In engineering, rotational speed in RPM is based on the turn.
• Arcminute (′): The arcminute is one-sixtieth of a degree, symbolized by a prime mark. In astronomy, the apparent diameter of the full Moon is about 31 arcminutes. The definition of 20/20 vision (visual acuity 1.0) is based on the ability to resolve details of one arcminute. Geographic coordinates are often expressed in degrees, minutes, and seconds, where one arcminute of latitude corresponds to approximately 1.852 km (one nautical mile) on Earth's surface.
• Arcsecond (″): The arcsecond is one-sixtieth of an arcminute, or one 3,600th of a degree. In astronomy, stellar parallax is measured in arcseconds, and one parsec (about 3.26 light-years) is defined as the distance at which a star shows a parallax of one arcsecond. In surveying, high-precision instruments achieve sub-arcsecond resolution. GPS coordinates expressed in degrees, minutes, and seconds use arcseconds for fine positional accuracy, where one arcsecond of latitude is approximately 31 meters on Earth's surface.
• Milliradian (mrad): The milliradian is one-thousandth of a radian, approximately 0.0573 degrees. It is widely used in military and shooting applications, where NATO standard scopes use milliradians for angular measurement. One mrad subtends approximately one meter at a distance of 1,000 meters, making range estimation intuitive. Laser beam divergence and optical aberrations are also often specified in milliradians.

How to Use

1. Select the unit you want to convert from in the "From" dropdown.

2. Select the unit you want to convert to in the "To" dropdown.

3. Enter a value and the result will be displayed in real time.

4. Use the swap button to reverse the conversion direction.