Angle Converter

The most common angle conversion is degrees to radians. One degree equals approximately 0.0174533 radians. This conversion is used constantly in mathematics, physics and programming where trigonometric functions expect radians.

To convert degrees to radians, multiply by π/180 (approximately 0.0174533). For example, 90 degrees equals π/2 radians (approximately 1.5708). Common values: 30° = π/6, 45° = π/4, 60° = π/3, 180° = π, 360° = 2π.

A full circle is 360 degrees but 400 gradians. Gradians (also called gon or grade) divide a right angle into exactly 100 units, making them convenient for surveying and civil engineering. One degree equals approximately 1.1111 gradians.

There are exactly 60 arcminutes in 1 degree, and 3600 arcseconds in 1 degree. Arcminutes and arcseconds are used in astronomy, navigation and cartography to measure very small angles, such as the apparent size of celestial objects.

One turn equals exactly 360 degrees or 2π radians. A turn represents one complete revolution. Turns are used in engineering for describing motor speeds, gear ratios and rotational position. Half a turn is 180 degrees and a quarter turn is 90 degrees.