Angle Converter

Convert between different angle units with this easy-to-use converter.

Conversion Result

Common Angle Conversions

From To Conversion Factor
1° (degree) radians π/180 ≈ 0.0174533 rad
1 radian degrees 180/π ≈ 57.2958°
1° (degree) gradians 10/9 ≈ 1.11111 grad
1° (degree) arcminutes 60′
1° (degree) arcseconds 3600″
1 revolution degrees 360°
1 mil degrees 0.05625°

About Angle Units

Common Units

Degrees (°): The most common unit for measuring angles. One full rotation equals 360 degrees.

Radians (rad): The SI unit for measuring angles. One full rotation equals 2π radians.

Gradians (grad): A unit where one full rotation equals 400 gradians. Used in some surveying and engineering applications.

Arcminutes (′): One degree equals 60 arcminutes. Used for precise angle measurements.

Arcseconds (″): One arcminute equals 60 arcseconds. Used for very precise angle measurements.

Revolutions (rev): One full rotation equals one revolution.

Mils (mil): Used in military and artillery applications. One full rotation equals 6400 mils.

Frequently Asked Questions

Radians are preferred because they make many mathematical formulas simpler and more elegant. For example, the derivative of sin(x) is cos(x) when x is in radians, but requires a conversion factor when x is in degrees. Radians also have a natural relationship with the unit circle and trigonometric functions.

Arcminutes and arcseconds are subdivisions of degrees, similar to how minutes and seconds subdivide hours. One degree equals 60 arcminutes, and one arcminute equals 60 arcseconds. These units are used when very precise angle measurements are needed, such as in astronomy, surveying, and navigation.

Mils (short for milliradians) are commonly used in military and artillery applications. One full rotation equals 6400 mils. They are particularly useful because 1 mil subtends approximately 1 meter at a distance of 1000 meters, making them convenient for range estimation and artillery calculations.