Angle Converter: Degrees, Radians, and Other Units
An angle converter expresses the same angle in a different measurement unit. Use it to convert between degrees, radians, gradians, turns, arcminutes, and arcseconds. Conversion changes the numerical representation of the angle, rather than its size.
What is the difference between degrees and radians?
A full turn is 360 degrees, written 360°. A radian measures an angle using the ratio of an arc’s length to the circle’s radius. A full circle is 2π radians, so a half-turn is 180° or π radians.
A right angle is 90° or π/2 radians. A quarter-turn also equals 100 gradians. Gradians divide the full circle into 400 equal parts, while turns describe the fraction of a complete rotation.
Angle conversion formulas
Radians = degrees × π ÷ 180
Degrees = radians × 180 ÷ π
Gradians = degrees × 10 ÷ 9
Turns = degrees ÷ 360
Arcminutes = degrees × 60
Arcseconds = degrees × 3,600
Conversions between any two units can use their relative scales. A full turn equals 360°, 2π radians, 400 gradians, 21,600 arcminutes, or 1,296,000 arcseconds.
Worked angle conversion examples
180° to radians: 180 × π ÷ 180 = π, approximately 3.1415926536 radians.
45° to radians: 45 × π ÷ 180 = π/4, approximately 0.7853981634 radians. The same angle is 50 gradians or 0.125 turns.
One radian to degrees: 180 ÷ π is approximately 57.2957795131°. 0.5 turns to degrees: 0.5 × 360 = 180°.
Arcminutes and arcseconds are angular measurements
One degree contains 60 arcminutes. One arcminute contains 60 arcseconds, so one degree contains 3,600 arcseconds. The prime symbol ′ denotes arcminutes, and the double-prime symbol ″ denotes arcseconds.
These are subdivisions of an angle, rather than minutes or seconds of time. For example, 30 arcminutes equal 0.5°, and 90 arcseconds equal 0.025°.
To convert degrees, minutes, and seconds notation to decimal degrees, add degrees + arcminutes/60 + arcseconds/3,600. An angle of 12° 30′ 0″ is 12.5°. Enter that decimal value in the angle field. For a negative angle, apply the sign to the complete magnitude.
Negative angles and angles greater than one turn
Negative values retain their sign during conversion. For example, −90° equals −π/2 radians or −0.25 turns. Positive and negative signs commonly distinguish opposite directions of rotation.
The converter preserves complete rotations rather than reducing every angle to a value between 0° and 360°. Thus, 720° converts to 2 turns or 4π radians. Although 720° and 0° reach the same final direction after rotation, they describe different rotation amounts.
Frequently asked questions
Can I enter decimal angles?
Yes. Values such as 12.5°, 0.25 turns, and decimal radians are supported.
Are gradians the same as degrees?
No. A full circle contains 400 gradians and 360 degrees. One gradian equals 0.9°.
Does swapping units reverse the conversion?
After a calculation, swapping uses the converted value as the new input and reverses the units. Before a calculation, swapping reverses the selected units while keeping the entered value.
Why are some results rounded?
The browser calculates with floating-point numbers. Displayed results use up to ten decimal places, while very large or very small numbers use scientific notation. Values involving π are decimal approximations.
Can I convert zero?
Yes. Zero in any supported unit converts to zero in every other supported unit.
Does this accept degrees-minutes-seconds text?
No. Enter a single numerical value. Convert compound notation to decimal degrees first, or select arcminutes or arcseconds for a value entirely in that unit.