Angle Converter
Convert degrees, radians, gradians, arcminutes, and turns.
What is Angle?
An angle measures rotation. Degrees divide a turn into 360, radians measure it by the radius wrapped along the arc (a full turn is 2π rad), and gradians divide it into 400 for surveying. Arcminutes and arcseconds are the sixtieths of a degree that astronomy and navigation use.
How it works
All units are factors to the radian: a degree is π/180, a gradian π/200, an arcminute π/10,800 and a turn 2π. Degrees and radians therefore convert exactly through the factor π rather than through a rounded decimal approximation.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
The standard pair
Enter 180° and read 3.14159 rad — the conversion that decides whether a calculator is in the right mode.
Common mistakes
Calculator in the wrong mode
Evaluating sin(30) with the calculator set to radians gives -0.988 instead of 0.5. Convert the angle to the mode your calculator is in before taking the function.
Gradians read as degrees
A 400-unit full turn uses gradians, so 100 grad is a right angle while 100° is not. On a survey instrument the difference is a real error.
Frequently asked questions
How many radians in a full circle?
2π ≈ 6.283185. Half a turn is π rad (180°), and a right angle is π/2 rad (90°).
What is a milliradian used for?
Riflescopes and artillery: 1 mrad at 1000 m subtends about 1 m, which is why it is the standard aiming unit.