๐ Angle Converter
Convert angle units in real time โ degrees, radians, gradians, and turns. Useful for trigonometry in programming, technical drawing, or surveying.
How to use
- Enter a value into any angle unit field (degree, radian, gradian, turn, etc.).
- The other unit fields update with the converted value in real time.
- Use the radian value directly in code that expects trig functions like sin/cos to take radians.
How the calculation works
Every angle is converted to degrees first. One full turn is 360 degrees, 2ฯ radians or 400 gradians. A radian is the angle subtended at the centre of a circle by an arc equal in length to the radius. A circle of radius r has circumference 2ฯr, so a full turn is 2ฯ radians and one radian is 180 รท ฯ โ 57.2958 degrees. Radians make calculus and series expansions come out cleanly, which is why almost every programming language's sin, cos and tan take radians. The gradian (gon) sets a right angle to 100, so 1 degree = 10/9 gradians and 1 gradian = 0.9 degrees. Its decimal friendliness keeps it in use in some surveying work. Arcminutes (โฒ) and arcseconds (โณ) are sexagesimal, like time: 1 degree = 60 minutes = 3,600 seconds.
Worked example
Converting 30 degrees Radians: 30 ร ฯ รท 180 = ฯ/6 โ 0.5236 Gradians: 30 รท 0.9 โ 33.33 Turns: 30 รท 360 โ 0.0833 In JavaScript, Math.sin(30) computes the sine of 30 radians, giving โ0.988. For the sine of 30 degrees (0.5), convert first: Math.sin(30 * Math.PI / 180).
Things to be aware of
- Trigonometric functions in most programming languages expect radians. Do not pass degrees directly.
- For latitude and longitude in degrees, minutes and seconds, the coordinate converter is more convenient.
- Gradians appear as "gon", "grad" or "g" depending on the source; a calculator's GRAD mode uses this unit.
- Angles beyond one turn (such as 400ยฐ) convert fine, but as a direction they wrap round every 360ยฐ.
FAQ
What is a radian?
A unit of angle based on the ratio of arc length to radius, commonly used in math and programming trig functions (sin, cos, etc.). One radian is about 57.2958 degrees.
How many radians are in 360 degrees?
360 degrees equals 2ฯ (about 6.2832) radians, or one full turn.
Can I use this to get the value to pass into Math.sin()?
Yes โ most programming languages' sin/cos functions expect radians, so converting degrees to radians here gives you the value to use directly.
What is a gradian?
A unit where a right angle equals 100 gradians, sometimes used in surveying. 360 degrees equals 400 gradians.
Can it convert arcminutes and arcseconds too?
Yes โ arcminute and arcsecond units, related to DMS notation, are supported and convert to and from degrees.