Free Angle Converter - Convert Degrees, Radians, Gradians Online
43 uses-
Conversion Result
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Degree (°)
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Radian (rad)
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Gradian
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Turn
Common Angle Conversion Table
| Degree (°) | Radian (rad) | Gradian (grad) | Turn |
|---|---|---|---|
| 0° | 0 | 0 | 0 |
| 30° | π/6 ≈ 0.524 | 33.33 | 1/12 |
| 45° | π/4 ≈ 0.785 | 50 | 1/8 |
| 60° | π/3 ≈ 1.047 | 66.67 | 1/6 |
| 90° | π/2 ≈ 1.571 | 100 | 1/4 |
| 120° | 2π/3 ≈ 2.094 | 133.33 | 1/3 |
| 180° | π ≈ 3.142 | 200 | 1/2 |
| 270° | 3π/2 ≈ 4.712 | 300 | 3/4 |
| 360° | 2π ≈ 6.283 | 400 | 1 |
Angle Conversion Tips
Full Circle
A full circle = 360 degrees = 2 pi radians = 400 gradians = 1 turn = 21,600 arcminutes = 1,296,000 arcseconds.
Key Formula
To convert degrees to radians, multiply by pi/180. To convert radians to degrees, multiply by 180/pi. Remember: pi radians = 180 degrees.
Common Angles
30 degrees = pi/6, 45 degrees = pi/4, 60 degrees = pi/3, 90 degrees = pi/2, 180 degrees = pi, 360 degrees = 2 pi.
Navigation
Gradians (gon) divide a right angle into 100 parts, making them useful in surveying. 100 grad = 90 degrees = 1 right angle.
Frequently Asked Questions
How do I convert degrees to radians?
Multiply the degree value by pi/180. For example, 90 degrees x pi/180 = pi/2 radians (approximately 1.5708).
What is a gradian (gon)?
A gradian divides a full circle into 400 parts (a right angle = 100 grad). It is mainly used in surveying and some European countries.
What are arcminutes and arcseconds?
An arcminute is 1/60 of a degree, and an arcsecond is 1/60 of an arcminute (1/3600 of a degree). They are used in astronomy and navigation for precise measurements.
When should I use radians vs degrees?
Radians are standard in mathematics and physics (especially calculus and trigonometry). Degrees are more intuitive for everyday use, navigation, and geometry.
What's the difference between a 'turn' and a 'degree' for angle measurement?
A 'turn' represents one complete rotation, equivalent to 360 degrees, 2π radians, or 400 gradians. It's a fundamental unit often used in mathematics, engineering, and sports to describe full rotations or revolutions. Degrees, on the other hand, subdivide a turn into 360 equal parts, offering finer granularity for angle measurements in navigation, geometry, and everyday contexts. Our online angle converter helps you instantly convert between these and many other angle units.
Does this online angle converter support Degree-Minute-Second (DMS) conversions?
While this online angle converter doesn't accept Degree-Minute-Second (DMS) format directly, you can efficiently convert its individual components. Simply convert your arcminutes and arcseconds to their decimal degree equivalents using the tool, then add them to your whole degree value. This method allows you to process precise angle measurements for navigation, surveying, or astronomy tasks, leveraging our support for degrees, arcminutes, and arcseconds.
How can I quickly and accurately convert angles between degrees, radians, and other units for my projects?
Our free online angle converter provides the simplest and most accurate method. Instead of remembering complex formulas for degrees, radians, gradians, arcminutes, or turns, you can input your value into one unit field and instantly see its equivalent in all other supported angle units. This saves time, reduces calculation errors, and ensures precision for engineering, astronomy, or any project requiring exact angle conversions.
How accurate are online angle converters compared to scientific calculators?
Online angle converters, like ours, typically use highly precise algorithms for calculations, often achieving the same or even greater accuracy than standard scientific calculators. Our free tool leverages robust mathematical libraries to ensure conversions between degrees, radians, gradians, arcminutes, arcseconds, and turns are performed with high fidelity, reducing human error. This makes it a reliable choice for academic, engineering, and navigational tasks requiring exact angle values.
How to Use the Angle Converter
- Enter an angle value in the input field
- Select the source unit (degrees, radians, etc.)
- Select the target unit from the dropdown
- The result updates instantly as you type
- Use quick preset buttons for common angles (30, 45, 60, 90, 180, 360 degrees)
- Click swap to reverse the conversion direction