Free Angle Converter - Convert Degrees, Radians, Gradians Online
336 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 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.
Can I convert fractional degrees, like 45.5 degrees, using this tool?
Absolutely. You can input decimal values for any supported unit, including degrees. For example, typing `45.5` into the degrees field will instantly show you its equivalent in radians, gradians, and other units. This feature is super handy for anyone working with precise measurements in fields like engineering or woodworking.
Can I convert negative angle values with this converter?
Yes, negative angles work fine here. Enter -90 degrees and you'll get -1.5708 radians or -100 gradians. This is useful for representing clockwise rotations or directional changes in physics and engineering. Just type your negative number directly into any unit field.
Does 1 radian equal 57.3 degrees exactly?
Close, but not exact. One radian equals 180/π degrees, roughly 57.2957795. That 57.3 figure is a rounded shortcut, fine for quick mental math but not for precision work. Our converter uses the full π value internally, so you'll get accurate results down to many decimal places. Try converting 1 radian in the tool and you'll see the exact decimal.
Why does 360 degrees equal 2π radians?
It comes from the geometry of a circle. The circumference is 2π times the radius, so a full rotation naturally maps to 2π radians. That's why π radians equals 180 degrees — half a turn. Our converter handles this math automatically, so you don't need to memorize the relationship. Just type in degrees and watch the radians field update in real time.
Can gradians help with surveying or construction work?
Yes, gradians divide a right angle into 100 units, making decimal calculations straightforward. One full circle equals 400 gradians, not 360. Surveyors in parts of Europe use them for slope calculations and land measurements. If you're working with a theodolite that reads in gradians, just enter your value here. The converter will show equivalents in degrees or radians instantly. Try 100 gradians — you'll get 90 degrees exactly.
Why does converting 90 degrees to gradians give exactly 100?
That's not a coincidence — it's by design. Gradians split a right angle into 100 units, so 90° always equals 100 gradians exactly. This makes decimal math cleaner for surveyors and engineers. Try converting 45 degrees in the tool, and you'll get 50 gradians. Makes trigonometry with decimal numbers far less messy than dealing with fractions of a degree.
What happens if I type in a value in radians and delete it — do the other fields clear too?
Yes, they do. Our converter works in real time, so clearing any input field resets all the other unit fields to zero or blank. This catches people off guard sometimes — you might want to convert degrees to radians, delete the degrees field, and wonder why radians disappeared too. A quick workaround: jot down your result before clearing, or just overwrite the old value with a new one.
Is the angle converter free to use without signing up?
Yes, completely free, no account needed. You can convert angles as often as you like, whether it's a single degree value or hundreds of gradians for a project. There's no hidden premium tier or usage limit, so it works well for quick checks and heavy batch work alike. Bookmark the page and it'll be there whenever you need it, even offline.
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