Angle Converter
Convert an angle between degrees, radians, gradians, arcminutes, arcseconds and turns.
What this tool does
To convert degrees to radians, multiply by π ÷ 180 (about 0.0174533); to convert radians to degrees, multiply by 180 ÷ π (about 57.2958). A full turn is 360 degrees, 2π radians or 400 gradians. Enter an angle above to convert it between all six units.
Converts between degrees, radians, gradians, arcminutes, arcseconds, turns (revolutions) using exact factors, and shows the factor used.
Updates as you type, and the swap button reverses the direction.
How to use it
- Enter the value in degrees, or press Swap units to start from radians.
- Pick another unit from the lists if you need a different one.
- Read the result and the factor beneath it.
- Press Copy to copy the result.
Why use this converter
Converts between degrees, radians, gradians, arcminutes, arcseconds and full turns in one place. Maths and programming use radians, maps and building use degrees, surveying sometimes uses gradians, and astronomy uses arcminutes and arcseconds. Switching between them by hand invites errors, especially with π.
Why we built it
We built the angle converter to cover degrees, radians, gradians, arcminutes, arcseconds and turns in one place with exact factors. Use it with the triangle calculator and the scientific calculator.
If your task goes further, try the Frequency Converter.
Handy alongside this: the Projectile Motion Calculator.
Who this tool is for
- Maths and physics students
- Programmers moving between degrees and radians
- Surveyors and astronomers
When to use it
- Maths and physics homework.
- Programming trigonometric functions.
- Reading survey, map and astronomy data.
- Checking calculator angle modes.
How it works
A full circle is 360 degrees, 2π radians, 400 gradians or one turn. So degrees × π/180 = radians, degrees × 400/360 = gradians, degrees × 60 = arcminutes and degrees × 3,600 = arcseconds.
| Degrees | Radians |
|---|---|
| 1 ° | 0.0174533 rad |
| 30 ° | 0.523599 rad |
| 45 ° | 0.785398 rad |
| 90 ° | 1.5708 rad |
| 180 ° | 3.14159 rad |
| 360 ° | 6.28319 rad |
What you give it, and what you get back
| Item | Details |
|---|---|
| Value | A number in the "from" unit. Decimals and negative numbers are accepted. |
| From and To | Any of 6 units: Degrees, Radians, Gradians, Arcminutes, Arcseconds, Turns (revolutions). |
| Result | The converted value and the exact conversion factor. |
Issues you may run into
| What you see | Why it happens | What to do |
|---|---|---|
| Calculator gives a different result | It is in the wrong angle mode (degrees versus radians). | Check the mode before using trig functions. |
| I need degrees, minutes, seconds | This converts decimal angles. | Convert minutes and seconds with the arcminute and arcsecond units, then add. |
| Result shows many decimals | Radians are irrational multiples of π. | Round as needed. |
Assumptions and limitations
- Results are shown with practical rounding; the calculation itself uses exact factors.
- It converts a number between units - it does not know what the quantity is.
Frequently asked questions
How do I convert degrees to radians?
Multiply degrees by π ÷ 180, about 0.0174533.
How many degrees is a radian?
One radian is about 57.2958 degrees.
What is a gradian?
A unit where a right angle is 100, used in some surveying. A full circle is 400 gradians.
How many arcseconds are in a degree?
There are 3,600 arcseconds in a degree.
What is π radians in degrees?
π radians is 180 degrees.
Is it free and private?
Yes. It runs in your browser.