Angle Converter
Convert degrees, radians, gradians, arcminutes, arcseconds and turns.
· CalcFlow Editorial
1 ° = 0.017453293 rad
Results shown are estimates for informational purposes only. Nothing on CalcFlow is financial, tax, legal, or medical advice. Always consult a qualified professional before making important decisions.
Common Angle Conversions
| Degrees | Radians | Gradians | Arcminutes | Arcseconds | Turns (revolutions) |
|---|---|---|---|---|---|
| 1 ° | 0.017453293 | 1.1111111 | 60 | 3,600 | 0.0027777778 |
| 15 ° | 0.26179939 | 16.666667 | 900 | 54,000 | 0.041666667 |
| 30 ° | 0.52359878 | 33.333333 | 1,800 | 108,000 | 0.083333333 |
| 45 ° | 0.78539816 | 50 | 2,700 | 162,000 | 0.125 |
| 60 ° | 1.0471976 | 66.666667 | 3,600 | 216,000 | 0.16666667 |
| 90 ° | 1.5707963 | 100 | 5,400 | 324,000 | 0.25 |
| 180 ° | 3.1415927 | 200 | 10,800 | 648,000 | 0.5 |
| 270 ° | 4.712389 | 300 | 16,200 | 972,000 | 0.75 |
| 360 ° | 6.2831853 | 400 | 21,600 | 1,296,000 | 1 |
Popular Angle Conversions
Formula
radians = degrees x pi / 180; 1 turn = 360 degrees = 400 gradians = 2 pi radiansUnderstanding Angle Conversion
An angle can be measured in degrees, where a full circle is 360, in radians, where a full circle is 2 pi, or in gradians, where a full circle is 400. Radians are the natural unit in mathematics and physics because they make formulas such as arc length equal to radius times angle. Arcminutes and arcseconds are 1/60 and 1/3600 of a degree and are used in navigation and astronomy.
Tips and Best Practices
- 1Multiply degrees by 0.017453 to get radians; multiply radians by 57.2958 to get degrees.
- 2A right angle is 90 degrees, pi/2 radians or 100 gradians.
- 3Set your calculator to the right angle mode before using sine or cosine.
Real-World Example
180 degrees is pi radians (3.14159). A bearing of 45 degrees is 0.7854 radians, or 50 gradians.
Common Mistakes to Avoid
- Leaving a calculator in degree mode when the formula expects radians.
- Confusing arcminutes with minutes of time.
- Treating gradians as degrees; a gradian is 0.9 degrees.
How to Use
- Pick the unit you have in the left selector and the unit you want in the right selector.
- Type a number in either box; the other box updates instantly.
- Use the swap button to reverse the direction and Copy result to copy the answer.
Frequently Asked Questions
How many degrees is one radian?
How many degrees in a full circle?
How many arcseconds are in a degree?
Sources: BIPM SI Brochure (radian; degree, arcminute, arcsecond as accepted units).