Enter the angle and choose from degrees, radians, gradians, arcminutes, arcseconds and turns. An angle’s numerical value depends on its unit. A full circle is 360 degrees, 2 pi radians, 400 gradians or 1 turn, and a degree is 60 arcminutes or 3,600 arcseconds.
Make sure your calculator's angle mode matches the unit you use.
Angle Converter: worked example
| Angle to convert | 180 |
|---|---|
| Starting unit | Degrees |
| Requested unit | Radians |
| Converted value | 3.1416 |
| 1 unit of "from" in "to" units | 0.0175 |
Angle Converter: formula
Common error: Treating arcminutes as hundredths of a degree. There are 60 arcminutes in a degree and 60 arcseconds in an arcminute, not 100.
Latitude and longitude use degrees, minutes and seconds, which are not decimal. Gradians are rarely used except in some surveying contexts. Rounding of pi affects results slightly.
Angle mode errors on calculators are a common source of wrong trigonometric answers. Angles wrap around, so 370 degrees points the same way as 10 degrees, and negative angles turn the other direction. Gradians divide a right angle into 100 parts and are mostly used in surveying, while arcminutes and arcseconds split a degree into 60 and 3,600 parts for navigation and astronomy.
Angle Converter: changing Angle to convert
| Angle to convert | Converted value | 1 unit of "from" in "to" units |
|---|---|---|
| 144 | 2.5133 | 0.0175 |
| 162 | 2.8274 | 0.0175 |
| 180 (example) | 3.1416 | 0.0175 |
| 198 | 3.4558 | 0.0175 |
| 216 | 3.7699 | 0.0175 |
Angle Converter: compare input ranges
| Input | Tested from | To | Converted value: low input | Converted value: high input | Swing |
|---|---|---|---|---|---|
| Starting unit | Degrees | Turns | 3.1416 | 1130.9734 | 1127.8318 (36000%) |
| Requested unit | Degrees | Turns | 180.0000 | 0.5000 | 179.5000 (20626465%) |
| Angle to convert | 162 | 198 | 2.8274 | 3.4558 | 0.6283 (20%) |
Angle Converter: individual input comparisons
| Input | Value | Converted value | 1 unit of "from" in "to" units |
|---|---|---|---|
| Angle to convert | 144 | 2.5133 | 0.0175 |
| 162 | 2.8274 | 0.0175 | |
| 180 | 3.1416 | 0.0175 | |
| 198 | 3.4558 | 0.0175 | |
| 216 | 3.7699 | 0.0175 | |
| Starting unit | Degrees | 3.1416 | 0.0175 |
| Radians | 180.0000 | 1.0000 | |
| Gradians | 2.8274 | 0.0157 | |
| Arcminutes | 0.0524 | 0.0003 | |
| Arcseconds | 0.0009 | 0.0000 | |
| Turns | 1130.9734 | 6.2832 | |
| Requested unit | Degrees | 180.0000 | 1.0000 |
| Radians | 3.1416 | 0.0175 | |
| Gradians | 200.0000 | 1.1111 | |
| Arcminutes | 10800.0000 | 60.0000 | |
| Arcseconds | 648000.0000 | 3600.0000 | |
| Turns | 0.5000 | 0.0028 |
Angle Converter: which assumptions move the result?
Angle Converter: values and definitions
| Quantity and definition | Value used |
|---|---|
| Angle to convert | 180 |
| Starting unit — Unit to convert from. | Degrees |
| Requested unit — Unit to convert to. | Radians |
| Converted value | 3.1416 |
| 1 unit of "from" in "to" units | 0.0175 |
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Angles are measured in different units in different fields, and the conversions all hang on one fact: a half turn is 180 degrees and also pi radians. So 180 degrees is 3.1416 radians, and one radian is about 57.2958 degrees. Programming languages and calculus want radians.
Maps, blueprints and survey work use degrees, arcminutes and arcseconds, and construction speaks in degrees. A right angle is 90 degrees, about 1.5708 radians.
Confirm the unit your tool expects before you type a value. A sine function fed degrees when it wants radians returns a plausible but wrong number.
Compute sine, cosine and tangent on the trigonometry calculator, arcs on the arc length and sector page, and triangles on the right triangle and law of sines calculators. The distance and slope page relates slope to angle, and the frequency converter handles cycles per second.
How do I turn an angle in degrees into radians?
Multiply by pi over 180. Ninety degrees is pi over 2, about 1.571 radians.
Why do mathematicians use radians?
Because formulas in calculus and physics are simpler in radians, where the arc length equals the radius times the angle.
How many arcseconds are in a degree?
3,600, since a degree is 60 arcminutes and each arcminute is 60 arcseconds.