Angle Converter
Convert between degrees, radians, gradians, turns, arcminutes and arcseconds.
Runs entirely in your browser. Nothing is uploaded, logged or stored.
90 °
1.570796 rad
Radian
In every unit
| Unit | Symbol | Value |
|---|---|---|
| Degree | ° | 90 |
| Radian | rad | 1.570796 |
| Milliradian | mrad | 1,570.796 |
| Gradian | gon | 100 |
| Turn | tr | 0.25 |
| Arcminute | ′ | 5,400 |
| Arcsecond | ″ | 324,000 |
The same angle written four ways. A right angle is 90 degrees, pi over two radians, 100 gradians or a quarter turn, and which one you need depends entirely on who is reading it: a protractor and a road sign use degrees, every trigonometric function in every programming language uses radians, surveying in continental Europe uses gradians, and astronomy subdivides the degree.
How it works
Every unit is expressed in degrees and conversions go through them. A full turn is 360 degrees, 400 gradians or two pi radians; a degree is 60 arcminutes and an arcminute is 60 arcseconds, the same sexagesimal division the hour uses.
Degrees rather than radians as the pivot, which is a deliberate departure from SI. A radian is 180 over pi degrees, and pi cannot be written exactly in any finite number of digits, so whichever unit is chosen as the base carries that rounding into every conversion that passes through it. Putting it on the radian confines it to the conversions that genuinely involve one: degrees to gradians, to turns, to arcminutes and to arcseconds stay exact.
Examples
| Case | Input | Result |
|---|---|---|
| Half a turn | 180 ° | 3.141593 rad |
| A full revolution | 1 tr | 360 ° |
| A degree in minutes of arc | 1 ° | 60 ′ |
Frequently asked questions
Why does my code give the wrong answer for sin(90)?
Because it is not reading 90 as a right angle. The trigonometric functions in C, Python, JavaScript, PHP and almost everything else take radians, so sin(90) is the sine of 90 radians — about 0.894, and a perfectly valid answer to a different question. Convert to radians first: 90 degrees is roughly 1.5708.
What is a gradian for?
Surveying, mostly, and mostly in France, Germany and Switzerland. It divides the right angle into 100 rather than 90, so a slope or a bearing works in whole units and decimals rather than in degrees, minutes and seconds. It is also called the gon, which is the name the ISO standard uses.
Are arcminutes the same as the minutes in a coordinate?
Yes. A latitude written 46 degrees 12 minutes 30 seconds is an angle, and those minutes and seconds are arcminutes and arcseconds. This page converts a single value between units; it does not parse or assemble the three-part form.
Why is a turn in the list?
Because it is what several things are actually specified in — a servo travel, a screw thread, a rotation in an animation. It is exactly 360 degrees, and having it here saves multiplying by 360 in your head.
Good to know
- Every factor here is an exact definition rather than a measurement. One of them cannot be written exactly in decimal, though: the radian is 180 over pi degrees, and pi is irrational. Conversions involving a radian or a milliradian are therefore correct to about fifteen significant figures rather than exactly, which is far beyond any angle anybody measures. The rest are exact.