° · rad · gon · turn
Angle converter
180 degrees is exactly π radians, or 3.14159 rad, and one full turn is 360 degrees. Enter an angle, pick a unit and read it in all seven units at once.
- 1 ° = 0.01745329 rad
- 1 rad = 57.29578 °
The result and the table below it update as you type. Only the printed figure is rounded, to six significant digits, so a rounded value is never carried into the next conversion.
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At a glance
- Price
- No charge
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- None needed
- Upload
- Not applicable — you type a value, nothing is sent anywhere
- Units
- Degree, radian, gradian, arcminute, arcsecond, turn and milliradian
- Precision
- Exact definitions, printed to six significant digits
- Works on
- Any modern browser
Common angle conversions
These tables are computed from the same factors as the converter. Read each one left to right: the first column is the value you start with and the second is its equivalent.
| ° | rad |
|---|---|
| 30 | 0.523599 |
| 45 | 0.785398 |
| 90 | 1.5708 |
| 180 | 3.14159 |
| 360 | 6.28319 |
| rad | ° |
|---|---|
| 30 | 1718.87 |
| 45 | 2578.31 |
| 90 | 5156.62 |
| 180 | 10313.2 |
| 360 | 20626.5 |
| ° | gon |
|---|---|
| 30 | 33.3333 |
| 45 | 50 |
| 90 | 100 |
| 180 | 200 |
| 360 | 400 |
| ° | turn |
|---|---|
| 30 | 0.0833333 |
| 45 | 0.125 |
| 90 | 0.25 |
| 180 | 0.5 |
| 360 | 1 |
| ° | ′ |
|---|---|
| 30 | 1800 |
| 45 | 2700 |
| 90 | 5400 |
| 180 | 10800 |
| 360 | 21600 |
| mrad | ° |
|---|---|
| 30 | 1.71887 |
| 45 | 2.57831 |
| 90 | 5.15662 |
| 180 | 10.3132 |
| 360 | 20.6265 |
Angle units and their exact size
| Unit | Symbol | Exact size |
|---|---|---|
| Degree | ° | 1 ° = 0.0174532925199433 rad |
| Radian | rad | 1 rad = 1 rad |
| Gradian | gon | 1 gon = 0.015707963267949 rad |
| Arcminute | ′ | 1 ′ = 0.000290888208665722 rad |
| Arcsecond | ″ | 1 ″ = 0.00000484813681109536 rad |
| Turn | turn | 1 turn = 6.28318530717959 rad |
| Milliradian | mrad | 1 mrad = 0.001 rad |
How to convert an angle
Enter the angle
Type a number in the first field. Negative values and decimals are accepted, so 45 and −90.5 both work.
Pick the two units
Choose the unit you have in the first menu and the unit you want in the second. The swap button reverses the two.
Read the table
The large figure is your answer. The table lists the same angle in every other unit, so you can copy the one you need without converting again.
How angle conversion works
Every unit on this page is defined from the radian, the angle at which an arc on a circle is as long as its radius. A full turn is 2π radians, which is 360 degrees and 400 gradians (also called gon). An arcminute is 1/60 of a degree and an arcsecond is 1/60 of an arcminute, so one degree is 3600 arcseconds. A milliradian is 0.001 rad.
A conversion is a multiplication and a division: the value times the source unit's size in radians, divided by the target unit's. Degrees to radians is value × π ÷ 180, which is value × 0.0174533 to six digits, and radians to degrees is value × 57.2958. The factors rest on π as stored in double precision, so a result such as 180° in radians is exact to about 15 digits. Some armies divide the circle into 6400 or 6000 mils, which is a different unit from the true milliradian (6283.19 per turn) and is not offered here.
Angle conversion questions
How many radians are in 180 degrees?
180 degrees is exactly π radians, which is 3.14159 rad to six digits. Multiply degrees by π ÷ 180 to get radians: 90° is 1.5708 rad, 45° is 0.785398 rad and 30° is 0.523599 rad.
How many degrees are in a radian?
One radian is 57.2958 degrees, found as 180 ÷ π. A full turn of 360 degrees is therefore 2π = 6.28319 radians.
What is a gradian?
A gradian, or gon, is 1/400 of a full turn, so a right angle is exactly 100 gradians and 1 degree is 1.11111 gradians. It is used mainly in surveying and some European engineering calculators.
How many arcseconds are in a degree?
One degree is 60 arcminutes and 3600 arcseconds. One arcsecond is 4.84814e-6 radians, which is the angle of a 1 mm object seen from about 206 metres away.
Do my numbers leave my device?
No. The unit tables are part of the page and the arithmetic runs in your browser, so nothing you type is sent anywhere. With the page already loaded, the converter also works offline.