📐 Angle Converter
Convert angle units, degrees, radians, gradians (gon), arcminutes, arcseconds, milliradians, full turns and compass points. π radians = 180°; 400 gon = 360°.
1 ° = 0.01745329252 rad
1 degrees = 0.017453293 radians
1 × 0.0174533 = 0.017453293
1 ° equals 0.0174533 rad, so multiplying by 0.0174533 converts the value. The result describes the exact same quantity, only the measuring stick changes.
Popular angle conversions
All angle units
| Unit | Symbol | Definition |
|---|---|---|
| Degree | ° | The everyday angle unit, 360 degrees make a full circle, so a right angle is 90° and a straight line 180°. Divided into 60 arcminutes each of 60 arcseconds. |
| Radian | rad | The SI angle unit, the angle subtended when the arc length equals the radius. A full circle is 2π radians, so 1 rad ≈ 57.2958°. Used throughout mathematics and physics. |
| Gradian | gon | Also called the gon or grad, 400 gradians make a full circle, so a right angle is exactly 100 gon. Used in surveying and some European engineering. |
| Arcminute | ′ | One-sixtieth of a degree (also "minute of arc"). Used in astronomy, navigation and optics, the Moon spans about 30 arcminutes in the sky. |
| Arcsecond | ″ | One-sixtieth of an arcminute, or 1/3600 of a degree. Astronomers measure star positions and telescope resolution in arcseconds; a parsec is defined by one arcsecond of parallax. |
| Milliradian | mrad | A thousandth of a radian, about 0.0573°. Used in optics, ballistics and rifle scopes ("mils"), where 1 mrad subtends roughly 10 cm at 100 m. |
| Turn | tr | One full revolution, 360°, 2π radians or 400 gon. Also called a revolution or cycle; rotational counts and phase are often given in turns. |
| Compass point | pt | A traditional navigation unit, the compass rose has 32 points of 11.25° each (N, NNE, NE…). Largely historical but still seen in wind and bearing descriptions. |
Frequently asked questions
How do I convert angle units?
Choose your two units in the converter above and type a value, the result updates instantly, entirely in your browser. All 8 angle units on this page are interchangeable, so you can convert in either direction.
Which angle units can I convert here?
This converter supports 8 angle units: Degree (°), Radian (rad), Gradian (gon), Arcminute (′) and 4 more. Pick any two to convert between them.
What is the most common angle conversion?
One of the most-used angle conversions is Degrees to Radians (° → rad). Every angle pair we support is linked below, each with its own formula and table.
Is this Angle Converter free and private?
Yes. It is free with no sign-up, uses the exact internationally defined conversion factors, and computes every result locally in your browser, nothing you type is uploaded, and the page keeps working offline.