UnitSnapAngle converter
An angle measures the amount of rotation between two lines that meet at a point. The SI unit is the radian, the angle subtended by an arc equal in length to the radius, so a full circle is 2π radians. Degrees, with 360 to a full circle, remain the most common unit in navigation, construction, and everyday use.
Convert between 9 angle units. Pick any two units below; results update as you type.
Popular angle conversions
About angle units
Degrees subdivide into 60 arcminutes and each arcminute into 60 arcseconds, used in astronomy and geographic coordinates. The gradian (grad or gon) divides a circle into 400 parts and appears in some surveying instruments. Military mils divide a circle into 6,400 parts in the NATO system, while some other armies have used 6,000.
Slope grade expressed as a percent is not a linear angle unit: it equals 100 times the tangent of the angle. A 100% grade is a 45° slope, and a vertical wall has an infinite grade.
Tips
- Spreadsheet and programming trigonometric functions usually expect radians; convert degrees first.
- Doubling a percent grade does not double the angle, because grade follows the tangent function.
- One radian is roughly 57.3°, a useful sanity check when results look off.
All angle units
| Unit | Symbol |
|---|---|
| Radians | rad |
| Degrees | ° |
| Arcminutes | ′ |
| Arcseconds | ″ |
| Gradians | grad |
| Percent Grade | % |
| Turns | tr |
| NATO Mils | mil |
| Mils (6000 per Circle) | mil (6000) |
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Factors: NIST SP 811 · SI Brochure · NIST Handbook 44 — Updated