Conversion Reference Table
| Unit | Symbol | Equivalent |
|---|---|---|
| Degrees | ° | 360° = full circle |
| Radians | rad | 2π rad = full circle; π/180 rad = 1° |
| Gradians (Gon) | grad | 400 grad = full circle; 1 grad = 0.9° |
| Turn | turn | 1 turn = 360° = 2π rad |
| Arcminutes | ' | 60 arcmin = 1°; used in navigation |
| Arcseconds | " | 3,600 arcsec = 1°; used in astronomy |
| Mils (NATO) | mil | 6,400 mils = 360° (military) |
| Mils (Swedish) | streck | 6,300 mils = 360° (Swedish mil) |
Frequently Asked Questions
What is a radian?
A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. Since the circumference is 2π × radius, a full circle = 2π radians ≈ 6.2832 rad. Radians are the natural angle unit in mathematics and physics — derivatives of trig functions are simplest in radians.
What are gradians used for?
Gradians (gons) divide a right angle into 100 parts (400 grad = full circle, 100 grad = right angle). They simplify certain surveying calculations. France introduced them during metrication in the 18th century. Gradians appear on some scientific calculators as the 'G' or 'GRAD' mode.
What is an arcminute and arcsecond?
An arcminute (') = 1/60 of a degree. An arcsecond (") = 1/60 of an arcminute = 1/3,600 of a degree. These tiny units are used in astronomy (star positions accurate to arcseconds), GPS coordinates, and optometry (visual acuity). The Moon's diameter is about 30 arcminutes as seen from Earth.
What is a mil in military context?
A NATO mil (milliradian) divides the full circle into 6,400 units. It is defined so that 1 mil of angle subtends approximately 1 meter at 1,000 meters distance — useful for artillery and targeting calculations. Different countries use slightly different mil definitions (Sweden: 6,300; Russia: 6,000).