Radians to Arcminutes (rad to ′)

1 radian equals 3,437.746771 arcminutes (rounded).

1 radian = 3,437.746771 arcminutes

How to convert radians to arcminutes

To convert radians to arcminutes, multiply the number of radians by 3,437.746771. The factor is rounded to 10 significant digits. To go the other way, multiply arcminutes by 0.0002908882087 (rounded).

arcminutes = radians × 3,437.746771

Example: 10 radians = 34,377.46771 arcminutes.

About these units

Radian (rad)

Metric (SI)Current unit

The SI unit of angle: the angle at the center of a circle subtended by an arc equal in length to the radius. A full turn is 2π radians (about 6.2832).

The radian builds its unit out of the circle itself. Lay a length of string equal to the radius along the circumference, and the angle that arc makes at the center is one radian. The SI Brochure calls it the coherent unit of plane angle, and it also serves as the coherent unit of phase angle, which grows by 2π radians over one period of a repeating wave. The same document notes that you could write rad as m/m, but warns that this is not intrinsic and can mislead, since angle is not the same kind of quantity as an ordinary ratio of lengths. It also records an alternative definition: a right angle equals π/2 radian.

A circle's circumference is 2π times its radius, so a full turn is 2π radians, about 6.2832, which makes one radian roughly 57.3 degrees, or about 0.159 of a turn. The SI Brochure's table of derived units expresses angular velocity in radians per second.

1 radian = 0.1591549431 turns (approximately).

Sources: BIPM SI Brochure, 9th edition (2019); Wikipedia: Angle; NIST Guide to the SI, Appendix B.8 (angle conversion factors)

Arcminute (′)

General & non-SICurrent unit

One sixtieth of a degree. Used in navigation, astronomy and rifle sighting (minute of angle).

An arcminute is a sixtieth of a degree, which makes it 1/21,600 of a turn or about 0.29 milliradian. The SI Brochure lists it among widely used non-SI units, equal to π/10,800 radian. The units come from Babylonian astronomy and its habit of splitting the degree into 60 parts.

It is a handy size for everyday precision. One arcminute of latitude is roughly one nautical mile, and navigation often writes positions in degrees and decimal minutes. Someone with 20/20 vision can just resolve details about an arcminute apart. The Sun and the Moon each measure around 30 to 32 arcminutes across. Property surveyors use degrees, minutes, and seconds in metes-and-bounds boundary descriptions. Shooters call the unit minute of angle, or MOA, where 1 MOA covers about 1.047 inches at 100 yards.

1 arcminute = 0.0000462962963 turns (approximately).

Sources: BIPM SI Brochure, 9th edition (2019); Wikipedia: Minute and second of arc; Wikipedia: Angular diameter

Related conversions

See all angle units.