Milliarcseconds to Radians (mas to rad)

1 milliarcsecond equals 4.848136811×10⁻⁹ radians (rounded).

1 milliarcsecond = 4.848136811×10⁻⁹ radians

How to convert milliarcseconds to radians

To convert milliarcseconds to radians, multiply the number of milliarcseconds by 4.848136811×10⁻⁹. The factor is rounded to 10 significant digits. To go the other way, multiply radians by 206,264,806.2 (rounded).

radians = milliarcseconds × 4.848136811×10⁻⁹

Example: 10 milliarcseconds = 4.848136811×10⁻⁸ radians.

About these units

Milliarcsecond (mas)

AstronomicalCurrent unit

One thousandth of an arcsecond. Used for the parallax of stars.

A milliarcsecond, abbreviated mas, is a thousandth of an arcsecond, or 1/3,600,000 of a degree. That is about 4.85 nanoradians, small enough to span only about 4.8 millimeters at a distance of 1,000 kilometers. The SI Brochure lists mas, along with microarcseconds and picoarcseconds, as the symbols astronomers use for very small angles.

Stellar parallax is the main customer. Because distance in parsecs is the reciprocal of parallax in arcseconds, a star with a parallax of 1 mas lies 1,000 parsecs away, roughly 3,260 light-years. Precision at this level is why astrometry missions work in microarcseconds. ESA's Gaia measured positions of objects about 4,000 times fainter than the naked-eye limit to around 24 microarcseconds, which is 0.024 mas, a precision ESA compares to the width of a human hair seen from 1,000 kilometers away.

1 milliarcsecond = 7.716049383×10⁻¹⁰ turns (approximately).

Sources: BIPM SI Brochure, 9th edition (2019); ESA Gaia: Cosmic distances; Wikipedia: Minute and second of arc

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)

Related conversions

See all angle units.