Degrees to Milliarcseconds (° to mas)

1 degree equals 3,600,000 milliarcseconds exactly.

How to convert degrees to milliarcseconds

To convert degrees to milliarcseconds, multiply the number of degrees by 3,600,000. This factor is exact. To go the other way, multiply milliarcseconds by 2.777777778×10⁻⁷ (rounded).

milliarcseconds = degrees × 3,600,000

Example: 10 degrees = 36,000,000 milliarcseconds.

About these units

Degree (°)

General & non-SICurrent unit

One 360th of a full turn. The everyday unit of angle, inherited from the ancient Babylonians' base-60 counting.

Dividing the circle into 360 parts traces back to the astronomers of ancient Babylon, who counted in base 60. Why 360 in particular is still debated. One explanation points to Persian and Babylonian calendars, which used a year of about 360 days, so the Sun seemed to advance roughly one degree each day. Another says the Babylonians started from the angle of an equilateral triangle and split it into 60 pieces, and a third credits early chord-based trigonometry, where a chord equal to the radius made a natural base. Greek astronomers such as Aristarchus and Hipparchus were among the first to use Babylonian astronomical knowledge systematically.

The number also divides well. 360 has 24 divisors and splits evenly by every whole number from 1 to 10 except 7, which suits a world cut into 24 time zones of 15 degrees of longitude each. Each degree breaks into 60 arcminutes, and each of those into 60 arcseconds. The SI Brochure lists the degree among the widely used non-SI units, equal to π/180 radian, about 0.01745. For scale, the Moon and the Sun each look about half a degree wide, and a little finger held at arm's length covers roughly one degree of sky.

1 degree = 0.002777777778 turns (approximately).

Sources: BIPM SI Brochure, 9th edition (2019); Wikipedia: Degree (angle); Wikipedia: Angular diameter

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

Related conversions

See all angle units.