#### Question

# How do you convert arcsecs to parsecs? Is there a formula?

If I have 0.75 arcsecs, what would this be in parsecs?

I would later needs to convert the parsec into a light year as well...

#### Answer

Arcseconds mean angular distance, whereas parsecs are for linear distance. They are not directly interconvertible, but if a star has a parallax of 1 arcsecond, it is at a distance of 1 parsec. The relationship is the reciprocal of the parallax. So 1/0.75 = 1 1/3 parsec.

The larger the parallax, the smaller the distance, so there is an inverse relationship, not a direct one as the first answerer suggested.

A parsec is 3.26 light years, so 1 1/3 parsec = 4.347 lightyears.

These are two totally different systems of units, measuring totally different thungs. Arc seconds measure angles while parsecs measure distances in space.

You don't. Arcsecond is a unit of angular measurement, while a parsec is a unit of distance. However, when observed from the distance of 1 AU, 1 arcsecond equals 1 parsec.

Parsec is a contraction of "parallax of one arc second," so if an object is observed to shift 1 arc second at an interval of 1 A.U., it is one pc away.

The exact formula for distance in A.U. is

D = 1/tan a

where a is the shift. In radians, since tan a = a for very small values, you can just divide 1 A.U. by the shift. Multiply by pi/6.48E5 to convert seconds to radians.

1/tan (.75 pi/6.48E5) = 275000 A.U. or 4.3 light years.