The parallax distance formula
As Earth orbits the Sun, nearby stars appear to shift slightly against the far more distant background. Half of that yearly shift is the parallax angle. Astronomers defined the parsec so this relationship is beautifully simple: the distance in parsecs is just the reciprocal of the parallax in arcseconds.
d (parsecs) = 1 ÷ p (arcseconds)
1 parsec = 3.26156 light-years = 206,265 AU
Worked example
Proxima Centauri has a parallax of 0.7687 arcseconds. Its distance is 1 ÷ 0.7687 = 1.30 parsecs, which is about 4.24 light-years, our nearest stellar neighbor.
Frequently asked questions
How do you calculate star distance from parallax?
Distance in parsecs equals 1 divided by the parallax in arcseconds: d = 1 / p. A 0.5″ parallax means 2 parsecs.
What is stellar parallax?
The small apparent shift of a nearby star against background stars as Earth orbits the Sun. Smaller shifts mean greater distances.
What is a parsec?
The distance at which a star shows a 1-arcsecond parallax, about 3.26 light-years or 3.086 × 10¹³ km.
How do I convert milliarcseconds to distance?
Divide by 1,000 to get arcseconds, then take the reciprocal. 100 mas = 0.1″ = 10 parsecs (about 32.6 light-years).
How far away is Proxima Centauri from its parallax?
Its 0.7687″ parallax gives 1 / 0.7687 = 1.30 parsecs, about 4.24 light-years.
Why does parallax only work for nearby stars?
Distant stars shift too little to measure. Ground telescopes reach a few hundred light-years; the Gaia mission extends parallax much farther with milliarcsecond precision.