Convert a stellar parallax angle into distance in parsecs and light-years.
Convert a stellar parallax angle into distance in parsecs and light-years. Small-angle approximation noted in the sections.
Distance (parsecs)
How to use this tool
The apparent annual shift of a star against distant background stars.
Arcseconds for nearby stars; milliarcseconds for the tiny angles measured by modern surveys.
Distance in parsecs is simply 1 divided by the parallax in arcseconds.
Multiply parsecs by 3.26156 for light-years.
Formula & worked example
Parallax 0.1 arcseconds: distance = 1 / 0.1 = 10 parsecs = 32.6156 light-years.
Limitations — read this before you rely on it
The formula itself is exact for the parallax definition, but measured parallaxes carry uncertainty that grows rapidly for distant stars; a small parallax error translates into a large distance error, so published distances for far stars are estimates with wide error bars.
Frequently asked questions
The distance at which a star shows a parallax of exactly one arcsecond: about 3.26 light-years.
Because the star appears to shift as Earth moves around the Sun, viewed from opposite sides of its orbit.
Proxima Centauri shows about 0.77 arcseconds, giving about 1.30 parsecs (4.24 light-years).
Most stars are far away, so their parallaxes are thousandths of an arcsecond; Gaia measures them routinely.
A measured value can come out negative from noise for very distant stars, but a negative angle has no physical distance meaning.