Parallax Calculator

Stellar parallax is the apparent shift in position of a nearby star against the background of distant stars as Earth moves from one side of its orbit to the other (a baseline of 2 AU). The parallax angle p is half of this total shift. The distance to the star in parsecs is simply d = 1/p, where p is in arcseconds. This is the origin of the parsec (parallax arcsecond).

Proxima Centauri has a parallax of 0.7687 arcseconds (annual parallax), placing it at 1/0.7687 = 1.301 parsecs = 4.244 light-years. This was measured with high precision by the Hipparcos satellite (1997) and confirmed by Gaia (2016 onwards). A parallax of 1 arcsecond would place a star at exactly 1 parsec; no star is this close.

Gaia is an ESA astrometry satellite launched in 2013. It measures stellar positions and parallaxes to microarcsecond precision. Gaia Data Release 3 (2022) provides parallaxes for about 1.5 billion stars. At 0.02 milliarcsecond (20 microarcsecond) precision, Gaia can measure distances to about 10,000 parsecs (10 kpc) with 10% accuracy, covering most of the Milky Way.

Trigonometric parallax measures the geometric shift directly (d = 1/p, no assumptions about physics). Spectroscopic parallax uses the star's spectrum to determine its absolute luminosity (from spectral type and luminosity class), then compares to apparent magnitude to find distance: d = 10^((m-M+5)/5). Spectroscopic parallax is a misnomer (it does not use actual parallax measurement) but it extends distance measurement much farther than trigonometric parallax.

Ground-based telescopes can measure parallaxes down to about 20 milliarcseconds, corresponding to 50 parsecs. Space-based Hipparcos reached 1 milliarcsecond (1 kpc). Gaia reaches 20 microarcseconds (50 kpc). The challenge is that parallax angles decrease as 1/d while measurement errors are roughly constant, so the fractional distance error increases with distance. For distances beyond about 1 Mpc, other methods (Cepheids, supernovae) are needed.