Parallax Calculator: Stellar Distance from Parallax Angle
Enter a star's parallax angle to get its distance in parsecs, light-years, and astronomical units (AU). Flip the mode to reverse-solve: enter a known distance and get the equivalent parallax angle. The full calculation is shown step by step, so you can follow the exact arithmetic.
Formula
Worked example
Sirius has a measured parallax of 0.3792 arcseconds (379.2 mas). Applying d = 1/p: d = 1 / 0.3792 = 2.64 pc. Converting to light-years: 2.64 x 3.26156 = 8.60 ly. Checking the reverse: p = 1 / 2.64 = 0.3788 arcseconds (rounding accounts for the small difference).
What is stellar parallax?
Stellar parallax is the apparent shift in a star's position on the sky when viewed from opposite sides of Earth's orbit around the Sun - six months apart. As Earth moves from one side of its orbit to the other, nearby stars appear to shift against the fixed background of much more distant stars. The angle of that shift - measured as half the total angular displacement - is the parallax angle. It is tiny: even the nearest star system (Alpha Centauri) has a parallax of only 0.742 arcseconds, less than one two-thousandths of a degree. The smaller the parallax, the more distant the star.
The parallax formula and the parsec
The relationship is beautifully simple: d = 1/p, where d is the distance in parsecs and p is the parallax angle in arcseconds. A parsec is defined as the distance at which a star would show exactly 1 arcsecond of parallax - making the formula unit-free by design. One parsec equals 3.26156 light-years or 206,265 astronomical units (AU). To convert to light-years, multiply parsecs by 3.26156. To reverse-solve (find the parallax from a known distance), just invert: p = 1/d.
How to use this calculator
Select "Parallax angle to distance" and enter the parallax angle in arcseconds or milliarcseconds. The calculator returns the distance in parsecs, light-years, and AU instantly. Switch to "Distance to parallax angle" mode to do the reverse: enter a distance in any of those three units and get the corresponding parallax. The "Show your work" panel below the result traces every arithmetic step with your actual numbers, and the reference table lists measured parallaxes for famous nearby stars so you can cross-check your inputs.
Parallax limits and the distance ladder
Ground-based telescopes can measure parallaxes down to about 0.01 arcseconds, which corresponds to a maximum reliable range of about 100 parsecs (326 light-years). Beyond that, the measurement uncertainty becomes too large relative to the angle itself. Space missions changed everything: the Hipparcos satellite (1989-1993) pushed the limit to around 1,000 parsecs by achieving about 1 milliarcsecond precision. The Gaia mission (launched 2013) achieves around 0.025 milliarcseconds for bright stars, extending reliable parallax distances to roughly 10,000 parsecs and providing accurate measurements for over a billion stars. For stars beyond that range, astronomers use the cosmic distance ladder: spectroscopic parallax, Cepheid variable stars, and ultimately Type Ia supernovae for extragalactic distances.
Famous nearby stars: parallax and distance
| Star | Parallax (mas) | Distance (pc) | Distance (ly) |
|---|---|---|---|
| Proxima Centauri | 768.9 | 1.30 | 4.24 |
| Alpha Centauri A | 742.1 | 1.35 | 4.40 |
| Barnard's Star | 548.3 | 1.82 | 5.96 |
| Sirius | 379.2 | 2.64 | 8.60 |
| Procyon | 284.6 | 3.51 | 11.46 |
| Vega | 130.2 | 7.68 | 25.05 |
| Arcturus | 88.8 | 11.3 | 36.7 |
| Capella | 77.3 | 12.9 | 42.2 |
| Betelgeuse | 6.6 | 150 | 490 |
| Canopus | 10.4 | 95.9 | 313 |
Annual parallax angles and distances for well-known stars, from Hipparcos and Gaia DR3 catalogues.
Frequently asked questions
What does parallax angle measure?
Parallax angle measures how much a nearby star appears to shift against the background of distant stars as Earth moves from one side of its orbit to the other. The angle quoted in catalogues is the semi-annual parallax - half the full back-and-forth shift. The larger the angle, the closer the star.
What is a parsec and why is it used?
A parsec is the distance at which a star would show exactly 1 arcsecond of annual parallax. The definition makes the parallax formula d = 1/p exact with no conversion factors. One parsec is about 3.26 light-years or 3.086 x 10^13 kilometres. It is the natural unit for stellar astronomy because parallax measurements directly produce it.
How close is the nearest star?
Proxima Centauri, a red dwarf in the Alpha Centauri system, is the closest known star to the Sun. Its parallax is 768.9 milliarcseconds (0.7689 arcseconds), giving a distance of about 1.30 parsecs or 4.24 light-years. Light from Proxima Centauri takes 4.24 years to reach Earth.
Why can ground telescopes not measure very distant stars by parallax?
At large distances the parallax angle becomes extremely small - smaller than the blurring caused by Earth's atmosphere (atmospheric "seeing"). A star 1,000 pc away has a parallax of only 0.001 arcseconds (1 milliarcsecond), which ground-based instruments cannot reliably resolve. Space telescopes avoid atmospheric blurring entirely, which is why Gaia can measure much smaller angles than any ground observatory.
How is milliarcseconds (mas) different from arcseconds?
One milliarcsecond is one-thousandth of an arcsecond. Modern Gaia catalogues report parallax in mas because most catalogued stars are farther than 1 parsec (where the parallax is less than 1 arcsecond). To use the d = 1/p formula, divide the mas value by 1,000 to convert to arcseconds first, or use the mas input in this calculator and it converts automatically.
Can I use parallax to find the distance to stars in other galaxies?
Not with current technology. Even with Gaia's precision, reliable parallax distances are limited to our own galaxy out to roughly 10,000 parsecs (10 kpc). The Andromeda Galaxy is about 770,000 parsecs away - the parallax of a star there would be 0.0000013 arcseconds (1.3 microarcseconds), far below any current instrument's reach. Extragalactic distances use other rungs of the cosmic distance ladder such as Cepheid variable stars and Type Ia supernovae.
What is the parallax of Betelgeuse?
Betelgeuse has a parallax of about 6.6 milliarcseconds (0.0066 arcseconds), placing it around 150 parsecs or 490 light-years from Earth. Its large angular diameter makes it one of the few stars whose distance can also be cross-checked by direct angular measurements with optical interferometers.