Parallax to Parsec Calculator
Measuring how far away a star sits is one of the oldest problems in astronomy, and parallax is the most direct solution. As Earth travels around the Sun, a nearby star appears to shift slightly back and forth against the distant background over the course of a year. Half of that apparent yearly swing, measured in arcseconds, is the star's parallax angle, and it shrinks the farther away the star lies. This calculator converts a parallax angle into a distance in parsecs using the defining relationship: distance in parsecs equals one divided by the parallax in arcseconds. The parsec itself is defined as the distance at which one astronomical unit subtends one arcsecond, which is why the conversion needs no extra constant. You enter the parallax, and the tool returns the distance, computed deterministically from the formula shown below, never estimated, so the worked example reconciles exactly with the figure on screen. Parallax is the first rung of the cosmic distance ladder, calibrating every method that reaches farther. Space missions such as Hipparcos and Gaia have measured parallaxes for billions of stars, mapping much of our galaxy. Use this tool to turn a measured parallax into a distance or to check an astronomy problem.
Distance from parallax uses the reciprocal relationship d = 1 / parallax, with the angle in arcseconds and distance in parsecs. A parallax of 0.1 arcseconds gives a distance of 10.00 parsecs (about 32.6 light-years).
Parallax to parsec formula
d (parsecs) = 1 / p
p = parallax angle in arcseconds
d (light-years) = d (parsecs) x 3.261564
1 parsec = about 3.26 light-years
Distance and parallax are inversely proportional, so the distance in parsecs is the reciprocal of the parallax in arcseconds. Multiplying by about 3.26 converts the result into light-years.
Worked example
Find the distance to a star with a parallax of 0.1 arcseconds.
- d = 1 / 0.1 = 10.00 parsecs
- 10 x 3.261564 = 32.62 light-years
The star lies 10 parsecs, about 32.62 light-years, away. This is the calculator's default input, so the result above matches the widget exactly.
Parallax and distance reference
| Parallax (arcsec) | Distance (parsecs) | Light-years |
|---|---|---|
| 1.000 | 1.00 | 3.26 |
| 0.500 | 2.00 | 6.52 |
| 0.100 | 10.00 | 32.62 |
| 0.010 | 100.00 | 326.16 |
Reference: US National Aeronautics and Space Administration (NASA).
Parallax to parsec: frequently asked questions
What is a parsec?
A parsec is the distance at which one astronomical unit (the average Earth-Sun distance) subtends an angle of one arcsecond. It equals about 3.26 light-years, or roughly 30.9 trillion kilometers. The name comes from parallax of one arcsecond, which is the definition this calculator uses.
How does parallax give a distance?
As Earth orbits the Sun, nearby stars appear to shift slightly against distant background stars. Half of that yearly back-and-forth shift, measured in arcseconds, is the parallax angle. The distance in parsecs is simply one divided by the parallax in arcseconds: smaller shifts mean greater distances.
Why divide one by the parallax?
The parsec is defined so that a parallax of exactly one arcsecond corresponds to a distance of one parsec. Because parallax angle and distance are inversely proportional, the distance in parsecs is the reciprocal of the parallax in arcseconds, with no extra constants needed.
What is the limit of the parallax method?
The smaller the parallax, the farther and harder to measure the star. Ground-based telescopes reach a few hundred parsecs; space missions such as Hipparcos and Gaia measure tiny angles and extend the method across much of the galaxy. Beyond that, astronomers switch to standard candles.
How do I convert parsecs to light-years?
Multiply the distance in parsecs by about 3.262 to get light-years. So a star 10 parsecs away lies roughly 32.6 light-years from us. This calculator reports distance in parsecs, the natural unit when starting from a parallax angle.
Official sources
- Stellar parallax and distance reference: US National Aeronautics and Space Administration (NASA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.