Stellar Parallax Calculator
Turn a star’s parallax angle into its distance in parsecs and light-years.
That is 32.62 light-years (1 pc = 3.2616 ly).
A parallax of 1 arcsecond means a star is exactly 1 parsec away — the definition of the parsec. Distance in parsecs is just d = 1 ÷ p, with p in arcseconds. So a parallax of 0.1″ gives d = 1 ÷ 0.1 = 10 parsecs, which is 10 × 3.2616 ≈ 32.6 light-years.
What stellar parallax is
Parallax is the tiny apparent shift in a nearby star’s position as Earth moves from one side of its orbit to the other. Measured six months apart, the star seems to jump against the far more distant background stars. Half of that total shift is the parallax angle p. Because the baseline is Earth’s orbit (one astronomical unit), a bigger angle means the star is closer, and a smaller angle means it is farther away. Parallax is the first rung of the cosmic distance ladder and the only direct, geometric way to measure how far the nearest stars are.
d = distance in parsecs, p = parallax angle in arcseconds. 1 parsec = 3.2616 light-years = 3.0857 × 10¹³ km. For a parallax in milliarcseconds, d = 1000 ÷ p (mas).
Worked example
Proxima Centauri, the nearest star to the Sun, has a measured parallax of p = 0.7687″. Its distance follows directly from d = 1 ÷ p:
- 1 Write the parallax relation. d (pc) = 1 ÷ p (arcsec). Distance in parsecs is one divided by the parallax angle in arcseconds.
- 2 Put the parallax in arcseconds. If the angle is given in milliarcseconds, divide by 1000 first. Here p = 0.7687″ is already in arcseconds.
- 3 Divide one by the parallax. d = 1 ÷ 0.7687 = 1.301 parsecs.
- 4 Convert to light-years if you like. d = 1.301 × 3.2616 ≈ 4.24 light-years — matching the known distance to Proxima Centauri.
Parallax angle to distance
A smaller parallax angle always means a larger distance — distance is one divided by the angle.
| Parallax p | Distance (parsecs) | Distance (light-years) | Example |
|---|---|---|---|
| 1″ | 1 pc | 3.26 ly | Definition of the parsec |
| 0.7687″ | 1.30 pc | 4.24 ly | Proxima Centauri |
| 0.1″ | 10 pc | 32.6 ly | Standard 10-parsec reference |
| 0.01″ (10 mas) | 100 pc | 326 ly | Nearby galactic neighbourhood |
| 0.001″ (1 mas) | 1000 pc | 3262 ly | Reach of ground-based parallax |
Why a smaller angle means a farther star
The relationship is a reciprocal, not a straight line. Since d = 1 ÷ p, halving the parallax doubles the distance. A star at 0.1″ sits at 10 pc; one at 0.01″ is ten times farther, at 100 pc. Distant stars barely shift as Earth orbits, so their parallax angles shrink toward zero — which is exactly why direct parallax only works for relatively nearby stars.
The parsec is defined by this geometry. One parsec — “parallax of one arcsecond” — is the distance at which one astronomical unit subtends an angle of exactly 1″. No star is actually that close: even Proxima Centauri, at p = 0.7687″, is 1.30 pc away. Ground-based telescopes struggle below about 0.01″ because Earth’s atmosphere blurs the tiny shift, so their reliable reach is a few hundred parsecs. The Gaia space mission measures parallaxes down to tens of microarcseconds — thousandths of the ground limit — mapping distances across much of the Milky Way.