About the Parallax Distance Calculator
This parallax distance calculator converts a star’s trigonometric parallax — the tiny back-and-forth shift it shows as Earth orbits the Sun — into its distance. Enter the parallax in arcseconds or milliarcseconds (the unit used by the Gaia and Hipparcos catalogues) and get the distance in parsecs, light-years, astronomical units and kilometres. You can also go the other way and find the parallax a star at a given distance would show.
Add the star’s apparent magnitude and the calculator also returns its distance modulus and absolute magnitude, so you can compare its true brightness with the Sun’s. It is aimed at astronomy students, amateur observers looking up Gaia data, and anyone curious how astronomers measure distances to the stars.
The relation d = 1/p is exact by definition of the parsec, but measured parallaxes carry uncertainties: for very small parallaxes (below about 1 mas, or when the error exceeds 10–20% of the value) simply inverting the parallax gives a biased distance, and catalogue distance estimates use statistical priors instead.
With the default inputs, the distance (parsecs) is 1.302 pc. Change any value above to recalculate instantly.
How to use the parallax distance calculator
- 1Choose whether to find distance from parallax or parallax from distance.
- 2Enter the parallax and pick milliarcseconds (Gaia/SIMBAD) or arcseconds.
- 3Optionally enter the star’s apparent magnitude to get its absolute magnitude.
- 4Read the distance in parsecs, light-years, AU and km.
Formula and method
As Earth moves from one side of its orbit to the other, a nearby star appears to shift against far more distant background stars. Half of that annual shift is the parallax angle p. A parsec is defined as the distance at which 1 AU subtends one arcsecond, so the distance in parsecs is simply 1 divided by the parallax in arcseconds — or 1,000 divided by the parallax in milliarcseconds.
One parsec is exactly 648,000/π AU, about 206,264.8 AU or 3.26156 light-years. When you supply an apparent magnitude m, the calculator applies the distance modulus m − M = 5·log₁₀(d) − 5 to get the absolute magnitude M, the brightness the star would have at 10 parsecs. Interstellar dust extinction is ignored here; use the magnitude calculator to include it.
- d
- Distance in parsecs
- p
- Parallax angle (arcseconds or milliarcseconds)
- m
- Apparent magnitude
- M
- Absolute magnitude (brightness at 10 pc)
Worked examples
Proxima Centauri (Gaia DR3: 768.0665 mas)
d = 1,000 ÷ 768.0665 = 1.302 pc, or 1.302 × 3.26156 = 4.246 light-years. With apparent magnitude 11.13, M = 11.13 − 5·log₁₀(1.302) + 5 ≈ 15.56 — a faint red dwarf about 19,000 times dimmer than the Sun in visible light.
Sirius (379.21 mas, m = −1.46)
1,000 ÷ 379.21 = 2.637 pc = 8.60 ly. The distance modulus is −2.894, so M = −1.46 + 2.894 ≈ 1.43, about 23 times the Sun’s visual luminosity.
Parallax of a star 100 light-years away
100 ly ÷ 3.26156 = 30.66 pc, so the parallax is 1 ÷ 30.66 = 0.0326″, or 32.6 mas — easily measured by Gaia, which reaches tens of microarcseconds for bright stars.
Frequently asked questions
How do you calculate distance from parallax?+
Divide 1 by the parallax in arcseconds to get the distance in parsecs, or divide 1,000 by the parallax in milliarcseconds. Multiply parsecs by 3.26156 to get light-years. A parallax of 100 mas means 10 pc, or 32.6 ly.
What is a parsec?+
A parsec (parallax-second) is the distance at which one astronomical unit subtends an angle of one arcsecond: exactly 648,000/π AU, about 3.26 light-years or 30.9 trillion km. It is the standard distance unit in professional astronomy.
Which star has the largest parallax?+
Proxima Centauri, the nearest star to the Sun, with a parallax of about 768 milliarcseconds (0.768″) measured by Gaia. Even that is smaller than the angle a coin makes several kilometres away.
How far can parallax measure distances?+
Ground-based parallaxes reach about 100 pc; ESA’s Hipparcos (about 1 mas precision) gave reliable distances out to a few hundred parsecs, and Gaia measures parallaxes for over a billion stars with precisions of tens of microarcseconds, giving useful distances across much of the Milky Way.
What is the distance modulus?+
The distance modulus m − M = 5·log₁₀(d) − 5 is the difference between a star’s apparent and absolute magnitudes. It is zero at 10 parsecs, negative closer and positive farther away, and is a compact way astronomers express distance.