Parallax Distance Calculator

Background.

Hold a finger at arm's length and look at it with one eye, then the other, and it jumps against the wall behind. Astronomers do the same thing with the Earth's orbit as the baseline. Six months apart, the Earth is about 300 million kilometres from where it was, and a nearby star shifts slightly against much more distant ones. Half of that yearly back-and-forth, measured as an angle, is the star's parallax p. For Proxima Centauri, the nearest star, it is 0.768 arcseconds — the width of a 2-centimetre coin seen from about 5.4 kilometres away — and every other star's is smaller.

Turning the angle into a distance takes one division. The parsec is defined as the distance at which one astronomical unit spans one arcsecond, so a star with a parallax of p arcseconds lies 1/p parsecs away, and with catalogue parallaxes in milliarcseconds, d = 1000/p. IAU 2015 Resolution B2 fixes the parsec at exactly 648,000/π au, so the conversion adds no uncertainty of its own: all of it arrives with the measured parallax.

That uncertainty decides whether the answer can be used. Because distance is the reciprocal of parallax, a symmetric error bar on p becomes a lopsided one on d, and Bailer-Jones (2015) showed that once the error reaches about 20 percent of the parallax, simple inversion stops being a sound distance estimate. Enter the catalogue's 1σ uncertainty along with the parallax and you get the near and far ends of the range, the fractional uncertainty and a note on which regime the measurement falls in, as well as the distance in parsecs, light-years, astronomical units and kilometres and the distance modulus.

Parallax is also where the cosmic distance scale begins. Cepheid variables, the tip of the red giant branch and Type Ia supernovae are calibrated against stars whose distances were fixed this way, so a systematic error in nearby parallaxes travels all the way up to estimates of how fast the universe is expanding.

What is parallax distance calculator?

Annual trigonometric parallax is half the angular displacement a star shows over a year as the Earth moves around the Sun, measured against a background of much more distant objects. It is quoted in milliarcseconds: one mas is a thousandth of an arcsecond, and an arcsecond is 1/3,600 of a degree. The distance is d = 1/p with p in arcseconds, giving parsecs; one parsec is 206,264.806 au, 3.2616 light-years or about 3.0857 × 10¹³ km. Friedrich Bessel made the first convincing stellar parallax measurement, of 61 Cygni, in 1838. The Hipparcos satellite later reached precisions of about a milliarcsecond, and Gaia's errors for bright stars are a few hundredths of a milliarcsecond, though many times larger for faint ones. The distance modulus μ = 5 log₁₀(d/pc) − 5 expresses the same distance on the magnitude scale: it is the apparent magnitude minus the absolute magnitude, zero at 10 parsecs and growing by 5 for every tenfold increase in distance.

How to use this calculator.

1. 01Look up the star's parallax in SIMBAD, the Gaia archive or the Hipparcos catalogue; all three list it in milliarcseconds. Note which catalogue and data release you used, because different reductions of the same star genuinely disagree.
2. 02Enter the parallax in mas. A value quoted in arcseconds needs multiplying by 1000 first; 0.37921″ becomes 379.21.
3. 03Enter the catalogue's 1σ uncertainty in the same unit, or leave it at 0 for a single distance with no range. It has to be smaller than the parallax itself.
4. 04Read the distance in parsecs, or in light-years for a general audience, and check the reliability note before quoting it. Below 2 percent fractional uncertainty the inversion is solid; between 2 and 20 percent it is usable with a lopsided range; at 20 percent or more it is only a rough guide.
5. 05Carry the distance modulus to a magnitude calculation if you want the star's absolute magnitude: M = m − μ.

The formula.

The parallax in milliarcseconds is divided by 1000 to give arcseconds, and the distance in parsecs is the reciprocal: d = 1 ÷ p(″) = 1000 ÷ p(mas). The other units are fixed multiples. One parsec is 648,000/π au by the IAU definition; the au is exactly 149,597,870,700 m; and a light-year is the distance light travels in a Julian year of 365.25 days, which makes one parsec about 3.2616 light-years. The distance modulus is μ = 5 log₁₀(d) − 5 with d in parsecs.

The range comes from inverting both ends of the parallax interval rather than from a linear error formula. The larger parallax, p + σ, gives the near end; the smaller, p − σ, gives the far end. Because 1/p curves, the far end always sits further from the central value than the near end does. A 1 mas parallax with a 0.1 mas error puts the star at 1000 pc with a range of 909.09 to 1111.11 pc, 90.91 pc short and 111.11 pc long. At a 0.25 mas error the range runs from 800 to 1333.33 pc, and the far side is already two-thirds wider than the near side.

The reliability note reads the ratio σ/p: under 2 percent the inversion is described as reliable, from 2 up to 20 percent as usable but asymmetric, and at 20 percent or more as biased, following Bailer-Jones. A parallax of zero or below has no distance and is rejected, as is an uncertainty equal to or larger than the parallax, which would push the far end of the range to infinity.

Three real effects are outside the arithmetic. Gaia parallaxes carry a small zero-point offset that depends on magnitude, colour and position on the sky. An unresolved binary's light centre wobbles and can corrupt the fitted parallax. And when stars are chosen by their measured parallax — everything above a cut, or everything with a small relative error — the sample favours stars whose parallaxes scattered upward, so distances come out too small on average, a bias associated with Lutz and Kelker. Each can move a distance by more than its quoted error bar.

A worked example.

Frequently asked questions.

References& sources.

1. [1]European Space Agency, Science & Technology education resource, "Stellar Distances" (retrieved 2026-07-29). Defines the parsec as "the distance at which an object has a parallax of one arcsecond", gives "d(parsec) = 1/p(arcsecond)", states "1 parsec = 3.26 light years", and gives the distance-modulus form M = m − 5 log(D/10). Independent of the IAU documents below; open access.
2. [2]Mamajek, E. E., et al. (2015), "IAU 2015 Resolution B2 on Recommended Zero Points for the Absolute and Apparent Bolometric Magnitude Scales", arXiv:1510.06262 (retrieved 2026-07-29). The resolution text states the parsec is "exactly (648 000/π) au", giving 3.085 677 581 × 10¹⁶ m — the exact conversion used here. Open-access preprint of an adopted IAU resolution.
3. [3]Bailer-Jones, C. A. L. (2015), "Estimating distances from parallaxes", Publications of the Astronomical Society of the Pacific 127 (October 2015); arXiv:1507.02105 (retrieved 2026-07-29). Shows that distance estimation by inverting the parallax breaks down once the fractional parallax error exceeds about 20%, affecting roughly 80% of Gaia's catalogue, and that a uniform distance prior performs poorly. Source of this page's 20% reliability threshold. Peer-reviewed; open-access preprint.
4. [4]SIMBAD astronomical database (CDS, Strasbourg), object "Proxima Centauri": parallax 768.0665 ± 0.0499 mas, reference 2020yCat.1350....0G (Gaia Early Data Release 3). Retrieved 2026-07-29. Source of the worked example. Independent data centre; open access.
5. [5]Pourbaix, D. & Boffin, H. M. J. (2016), "Parallax and masses of α Centauri revisited", Astronomy & Astrophysics 586, A90; arXiv:1601.01636 (retrieved 2026-07-29). Reports α Cen at 743 mas, "right where Hipparcos (ESA 1997) had put it", against van Leeuwen's 2007 re-reduction — the documented parallax disagreement quoted on this page. Peer-reviewed; open-access preprint.
6. [6]van Leeuwen, F. (2007), "Validation of the new Hipparcos reduction", Astronomy & Astrophysics 474, 653–664; arXiv:0708.1752 (retrieved 2026-07-29). The re-reduction that supplies SIMBAD's parallaxes for bright stars such as Sirius (379.21 ± 1.58 mas), used as an independent check on this page. Peer-reviewed; open-access preprint.