Parallax Distance Calculator

Background.

Trigonometric parallax is the only direct, geometric distance measurement in astronomy. As the Earth swings from one side of its orbit to the other, a nearby star appears to shift slightly against the far more distant background. Half of that annual angular shift is the star's parallax, p, and the distance follows from a single reciprocal: d in parsecs equals 1 divided by p in arcseconds. Enter a parallax in milliarcseconds — the unit Gaia, Hipparcos and SIMBAD all publish in — and this calculator returns the distance in parsecs, light-years, astronomical units and kilometres, plus the distance modulus and, if you supply the catalogue's error bar, the 1σ distance range.

The relation d = 1/p is exact by construction, not a fitted approximation. That is worth being precise about because it is often taught as though a small-angle approximation were being made. It is not: the parsec is *defined* as the distance at which one astronomical unit subtends one arcsecond, and IAU 2015 Resolution B2 fixes it at exactly (648000/π) astronomical units. The small-angle step lives inside the definition of the unit, so once you accept the parsec, the inversion introduces no error of its own. Every scrap of uncertainty in your answer came in with the parallax.

Which is exactly why this page makes you look at the fractional parallax uncertainty. Inverting a measured parallax is not the same operation as inverting a true one. Because 1/p is a convex function, symmetric error bars on p map to *asymmetric* error bars on d — the far end of the range is always further from the central value than the near end — and the mean of the inverted distribution is not the inverse of the mean. Bailer-Jones showed in 2015 (PASP 127) that once the fractional parallax uncertainty passes roughly 20%, naive inversion stops being a defensible distance estimator at all, and a Bayesian estimate with an explicit distance prior is required instead. He noted this affected roughly 80% of the stars Gaia would catalogue. This calculator computes σ/p, tells you which regime you are in, and says plainly when the number it has just printed should be read as an order of magnitude rather than a distance.

Parallax is also the rung the whole cosmic distance ladder stands on. Everything above it — Cepheid period-luminosity relations, the tip of the red giant branch, Type Ia supernovae, and ultimately the Hubble constant — is calibrated against geometric parallaxes of nearby stars. That makes parallax systematics unusually consequential, and it is why published parallaxes for the same star genuinely disagree. Pourbaix and Boffin (2016) revisited α Centauri and found the original Hipparcos value near 742 mas, van Leeuwen's 2007 re-reduction at 754.81 ± 4.11 mas, and their own solution at 743 ± 1.3 mas — a spread of about 1.7%, far larger than any individual error bar. A parallax is a measurement with a provenance, not a fact; always record which catalogue and which reduction yours came from.

On conventions and limits: parallax here is an angle in milliarcseconds and distance is a length; the only dimensionless output is the distance modulus, in magnitudes. Parallax is treated as a strictly positive quantity. Real catalogues do publish negative parallaxes for faint, distant sources — those are noise excursions, not negative distances, and this page rejects them rather than returning nonsense. It likewise rejects an uncertainty equal to or larger than the parallax, because the 1σ lower bound on p would then be zero or below and the far end of the distance range would sit at or past infinity. What the page does not model: Gaia's documented parallax zero-point offset, the photocentre wobble of unresolved binaries, and Lutz–Kelker style selection bias in magnitude-limited samples. Each of those can move a distance by more than the quoted error bar, and none of them can be recovered from a single parallax number.

What is parallax distance calculator?

Annual (trigonometric) parallax is half the total angular displacement a star appears to undergo over six months as the Earth moves from one side of its orbit to the other. It is an angle, conventionally quoted in milliarcseconds (mas); one milliarcsecond is a thousandth of an arcsecond, and an arcsecond is 1/3600 of a degree. A parallax of 1 arcsecond corresponds to a distance of exactly 1 parsec, about 3.26 light-years. No star is that close: the largest stellar parallax known, Proxima Centauri's, is about 0.768 arcseconds.

The distance follows as d(pc) = 1/p(arcsec). Because parallaxes are published in mas, the practical form is d(pc) = 1000/p(mas). The distance modulus μ = 5 log₁₀(d/pc) − 5 is a logarithmic restatement of the same distance in magnitudes, and it is what photometry actually uses: an object's apparent magnitude minus its absolute magnitude equals μ, by definition of absolute magnitude as the apparent magnitude the object would have at 10 parsecs.

What parallax is not: it is not a redshift, and it has nothing to do with cosmic expansion. Parallax works only where the geometry is measurable — currently out to a few thousand parsecs with Gaia, and reliably to a few hundred. Beyond that, distances come from standard candles calibrated on parallaxes, then from Hubble's law, each rung inheriting the systematic errors of the one below it.

How to use this calculator.

1. 01Look up your star's parallax in a catalogue — SIMBAD, the Gaia archive and the Hipparcos catalogue all publish it in milliarcseconds.
2. 02Enter that parallax. Note which catalogue and which data release it came from; different reductions of the same star genuinely differ.
3. 03Enter the catalogue's 1σ uncertainty if you have it. Leave it at zero to get a single distance with no range.
4. 04Read the distance in parsecs (the primary result), and in light-years if you are writing for a general audience.
5. 05Check the reliability note before you use the number. If the fractional uncertainty is above about 20%, the inverted distance is biased and should be replaced with a Bayesian estimate.
6. 06Carry the distance modulus across to the stellar magnitude calculator if you want an absolute magnitude.

The formula.

The whole calculation is one reciprocal. Your parallax in milliarcseconds is divided by 1000 to get arcseconds, and the distance in parsecs is the reciprocal of that. Everything else is a unit conversion by an exact factor: × 3.2615637772 for light-years, × 206,264.806247 for astronomical units, × 3.0856775814913673 × 10¹⁶ for metres. The distance modulus is μ = 5 log₁₀(d/pc) − 5, which returns exactly −5 at d = 1 pc and exactly 0 at d = 10 pc, as it must.

The error range is computed by inverting the parallax at both ends of its 1σ interval rather than by propagating a linearised error. The near end of the distance range comes from the *larger* parallax, p + σ; the far end from the *smaller*, p − σ. Because 1/p is convex, those two ends are not equidistant from the central value: for Proxima Centauri's 768.0665 ± 0.0499 mas the near end sits 0.00008458 pc below the central distance while the far end sits 0.00008459 pc above it — a lopsidedness of about one part in ten thousand of the error bar, invisible at this precision but real. The asymmetry grows rapidly and becomes obvious once σ/p reaches a few per cent, and it dominates past 20%. Doing it this way rather than by linear propagation is deliberate — linear propagation hides exactly the asymmetry that matters.

Rounding stage: there is no intermediate rounding. All arithmetic runs at 40 significant digits and is rounded once, at the return boundary, to ten decimal places. The reliability bands are decided on the unrounded ratio σ/p, so a value sitting exactly on 2% or exactly on 20% falls in the higher band deterministically rather than depending on display rounding.

Invalid-domain behaviour is explicit. A parallax of zero is the singularity of d = 1/p — an infinitely distant source — and raises a field error rather than returning Infinity. A negative parallax raises an error too: catalogues really do publish them for noisy faint sources, but a negative parallax is a noise excursion, not a negative distance, and inverting it would produce a confidently signed nonsense. An uncertainty greater than or equal to the parallax also raises an error, because p − σ ≤ 0 puts the far end of the range at or beyond infinity; in that situation the parallax is simply not significantly detected.

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 this page's independent test case. Peer-reviewed; open-access preprint.