Parallax and Parsec Distance Calculator

Convert stellar parallax angle to distance in parsecs, light-years, and AU, or find the parallax angle from any distance.

📐 Parallax & Parsec Distance Calculator
Parallax angle100.0000 mas
mas
0.1 mas750 mas
Distance10.0000 pc
pc
0.01 pc5,000 pc
Distance
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In Light-Years
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In AU
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Distance Modulus (μ)
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Parallax in Arcseconds
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Parallax Angle
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In Arcseconds
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Distance in Light-Years
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Distance Modulus (μ)
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📐 What is Stellar Parallax?

Stellar parallax is the apparent shift in a nearby star's position against the background of more distant stars, caused by Earth's orbital motion around the Sun. As Earth moves from one side of its orbit to the other (a baseline of 2 AU), nearby stars appear to shift slightly in position. The parallax angle p is defined as half this total shift, corresponding to the angle subtended by 1 AU at the star's distance. The measurement technique is called trigonometric parallax or annual parallax and is the most direct and model-independent method for measuring stellar distances.

The parsec (pc) is defined as the distance at which a star has an annual parallax of exactly 1 arcsecond. This definition makes the distance formula d(pc) = 1/p(arcsec) exact by construction. For practical measurements, parallaxes are quoted in milliarcseconds (mas), so d(pc) = 1000/p(mas). The nearest star, Proxima Centauri, has p = 768.5 mas, placing it at 1.30 pc = 4.24 light-years. Alpha Centauri A and B have p = 742.12 mas (1.35 pc, 4.40 ly).

Ground-based astrometry reaches about 10 mas precision, limiting parallax distances to within roughly 100 pc. The Hipparcos satellite (1989 to 1993) achieved 1 mas precision for about 120,000 stars, covering the local disk out to about 1 kpc. The Gaia satellite (2013 to present) revolutionized this field, measuring parallaxes to 7 to 25 microarcseconds (μas) precision for over 1 billion stars, enabling direct distance measurements across most of the Milky Way disk. Gaia DR3 (2022) contains parallax measurements for 1.46 billion stars, many with distances accurate to a few percent out to 10 kpc.

The simple d = 1/p formula assumes the measurement is perfect. For faint stars with noisy parallax measurements, statistical biases emerge: in particular, 1/p is not an unbiased estimator of distance when p has measurement uncertainty. Surveys like Gaia use Bayesian distance estimators with spatial priors to correct for this. The calculator above is accurate for well-measured parallaxes (fractional uncertainty below about 20 percent) and is ideal for interpreting Hipparcos or Gaia catalog values for nearby, bright stars.

📐 Formula

d  =  1 / p    (d in pc, p in arcsec)   ≡   d  =  1000 / pmas
d = distance in parsecs (pc)
p = annual parallax angle in arcseconds (″); 1 arcsec = 1/3600 degree
pmas = parallax in milliarcseconds; p(arcsec) = p(mas) / 1000
Distance modulus: μ = 5 log10(d) − 5  (gives μ in magnitudes when d is in pc)
Unit conversions: 1 pc = 3.26156 ly = 206,264.806 AU = 3.0857 × 1013 km
Example: p = 100 mas = 0.1 arcsec → d = 1/0.1 = 10 pc = 32.62 ly → μ = 5 log10(10) − 5 = 0.00 mag

📖 How to Use This Calculator

Steps

1
Select a calculation mode — choose Find Distance to convert a parallax angle to a distance, or Find Parallax to compute the expected parallax angle for a known distance (useful when comparing catalog predictions to observations).
2
Enter the parallax or distance — in Find Distance mode, type the annual parallax in milliarcseconds (mas) as found in the Hipparcos or Gaia catalog, or drag the slider (range 0.1 to 750 mas). Type values outside the slider range for more distant stars. In Find Parallax mode, enter a distance in parsecs.
3
Read all outputs — the calculator shows the distance in parsecs, light-years, and AU, plus the parallax in arcseconds, and the distance modulus μ = 5 log10(d/10 pc) for use in absolute/apparent magnitude calculations.

💡 Example Calculations

Example 1 — Alpha Centauri (Nearest Bright Star System)

Alpha Centauri AB has a Hipparcos parallax of 742.12 mas. How far away is it?

1
Convert mas to arcsec: p = 742.12 / 1000 = 0.74212 arcsec.
2
Apply d = 1/p: d = 1/0.74212 = 1.3475 pc.
3
Convert: d = 1.3475 × 3.26156 = 4.395 ly. Distance modulus: μ = 5 log10(1.3475) − 5 = −4.353 mag.
Distance = 1.3475 pc = 4.395 ly = 277,923 AU  |  μ = −4.353 mag
Try this example →

Example 2 — Sirius (Brightest Star in the Sky)

Sirius has a Hipparcos parallax of 379.21 mas. What is its distance and distance modulus?

1
d = 1000/379.21 = 2.6370 pc.
2
d = 2.6370 × 3.26156 = 8.601 ly. Sirius's absolute magnitude is M = +1.43; apparent magnitude m = −1.46.
3
Distance modulus: μ = 5 log10(2.6370) − 5 = −2.895 mag. Check: m − M = −1.46 − 1.43 = −2.89 ≈ μ ✓
Distance = 2.6370 pc = 8.601 ly  |  μ = −2.895 mag
Try this example →

Example 3 — Betelgeuse (Red Supergiant in Orion)

Betelgeuse has a Hipparcos parallax of approximately 5.95 mas. How far away is it?

1
d = 1000/5.95 = 168.07 pc.
2
d = 168.07 × 3.26156 = 548.3 ly. In AU: 168.07 × 206,265 = 34,670,000 AU.
3
Distance modulus: μ = 5 log10(168.07) − 5 = 6.13 mag. With apparent magnitude m ≈ 0.5, absolute magnitude M ≈ 0.5 − 6.13 = −5.63 (supergiant luminosity class I).
Distance = 168.07 pc = 548.3 ly  |  μ = 6.13 mag
Try this example →

Example 4 — Inverse Mode: Galactic Center Distance

The Galactic Center is 8,178 pc away (Gravity Collaboration 2019). What parallax would it show?

1
Switch to Find Parallax mode. Enter d = 8178 pc.
2
p = 1/8178 = 1.2228 × 10−4 arcsec = 0.12228 mas = 122.28 μas.
3
d = 8178 × 3.26156 = 26,675 ly. Distance modulus: μ = 5 log10(8178) − 5 = 14.56 mag. This matches the known K-band extinction-corrected distance modulus to the Galactic Center.
Parallax = 0.1223 mas (122.28 μas)  |  d = 26,675 ly  |  μ = 14.56 mag
Try this example →

❓ Frequently Asked Questions

What is stellar parallax and how is it measured?+
Stellar parallax is the apparent shift in a nearby star's position against background stars as Earth orbits the Sun. The parallax angle p is half the total angular shift over six months, measured against distant reference stars. Ground-based telescopes reach about 10 mas precision; Hipparcos reached 1 mas for 120,000 stars; Gaia achieves 7-25 microarcseconds for over 1 billion stars.
What is the definition of one parsec?+
A parsec is the distance at which a star has an annual parallax of exactly 1 arcsecond. The name combines parallax and arcsecond. One parsec equals 3.26156 light-years, 206,264.806 AU, or 3.0857 × 1013 km. The definition makes d(pc) = 1/p(arcsec) exact by construction, with no conversion factor needed.
How do you convert parallax in milliarcseconds to parsecs?+
Divide 1000 by the parallax in milliarcseconds: d(pc) = 1000/p(mas). For Alpha Centauri at p = 742.12 mas: d = 1000/742.12 = 1.348 pc. For a Gaia star at p = 10 mas: d = 100 pc. For p = 1 mas: d = 1000 pc = 1 kpc. For p = 0.1 mas: d = 10 kpc (near Galactic Center).
What is the distance modulus and how is it used?+
The distance modulus is μ = 5 log10(d) − 5, where d is in parsecs. It equals the difference between a star's apparent magnitude m and its absolute magnitude M: μ = m − M. A star at 10 pc has μ = 0. At 100 pc, μ = 5 (100 times fainter in flux, 5 magnitudes). At 1 Mpc, μ = 25.
What is the nearest star's parallax?+
Proxima Centauri has a parallax of 768.5 mas, placing it at 1.2948 pc = 4.2438 ly. It is the nearest known star to the Sun. Alpha Centauri A and B have a combined parallax of 742.12 mas (1.348 pc, 4.395 ly) and form the nearest bright stellar system visible to the naked eye.
What is the maximum distance measurable by parallax?+
Ground-based telescopes can reach about 100 pc reliably. Hipparcos reached about 1 kpc for well-measured stars. Gaia DR3 provides parallaxes accurate to a few percent out to 10-30 kpc for bright giant stars, covering most of the Milky Way disk and enabling the largest 3D stellar maps ever made.
Why does the 1/p formula break down at large distances?+
When parallax uncertainty is significant, 1/p is a biased distance estimator. Stars with noisy parallax measurements have an asymmetric error distribution: underestimated parallaxes give distances that are too large by much more than overestimated parallaxes underestimate distance. For Gaia stars with fractional parallax uncertainty above about 20%, use Bayesian distance estimates instead.
What is 1 parsec in light-years?+
One parsec equals 3.26156 light-years exactly (given the IAU 2012 definition of the AU and the speed of light). Conversely, 1 light-year = 0.30660 parsecs. The Milky Way disk is about 30 kpc (97,800 light-years) in diameter, and the nearest large galaxy (Andromeda, M31) is 770 kpc (2.51 million light-years) away.
What parallax corresponds to the Galactic Center?+
The Galactic Center (Sgr A*) is about 8.178 kpc away, implying a parallax of p = 1/8178 = 1.22 × 10−4 arcsec = 0.122 mas = 122 μas. Gaia can in principle detect this, but heavy dust extinction makes optical parallax measurements unreliable toward the Galactic Center. Radio parallaxes of water masers near Sgr B2 provide the most accurate measurements.
What is the difference between annual and secular parallax?+
Annual parallax (trigonometric parallax) uses Earth's 1 AU orbital radius as the baseline, producing an elliptical apparent path for nearby stars over one year. Secular parallax uses the Sun's motion through the galaxy (20 km/s toward the solar apex) as a growing baseline over decades, enabling statistical mean distances to stellar groups too distant for annual parallax. Secular parallax cannot give individual star distances.
How accurate is the parsec as a unit?+
The parsec is defined exactly in terms of the IAU 2012 astronomical unit (1 AU = 149,597,870,700 m exactly). Therefore 1 pc = 648000/π AU = 3.0856775814913673 × 1016 m, with no rounding uncertainty. All distance uncertainty comes from the measured parallax, not the unit definition itself.
What are the parallaxes of famous stars?+
Alpha Centauri: 742.12 mas (1.348 pc, 4.395 ly). Sirius: 379.21 mas (2.637 pc, 8.60 ly). Vega: 130.23 mas (7.68 pc, 25.05 ly). Arcturus: 88.83 mas (11.26 pc, 36.72 ly). Betelgeuse: ~5.95 mas (~168 pc, ~548 ly). Deneb: ~2.3 mas (~430 pc, ~1400 ly). The Pleiades cluster: 7.36 mas (136 pc, 444 ly).
Tags: Parallax Calculator Parsec Distance Calculator Stellar Parallax Distance Modulus Light-Years to Parsecs Calculator Formula Free Online

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What is stellar parallax and how is it measured?

Stellar parallax is the apparent shift in a nearby star's position against the background of more distant stars as Earth orbits the Sun. The parallax angle p is half the total angular shift measured over six months (the baseline being 1 AU from Earth to Sun). Hipparcos (1989-1993) measured parallaxes to about 1 milliarcsecond precision for 120,000 stars. Gaia (2013-present) has extended this to over 1 billion stars with microarcsecond precision.

What is the definition of one parsec?

A parsec is the distance at which a star would have an annual parallax of exactly one arcsecond. The name comes from parallax-arcsecond. One parsec equals 3.26156 light-years, 206,264.806 AU, or 3.0857e13 km. The parsec definition makes the distance formula d(pc) = 1/p(arcsec) exact by construction.

How do you convert parallax in milliarcseconds to parsecs?

Divide 1000 by the parallax in milliarcseconds: d(pc) = 1000 / p(mas). For Alpha Centauri with p = 742.12 mas: d = 1000/742.12 = 1.348 pc. For a star at p = 10 mas: d = 100 pc. For p = 1 mas: d = 1000 pc = 1 kpc.

What is the distance modulus and how is it used?

The distance modulus is mu = 5 log10(d) - 5, where d is in parsecs. It equals the difference between a star's apparent magnitude m and its absolute magnitude M: mu = m - M. A star at 10 pc has mu = 0 by definition. A star at 100 pc has mu = 5, meaning it appears 5 magnitudes fainter than if it were at 10 pc.

What is the nearest star's parallax?

Proxima Centauri is the nearest star at 1.2948 pc (4.2238 ly). Its annual parallax is 768.5 mas, measured by Hipparcos and confirmed by Gaia. The Alpha Centauri AB system has a parallax of 742.12 mas (1.348 pc, 4.395 ly) and is also commonly cited as the nearest stellar system.

What is the maximum distance measurable by parallax?

Ground-based telescopes can measure parallaxes down to about 10 mas, reaching only 100 pc with useful accuracy. The Hipparcos satellite reached 1 mas precision, good to about 1 kpc. Gaia's microarcsecond precision (about 7 to 25 μas for bright stars) extends reliable trigonometric parallaxes to 10-30 kpc, covering most of the Milky Way disk.

Why does the parallax formula break down at large distances?

At large distances, parallax angles become smaller than the measurement error. For Gaia with 25 μas precision, a 10 kpc star has p = 0.1 mas, giving a 25% distance uncertainty. Beyond 20-30 kpc, statistical biases from catalog noise make the simple d = 1/p formula unreliable. Probabilistic methods (Bayes estimation with a prior on the stellar density distribution) give better distances.

What is 1 parsec in light-years?

One parsec equals 3.26156 light-years. This comes from the definition: 1 pc = 1 AU / tan(1 arcsecond) = 1 AU / (pi/(180*3600)) = 206264.8 AU, and 1 AU = 1.58125e-5 ly, so 1 pc = 206264.8 x 1.58125e-5 = 3.26156 ly.

What parallax corresponds to the Galactic Center distance?

The Galactic Center is approximately 8.178 kpc away (Gravity Collaboration 2019). Its parallax would be p = 1/8178 = 1.223e-4 arcsec = 0.1223 mas = 122.3 μas. This is measurable in principle by Gaia but is confused by interstellar dust extinction in the optical band. Radio parallax measurements of masers near Sgr A* give the most direct distance.

What is the difference between annual parallax and secular parallax?

Annual parallax (also called trigonometric parallax) is the shift due to Earth's 1 AU baseline around the Sun, forming a complete ellipse over one year. Secular parallax uses the Sun's motion through the galaxy (20 km/s toward Vega, the solar apex) as a much longer baseline, enabling statistical distance estimates for star clusters too far for annual parallax. Secular parallax gives only average distances for a group, not individual star distances.

How accurate is the parsec as an astronomical unit of distance?

The parsec is defined precisely in terms of the astronomical unit (1 AU = 149,597,870,700 m exactly, per IAU 2012). So 1 pc = 648000/pi AU = 3.0856775814913673e16 m exactly. The only source of uncertainty in a stellar distance is the measured parallax angle itself, not the parsec definition.

What is the distance in parsecs to famous stars?

Alpha Centauri: 1.348 pc (742.12 mas). Sirius: 2.637 pc (379.21 mas). Vega: 7.68 pc (130.23 mas). Betelgeuse: about 168 pc (5.95 mas, with significant uncertainty). Deneb: approximately 430 pc. The Pleiades cluster: 136 pc. The Orion Nebula: 412 pc.

📌 Quick Tips

💡One parsec equals the distance at which 1 AU subtends an angle of exactly 1 arcsecond. Alpha Centauri at 742.12 mas is only 1.348 pc away.
💡Gaia DR3 measures parallaxes to about 7 microarcseconds precision for bright stars, reaching distances of over 10 kpc with useful accuracy.
💡The distance modulus mu = 5 log10(d/10 pc) links apparent magnitude m, absolute magnitude M, and distance: m - M = mu.
💡For negative parallaxes (which appear in catalogs for faint, noisy measurements) this formula breaks down. Use probabilistic distance estimates for those cases.
💡1 parsec = 3.26156 light-years = 206,265 AU = 3.0857e13 km.