Calculate the distance to a star from its parallax angle (distance in parsecs = 1/parallax in arcseconds), in parsecs and light years.
Inputs
The star's apparent shift in position (″), measured against distant background stars over Earth's orbit.
Result
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Enter a parallax angle above to compute.
Distance
How far away the star is.
Required parallax angle
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Enter a distance above to compute.
Parallax, Parsecs & Light Years
Reference table of parallax angles and their corresponding distances in parsecs and light years
Parallax
Distance (pc)
Distance (ly)
1″
1 pc
≈ 3.26 ly
0.772″ (Proxima Centauri)
≈ 1.30 pc
≈ 4.24 ly
0.1″
10 pc
≈ 32.6 ly
0.01″
100 pc
≈ 326 ly
0.001″ (1 mas)
1,000 pc
≈ 3,262 ly
Why smaller angles mean farther stars
A parsec ("parallax second") is defined as the distance at which 1 astronomical unit — the Earth–Sun distance — subtends an angle of exactly 1 arcsecond as seen from a star. Because distance and parallax angle are reciprocals (d = 1/p), a star with a smaller measured shift is farther away. Even the nearest star system, Proxima Centauri, has a parallax of well under 1 arcsecond — real stellar parallaxes are always tiny, which is why they weren't reliably measured until the 1830s and why space telescopes like Gaia now measure them to microarcsecond precision.
4 min read3 steps6 terms3 examples6 FAQsd (pc) = 1 / p (arcsec)
Stellar parallax is the most fundamental method astronomers have for measuring distances to nearby stars — it relies on nothing but geometry and Earth's own orbital motion.
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Walk-through
How to Use This Calculator
3 steps▸
1
Enter the parallax angle
Type the star's parallax angle in arcseconds (″) on the Distance tab. This is the tiny annual back-and-forth shift the star appears to make against distant background stars as Earth orbits the Sun. The result updates instantly.
2
Read the distance
The Distance tab shows the star's distance in parsecs and light years, using d(pc) = 1/p(arcsec). The interpretation line spells out both units in plain language.
3
Work backward from a known distance
Switch to the Solve Parallax tab, enter a distance in parsecs or light years, and the calculator returns the parallax angle a star at that distance would show — useful for checking what a telescope would need to measure.
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Reference
Formula & Methodology
1 formula▸
Distance from parallax angle
d (pc) = 1 / p (arcsec)
A star's distance in parsecs is the reciprocal of its parallax angle in arcseconds. This is the defining relationship for the parsec itself: 1 parsec is the distance at which 1 astronomical unit (the Earth–Sun distance) subtends an angle of exactly 1 arcsecond. To convert to light years, multiply by 3.2616 (1 pc ≈ 3.2616 ly).
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Glossary
Key Terms Explained
6 terms▸
Parallax ↗The apparent shift in a nearby star's position against more distant background stars, caused by Earth's changing viewpoint as it orbits the Sun. Astronomers measure this shift twice, six months apart, and use half the total angular shift as the parallax angle.
Parsec ↗"Parallax second" — the distance at which 1 astronomical unit subtends an angle of exactly 1 arcsecond, about 3.2616 light-years or 3.0857×10¹⁶ meters. It's the standard distance unit in professional astronomy because it comes directly from a parallax measurement.
Arcsecond ↗1/3600 of a degree — an extremely small angle. Even the nearest star beyond the Sun has a parallax under 1 arcsecond, which is why reliable stellar parallax measurements weren't achieved until 1838 (Friedrich Bessel, for 61 Cygni).
Stellar Parallax ↗The parallax effect applied specifically to stars: the tiny annual wobble in a star's apparent position caused by Earth's orbital motion. It is the most direct, geometry-based method for measuring astronomical distances, with no assumptions about the star's brightness or type.
Baseline ↗The fixed distance between the two observation points used to measure a parallax angle. For stellar parallax, the baseline is the diameter of Earth's orbit — 2 astronomical units — since observations are taken six months apart at opposite points in the orbit.
Light Year ↗The distance light travels in one Julian year, about 9.461 trillion kilometers. It's a more familiar unit than the parsec for general audiences, though astronomers usually work directly in parsecs since that's what a parallax measurement yields.
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Scenarios
Real-World Examples
3 worked examples▸
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Astronomy student
Textbook parallax angle
Parallax angle 0.1″
A parallax of 0.1″ gives d = 1/0.1 = 10 pc, which is about 32.6 light years. This is the classic textbook example because the numbers are round: doubling the parallax angle to 0.2″ would halve the distance to 5 pc, illustrating the reciprocal relationship directly.
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Nearest-star lookup
Proxima Centauri
Parallax angle 0.768″
Proxima Centauri, the closest known star to the Sun, has a measured parallax of about 0.768″ (768 milliarcseconds). Plugging that in gives d = 1/0.768 ≈ 1.30 pc, or about 4.24 light years — matching the commonly cited distance to Proxima Centauri.
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Mission planner
Solving for required precision
Target distance 1,000 pc
On the Solve Parallax tab, entering a distance of 1,000 pc (about 3,262 light years) returns a required parallax of just 0.001″ (1 milliarcsecond). This shows why measuring parallax for distant stars demands extraordinary precision — the Gaia space telescope was built specifically to measure angles this small and smaller.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
Stellar parallax is the most fundamental method astronomers have for measuring distances to nearby stars — it relies on nothing but geometry and Earth's own orbital motion. This calculator converts a measured parallax angle directly into a distance, and can also work the calculation in reverse.
How the Parallax Calculator works
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The calculator applies the defining relationship of the parsec: d (pc) = 1 / p (arcsec). Hold up a finger at arm's length and close one eye, then the other — the finger appears to shift against the background. Do the same thing with a star, using Earth's orbit as the "arm," and you get the same effect on an astronomical scale. Astronomers observe a star's position from opposite sides of Earth's orbit (six months apart) and measure the angular shift; half of that total shift is the parallax angle, p. Because the geometry is a simple right triangle with a known baseline (1 AU), the distance falls out as the reciprocal of the angle in arcseconds. To express the result in light years, the calculator multiplies the parsec value by 3.2616, the fixed ratio between the two units.
Inputs and what they mean
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The Distance tab takes one input: the parallax angle in arcseconds. Real stellar parallaxes are small — even Proxima Centauri, the nearest star system, has a parallax under 1 arcsecond — so the field also accepts decimals well below 1 (e.g. 0.001″ for a star roughly 1,000 parsecs away). The Solve Parallax tab flips the calculation: enter a distance (in parsecs or light years) and the calculator returns the parallax angle a star at that distance would show, which is useful for judging what precision a telescope or survey needs to detect it.
Limits and edge cases
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The parallax angle must be a positive number — a parallax of exactly zero would imply an infinite distance, so the calculator will not divide by zero and instead prompts for a valid angle. Trigonometric (geometric) parallax is only practical for relatively nearby stars; beyond a few thousand parsecs the angles become too small to measure reliably even with space-based instruments, and astronomers switch to indirect distance methods (standard candles, redshift, etc.) instead. This calculator performs the pure geometric conversion only — it does not account for measurement uncertainty, which in practice is the limiting factor on how far parallax can reach.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for distance from parallax?+
d (pc) = 1 / p (arcsec). A star's distance in parsecs equals the reciprocal of its parallax angle measured in arcseconds. This relationship is exact by definition — it's how the parsec unit itself was created.
What exactly is a parsec?+
A parsec is the distance at which 1 astronomical unit (the average Earth–Sun distance) subtends an angle of exactly 1 arcsecond. It equals about 3.2616 light-years, or roughly 3.0857×10¹⁶ meters. Astronomers prefer parsecs over light-years because a parsec value comes directly out of a parallax measurement.
How far away is Proxima Centauri based on its parallax?+
Proxima Centauri has a measured parallax of about 0.768 arcseconds, giving a distance of roughly 1.30 parsecs — about 4.24 light years. It's the closest known star to the Sun besides the Sun itself.
What units does the Parallax Calculator use?+
Parallax angle is entered in arcseconds (″). The Distance tab reports the result in both parsecs (pc) and light years (ly). The Solve Parallax tab accepts a distance in either parsecs or light years and returns the corresponding parallax angle.
Why does a smaller parallax angle mean a farther star?+
Distance and parallax angle are reciprocals of each other (d = 1/p): as the angle a star appears to shift gets smaller, the calculated distance gets larger. This is intuitive by analogy — a farther object appears to move less against the background when you shift your viewpoint than a nearby one does.
What is the baseline used for stellar parallax?+
The baseline is Earth's orbit around the Sun. Astronomers observe a star's position from opposite ends of Earth's orbit, six months apart — a baseline of 2 astronomical units — and use half of the total observed angular shift as the parallax angle, p.
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