Case 1
- Parallax angle
- 0.1arcsec
10.000000pc
Open with these valuesParallax Distance Calculator
10.000000pc
Result: 10.000000 pcA parsec is defined as the distance at which one astronomical unit spans one arcsecond, so the distance in parsecs is simply one divided by the parallax angle. Halve the angle and the star is twice as far. Gaia catalogues list milliarcseconds — divide those by 1000 first.
Worked examples
Case 2
- Parallax angle
- 0.7687arcsec
1.300898pc
Open with these valuesCase 3
- Parallax angle
- 0.05arcsec
20.000000pc
Open with these valuesHow it's calculated
d = 1 ÷ p
- StepLook up the star's annual parallax in arcseconds.
- StepA catalogue in milliarcseconds (mas)? Divide by 1000 first.
- StepDivide one by the angle — that is the distance in parsecs.
- ResultMultiply by 3.26156 to read the same distance in light-years.
What this number means
The distance in parsecs is one over the angle
The parsec is defined as the distance at which one astronomical unit spans one arcsecond, so d = 1 / p carries no measured constant at all. Halve the angle and the star is twice as far: 0.1 arcsec gives 10 pc, 0.05 arcsec gives 20 pc.
Gaia lists milliarcseconds, this box wants arcseconds
One milliarcsecond is a thousandth of an arcsecond, so a catalogue value has to be divided by 1000 before it goes in. Typing Proxima Centauri as 768.7 instead of 0.7687 puts the nearest star at 0.0013 pc.
Small angles are the hard ones to measure
Because the distance is the reciprocal, remote stars show vanishingly small angles. Ground-based telescopes stay reliable out to a few hundred parsecs and Gaia carries the method into the thousands; past that, astronomers move to other rungs of the distance ladder.
Parsecs to light-years: multiply by 3.26156
One parsec is about 3.26156 light-years, so 10 pc are 32.6156 ly and 20 pc are 65.2312 ly. Divide rather than multiply to go the other way.
Commonly misread
Entering Gaia's 768.7 mas for Proxima Centauri straight into the box.
Divide milliarcseconds by 1000 first: 0.7687 arcsec gives 1.300898 pc, about 4.24 light-years. The raw 768.7 would answer 0.0013 pc.
A parallax twice as large means a star twice as far away.
It means half the distance, because the relation is a reciprocal. A parallax of 0.5 arcsec gives 2 pc, while 0.2 arcsec gives 5 pc.
Reading an output of 10 as light-years.
The result is in parsecs, and 10 pc are 32.6156 light-years once multiplied by 3.26156. The reference table lists both columns side by side.
Reference table
| Parallax (arcsec) | In light-years | Distance (pc) |
|---|---|---|
| 1 | 3.26 | 1 |
| 0.7687 | 4.24 | 1.300898 |
| 0.5 | 6.52 | 2 |
| 0.2 | 16.31 | 5 |
| 0.1 | 32.62 | 10 |
| 0.05 | 65.23 | 20 |
Questions
How do I calculate distance from parallax?
Take the reciprocal of the parallax angle measured in arcseconds: d = 1 / p. The result is the distance in parsecs. A parallax of 0.1 arcsec gives 1 ÷ 0.1 = 10 parsecs, about 32.6 light-years.
What is a parsec?
A parsec is the distance at which one astronomical unit — the Earth–Sun distance — subtends an angle of one arcsecond. By definition a star with a parallax of exactly one arcsecond is one parsec away. One parsec equals about 3.26156 light-years.
My catalogue lists milliarcseconds. What now?
Divide by 1000 before entering the value, because one milliarcsecond is a thousandth of an arcsecond. Gaia publishes parallaxes in mas, so its 768.5 mas for Proxima Centauri becomes 0.7685 arcsec here. Getting this wrong shifts every distance by a factor of a thousand.
How do I convert parsecs to light-years?
Multiply the distance in parsecs by 3.26156, the number of light-years in one parsec. So 10 parsecs equal 32.6156 light-years. To go the other way, divide the light-years by 3.26156.
Why does parallax only work for nearby stars?
Distance is the reciprocal of the angle, so distant stars have vanishingly small angles that are hard to measure. Ground-based telescopes stay reliable to a few hundred parsecs, and space missions like Gaia extend the method to thousands. Beyond that, astronomers switch to other rungs of the distance ladder.
Sources and last check
Information, not professional advice.