How to use it
- Enter the parallax and choose mas (milliarcseconds, as in modern catalogues) or arcseconds.
- Tick the box and enter the apparent magnitude if you want the absolute magnitude and the luminosity.
- Read the distance in parsecs and light-years; au and km are listed below.
Formulas
- Distance: d (pc) = 1 ÷ p (arcsec) = 1000 ÷ p (mas)
- Units: 1 pc = 648,000 ÷ π au = 3.0857 × 10¹³ km = 3.2616 light-years; 1 au = 149,597,870,700 m, 1 light-year = 9,460,730,472,580,800 m
- Absolute magnitude: M = m − 5 × log₁₀(d ÷ 10)
- Distance modulus: m − M = 5 × log₁₀(d) − 5
- Luminosity in V: L ÷ L☉ = 10^(0.4 × (4.83 − M))
Interstellar dust (extinction) is not included: it makes stars look fainter, so M comes out too faint for distant stars in dusty directions.
Worked example
A star with a parallax of 100 mas and apparent magnitude 6:
- d = 1000 ÷ 100 = 10 pc = 32.616 light-years = 2,062,648 au
- M = 6 − 5 × log₁₀(10 ÷ 10) = 6, distance modulus 0
- luminosity 10^(0.4 × (4.83 − 6)) = 0.3404 times the Sun
A parallax of 1 mas puts a star at 1,000 pc; if it appears at magnitude 10, its absolute magnitude is 0 and it is 85.5067 times as luminous as the Sun.
Tips
- Small parallaxes are uncertain. When the error is a sizeable fraction of the parallax, 1/p is a poor distance estimate.
- Magnitudes run backwards: a lower number means brighter, and 5 magnitudes are a factor of 100 in brightness.
- Use the same band for m and the Sun’s magnitude; 4.83 is for the visual (V) band.