A parsec is the distance at which a star would have a parallax angle of exactly 1 arcsecond. It equals about 3.086 × 10¹³ km or 3.26156 light-years. The name comes from "parallax arcsecond."

Why is the formula d = 1/p so simple?

The parsec is defined to make this relationship exact. Because 1 pc is defined as the distance giving a 1″ parallax, any other parallax p (in arcseconds) gives a distance of 1/p parsecs by direct proportion.

What is the smallest parallax that can be measured?

The Hipparcos satellite achieved ~1 milliarcsecond precision, reaching stars out to ~1 kpc. The Gaia mission reaches ~20 microarcseconds, extending reliable parallax distances to several kiloparsecs.

Can I enter a parallax in milliarcseconds?

Use the unit selector to switch to milliarcseconds (mas). The calculator converts internally before applying d = 1/p.

What if I enter a negative parallax?

Negative parallax measurements arise from noise in real catalogs. They have no physical distance interpretation; the tool will flag this as an invalid input.

How do I add a measurement uncertainty?

Enter the ±error in the uncertainty field. The calculator propagates it via σ_d = σ_p / p² (in parsecs), a first-order symmetric approximation that is most useful when the fractional parallax uncertainty is small.

Stellar Parallax Calculator

Enter a star's parallax angle in arcseconds to instantly calculate its distance in parsecs and light-years using d = 1/p.

Parallax Input

Parallax angle (p)

Measurement uncertainty ± (optional)

arcsec

Quick examples

Distance Results

Enter a parallax angle and click Calculate.

Results copied!

Summary

Stellar parallax is the apparent shift in a nearby star's position against background stars as Earth orbits the Sun. The parallax angle (p) in arcseconds gives the distance directly via d = 1/p parsecs — the definition of the parsec. This calculator takes a parallax measurement and returns the distance in parsecs, light-years, and astronomical units so you can quickly interpret trigonometric parallax data from catalogs such as Hipparcos and Gaia.

How it works

Enter the parallax angle in arcseconds. For most stars this is a very small number (e.g., Proxima Centauri = 0.7687″).
The calculator applies d (pc) = 1 / p, where p is in arcseconds.
Distance in light-years is found by multiplying parsecs by 3.26156.
Distance in astronomical units is parsecs × 206,265.
Click Calculate Distance to update the results, with first-order uncertainty propagation if you enter a ±error.

Use cases

Convert Hipparcos or Gaia catalog parallax values to distances for a star.
Solve introductory astronomy homework involving the parsec definition.
Cross-check published distances against measured parallax angles.
Explore how distance uncertainty scales with parallax measurement error.
Build intuition for how far away stars at different parallaxes actually are.
Quickly compare distances for a list of nearby stars.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu