Last updated: 2026-06-16

Measuring Distance by Parallax

Parallax is the apparent shift of a nearby object against a distant background when you view it from two different positions. Hold a finger at arm's length and blink each eye in turn: the finger jumps relative to the wall behind it. Astronomers use the same effect on a cosmic scale, with the two viewpoints being the Earth's position at opposite ends of its orbit.

As the Earth circles the Sun, a nearby star traces a tiny ellipse against the background stars over the course of a year. The parallax angle $p$ is half the maximum shift, corresponding to a baseline of one astronomical unit. The distance follows from simple trigonometry, and with the parsec defined for exactly this purpose it reduces to:

$d\,[\text{pc}] = \frac{1}{p\,[\text{arcsec}]}$

The Parsec

A parsec is the distance at which one astronomical unit subtends an angle of one arcsecond. This definition is what makes the formula so clean — the distance in parsecs is just the reciprocal of the parallax in arcseconds.

One parsec equals about 3.26 light-years, or $3.086 \times 10^{13}$ km.

Worked Example

A star is measured to have a parallax of 0.1 arcsec.

$d = \frac{1}{0.1} = 10\ \text{pc} \approx 32.6\ \text{light-years}$

The nearest star, Proxima Centauri, has a parallax of 0.769 arcsec, giving a distance of 1/0.769 = 1.30 parsecs, or 4.24 light-years.

Reach and Limits

Because parallax angles shrink as distance grows, the method is limited by measurement precision. The angles involved are minuscule: even the nearest stars shift by less than one arcsecond, far smaller than the resolution of the naked eye. Ground-based telescopes can measure parallaxes for stars out to a few hundred parsecs. The European Space Agency's Gaia mission pushes this to microarcsecond precision, fixing distances to more than a billion stars across the Milky Way. For galaxies far beyond our own, parallax is hopeless and astronomers turn to standard candles and the distance modulus instead.