How do we know how far away stars are?
Through a ladder of methods, each calibrated against the one below it — because no single technique works across the enormous range of distances involved, and the whole structure is only as sound as its bottom rungs.
Rung one: parallax. As Earth orbits the Sun, nearby stars appear to shift slightly against distant background stars. Measuring that tiny angle from opposite sides of the orbit gives distance by simple geometry. This is the only truly direct method — it requires no assumptions about the star itself. Space astrometry missions have measured parallaxes for over a billion stars, extending this rung enormously.
Rung two: standard candles. Certain objects have a known intrinsic brightness, so comparing that with how bright they appear gives distance, since brightness falls with the square of distance.
Cepheid variable stars pulsate with a period directly related to their true luminosity — a relationship discovered by Henrietta Leavitt, which made the method possible and is one of the foundational measurements in astronomy.
Type Ia supernovae, which explode at a characteristic brightness and are visible across enormous distances, extending the ladder to other galaxies.
Rung three: redshift. For very distant galaxies, the stretching of light by the expansion of space gives distance via the relationship between redshift and distance — which itself had to be calibrated using the rungs below.
Other techniques in between: spectroscopic parallax, using a star's spectrum to infer its true brightness; the Tully-Fisher relation for spiral galaxies; and the brightness of the brightest red giants in a galaxy.
Why the ladder structure matters. An error low down propagates all the way up. This is why the disagreement between different measurements of the expansion rate — the Hubble tension — is taken so seriously: it may indicate a calibration problem somewhere in the ladder, or genuinely new physics, and distinguishing the two is an active problem.
Why any of it is believable: the methods overlap in range, and where they overlap they agree.