Choose an appropriate distance scale
The au suits Solar System distances, pc and kpc suit stars and Galactic structures, and Mpc suits intergalactic scales. Choosing a unit does not change the length. 2 kpc means 2000 pc, not 2000 au. Carry units through intermediate steps; a catalogue number without its unit can be misread by many orders of magnitude.
Distance and light travel time are different quantities. A light-second is length c×1 s, whereas a second is time. A distance in light-years permits d/c in a simple vacuum model. It establishes neither an object’s current position nor automatically a cosmological age.
The au is fixed while Earth moves
In 2012 the IAU fixed this length exactly and recommended the unique symbol au. Earth–Sun separation varies along the orbit; the conversion factor does not vary with it. “Exactly one au” denotes a defined length rather than a measured instantaneous separation.[1]
Historically, the au was tied to planetary dynamics and the Gaussian gravitational constant. Today the solar mass parameter GM☉ is determined observationally while the unit stays fixed. Consequently the au definition alone cannot determine an exact solar mass or an exact Earth orbital period.[1]
Light-year from vacuum light and a Julian year
The Julian year used here is exactly 31 557 600 s. Exact c therefore gives an exact length. A calendar year with leap rules, a tropical year or a sidereal day is a different time convention and must not silently replace it.[3][7]
One light-year equals 9.4607304725808×1012 km. The shorter 9.46×1012 km display rounds the same definition. A measured distance of 12.0 ly still has the precision of the observation; an exact unit does not make the measured distance known to all digits.
Parsec and the small angle
The exact conventional definition uses the radian value of an arcsecond: 1″=π/648000 rad. The finite metre display is rounded rather than an experimentally uncertain conversion factor.[2]
Convert with cancelling factors
mas denotes milliarcseconds. Changing the angular unit changes the number by a factor 1000. kpc, Mpc and Gpc use decimal factors 103, 106 and 109. Also distinguish arcminutes from minutes of time and microarcseconds from milliarcseconds.
Build conversions using unit ratios: a distance in pc times metres per pc yields metres; division by metres per light-year yields light-years. Retain extra digits internally. Catalogue precision and measurement uncertainty determine the useful output, not the many available digits of an exact conversion factor.
Example: a radar path with outbound and return travel
The au/c baseline is checked against JPL parameters. The echo delay below is an original calculation for an assumed stationary path rather than a claimed actual planetary separation.[9]
From au to echo delay
- Given
- A simplified stationary target is 0.420 au away. Light travels in vacuum; ignore motion, gravity and instrument delays.
- Find
- Find one-way travel time and echo delay.
Multiply 0.420 by the exact au length.
Divide one-way distance by c.
The echo follows outbound and return paths: twice the same distance.
Result: Approximately 210 s one-way and 419 s for the echo, or about 6.99 min total.
Check: c×tEcho/2 returns 0.420 au. Treating echo delay as one-way time doubles the inferred distance.
Retained baseline: one au
- Given
- d=1 au in vacuum.
- Find
- Find one-way travel time.
Insert exact au and c.
Divide the result by 60 for minutes.
Result: Approximately 8 min 19 s; this is one-way travel across the defined au.
Check: c×t returns 149597870700 m. Instantaneous Earth–Sun distance need not equal one au.
Example: distance and small parallax uncertainty
A high-significance model parallax
- Given
- p=(40.0±0.4) mas, with ± denoting standard uncertainty. Assume calibration is already accounted for.
- Find
- Find d in pc and ly, including linear u(d).
40.0 mas is 0.0400″, so d≈1/0.0400=25.0 pc.
The derivative of the reciprocal gives u(d)/d≈u(p)/p=0.01.
Multiply both values by 3.261563777 to obtain light-years.
Result: A suitable output is d=(25.00±0.25) pc or approximately (81.5±0.8) ly.
Check: For p=39.6 and 40.4 mas, inverse distances are 25.2525 and 24.7525 pc. Their slight asymmetry shows why linear uncertainty is only a local approximation.
Measurement, proper motion and uncertainty
Annual parallax is superposed on proper motion, possible orbital motion and instrumental effects. A real star therefore requires modelling a sequence of observations. Its p value is not simply the positional difference between two photographs, and uncertainty is not determined by the exact au alone.[6]
When relative parallax uncertainty is large or the measured value is near zero or negative, d=1/p is not a reliable distance estimate. Negative measurement estimates do not mean negative physical distances. Distance inference accounts for the measurement model, uncertainty and, where used, an explicitly stated prior; resulting intervals can be strongly asymmetric.[5]
What conversion cannot determine
For nearby stationary targets, d/c is a useful geometric travel time in a simple model. In an expanding cosmological setting, luminosity distance, angular-diameter distance and light travel time must be distinguished. A value in Mpc alone does not identify which quantity is meant. The unit stays the same while the observation model changes.[8]
A stellar distance also refers to an observer and epoch. Actual light travel times can require relativistic corrections. Label results with unit, measurement or model status and, where appropriate, epoch. Fixed pc and ly definitions support clear communication rather than guaranteeing an exactly known three-dimensional position.
Three problems with solutions
Convert 1.80 kpc to pc and ly.
Show hint
Remove the prefix first.
Show solution and calculation
1.80 kpc=1800 pc≈5870.8148 ly, or 5.87×103 ly to three significant figures.
What one-way vacuum light travel time corresponds to 3.00 ly?
Show hint
Use the Julian-year definition.
Show solution and calculation
3.00 Julian years=94672800 s.
This is the model travel time, not a statement about cosmological distance measures.
A well-determined positive parallax is 2.50 mas. Find the approximate distance.
Show hint
Do not insert mas as arcseconds.
Show solution and calculation
d≈1000/2.50=400 pc=0.400 kpc≈1304.6255 ly.
Standard uncertainty cannot be stated without u(p).
Sources for this explanation
Quanta · Updated October 1, 2026
- IAU 2012 Resolution B2: astronomical unit
- Mamajek et al.: IAU 2015 Resolution B2, exact parsec definition
- IAU: Measuring the Universe — Julian year
- OpenStax Astronomy 2e §19.2: Surveying the Stars
- Bailer-Jones et al. (2018): Estimating distances from parallaxes IV
- ESA: How does Gaia study the Milky Way?
- BIPM: SI Brochure
- Hogg: Distance measures in cosmology
- JPL: Astrodynamic Parameters — Julian year and one-au light time
Editorial responsibility: Quanta Study editorial team
Review scope
This explanation, 3 worked examples and 3 exercises are available in German and English. Structure, source references and mathematical notation undergo automated checks. Calculations, model assumptions and both language versions receive a separate AI review.
An internal human subject review is documented for an earlier release of this page. That confirmation does not apply automatically to the revised explanation and new exercises.
An independent, named human subject review has not yet been documented. Our exercise numbers are worked examples, rather than measurements published by the cited sources.
Editorial responsibility, sources and methodsCite this reference page
Quanta. Astronomical distance units. Updated October 1, 2026. https://quanta-study.de/en/formula-sheet/tables/astronomische-laengeneinheiten
When citing a specific scientific statement, also cite the specialist source linked to that statement.