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What is the exact measurement of a light year? I searched google for the answer in meters and came up with $9.461\cdot 10^{15}$ meters. When I calculated the answer considering $299\,792\,458 \;\text{m/s}$ as the speed of light, I came up with:

$$ 299\,792\,458 \times 365 \times 24 \times 3\,600 = 9\,454\,254\,955\,508\,926 \;\text{m} $$ Why is there such a gap? Did I miss something to add in the equation or is it just wrong?

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  • $\begingroup$ 9,460,514,622,032,012 meters is not quite correct; it assumes a year of about 365.2417 days. $\endgroup$
    – Keith Thompson
    Commented Aug 29, 2016 at 21:44

2 Answers 2

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By convention, astronomy uses the Julian Year for the computation of a light year:

Although there are several different kinds of year, the IAU regards a year as a Julian year of 365.25 days (31.5576 million seconds) unless otherwise specified.

Wikipedia gives the length as

31 557 600 s ✕ 299 792 458 m/s = 9 460 730 472 580 800 m (exactly)

The reason that it's exact (and not subject to experimental error) is that the metre itself is defined in terms of the speed of light, so the quantities are fixed by definition.

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    $\begingroup$ One way to avoid this ambiguity would be to lookup the length of a lightsecond (where second is a well-defined SI unit) and then convert that into whatever notion of years you care about. But for astronomy purposes you probably just want to use the usual convention. $\endgroup$
    – R.. GitHub STOP HELPING ICE
    Commented Aug 29, 2016 at 13:39
  • $\begingroup$ One light-second is 299 792 458 metres of course, and that's exactly the conversion that's being done in the quoted text. $\endgroup$
    – Toby Speight
    Commented Dec 13, 2022 at 16:31
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You're forgetting that one year is not 365 days, but 365.2422 or something close to that.

That change will give you a number much much closer to the google provided number.

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  • $\begingroup$ Ah got it now.. the calculator rounded the darn answer for some reason. $\endgroup$
    – CipherBot
    Commented Aug 29, 2016 at 6:12
  • $\begingroup$ There's always websites on the internet who simplifies a lot of things, this is one such example. Not surprised actually. $\endgroup$
    – CipherBot
    Commented Aug 29, 2016 at 6:22
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    $\begingroup$ See Toby's answer. $\endgroup$
    – Keith Thompson
    Commented Aug 29, 2016 at 21:42
  • $\begingroup$ His days per year is wrong, and his answer didn't answer the op either. However it is a nice explanation/calculation of a light year. $\endgroup$
    – LaserYeti
    Commented Aug 30, 2016 at 3:11
  • $\begingroup$ The average length of a year on the Gregorian calendar (over a 400-year leap-year cycle) is exactly 365.2425 days. Astronomically, it's between 365.2416 and 365.2428 days depending on which moment of Earth's orbit you're measuring it from. $\endgroup$
    – dan04
    Commented Sep 1, 2021 at 22:32

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