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This question already has an answer here:

I want to know the exact numbers and preferably the calculations that gives the size of the universe at the Big Bang and the initial rate of expansion at the moment of big bang. Does somebody know this? thanks!

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marked as duplicate by ZeroTheHero, Ben Crowell, stafusa, Qmechanic Oct 8 '18 at 10:20

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    $\begingroup$ "size of the universe" is not really a well-defined notion. See Did the Big Bang happen at a point? $\endgroup$ – ACuriousMind Oct 7 '18 at 19:50
  • $\begingroup$ Did you look up some values that you'd like to use as the basis for a question? $\endgroup$ – ZeroTheHero Oct 7 '18 at 20:28
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    $\begingroup$ I'm voting to close this question as off-topic because of lack of prior research. $\endgroup$ – ZeroTheHero Oct 7 '18 at 20:29
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    $\begingroup$ Possible duplicate of At what speed does our universe expand? $\endgroup$ – Ben Crowell Oct 7 '18 at 21:17
  • $\begingroup$ @ACuriousMind: "size of the universe" is not really a well-defined notion. It's a well-defined notion if the universe is spatially closed. We actually don't know whether the universe is spatially closed, but if it is, then we have a lower bound on its size. $\endgroup$ – Ben Crowell Oct 7 '18 at 21:19
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Here is the history of the universe as we have fitted it with the mainstream physics model.

univ

Note that the big bang is a fuzzy region in this diagram, due to the quantum mechanical uncertainty , quantum mechanics is expected to hold at the beginning of time, as it is at present considered to describe the underlying frame work of all nature.

Here is a plot, also seen here, where numbers are given in meters:

bbin meters

figure 1. Expansion of the Universe: This graph shows how the scale factor of the observable universe changes with time for the standard Big Bang model (red line) and for the inflationary model (blue line). (Note that the time scale at the bottom is extremely compressed.) During inflation, regions that were very small and in contact with each other are suddenly blown up to be much larger and outside each other’s horizon distance. The two models are the same for all times after $10^{–30}$ second.

The original big bang model ( called standard here) goes to the to 0 time with 0 volume so your question has no answer , as the universe expanded from a singularity.

Inflationary models, which are the ones that are currently standard as they fits all astrophysical observations up to now, going towards the fuzzy area at the beginning of time , point to an envelope of order $10^{-60}$meters for the fuzzy region at much earlier times than the original Big Bang Model. In any case numbers will be dependent on the specific inflationary model used.

So there are no exact numbers as calculations are quantum mechanical, with an inherent uncertainty value, just envelopes estimated for a size dependent on the time line. Try this for a calculational background.

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