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As mentioned in wiki/Age_of_the_universe,

The current measurement of the age of the universe is around 13.8 billion years (as of 2015) – 13.799±0.021 billion years

When my friend who is not from science background asks me how do we measure the age of the universe? How should I explain to him?

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Once we look far enough away to get past "local effects" we see everything moving apart, spreading out in all directions, like a set of dots on a balloon being inflated, or like currants in a loaf of bread rising in the oven.

We can use the laws of physics to follow those movements back in time to work out how far apart all the galaxies were at various dates in the past. If we do this we find that 13.8 billion years ago they were all in the same place (there are a lot of subtle details to get right in this calculation, but a lot of people have worked on it over a long time). That much matter and energy packed into that small a space warps both space and time so that it is not really possible to talk about time "before" that event. Hence that is taken as the origin of the universe.

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    $\begingroup$ But how can we be sure that the rate at which two points are moving apart has always been same constant throughout billions of years? Certainly we only can experience the tiny fraction of that huge time right? $\endgroup$
    – Sazzad Hissain Khan
    Apr 29, 2020 at 22:15
  • $\begingroup$ @SazzadHissainKhan Basically, things in space keep moving at the same speed in the same direction unless there is a force acting on them. On these scales, the only force that matters in gravity and we can calculate that and allow for it. Less basically, the matter in space, its movement and the shape of space itself are all interrelated, according to General Relativity, but we can use the equations of GR to track all of these things back in time and allow for the forces. $\endgroup$
    – Steve Linton
    Apr 29, 2020 at 22:30
  • $\begingroup$ @SteveLinton This seems like a simplification; dark energy is known to have a large effect, but we cannot explain it yet. $\endgroup$
    – TheGreatCabbage
    May 1, 2020 at 7:36
  • $\begingroup$ @TheGreatCabbage We can’t explain it, but we can measure the effect and allow for it $\endgroup$
    – Steve Linton
    May 1, 2020 at 7:57
  • $\begingroup$ @SteveLinton as you said "unless there is a force acting on them". My question was, are we sure about the claim there was no unidentified/undiscovered force throughout billions of years? Did science already get the evidence or not? If yes, how? $\endgroup$
    – Sazzad Hissain Khan
    May 3, 2020 at 15:00
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In the same way that if you were to measure the height and speed of something thrown into the air, you would be able to work out how hard it had been thrown and how long ago. The assumption is made that the trajectory of the thrown object obeys the known laws of physics.

A further advantage one has in astronomy is that you are not limited to making a single measurement in the present day, you can observe distant things as they were in the past. This gives you multiple opportunities to measure the size and expansion rate of the universe to corroborate your answer and/or uncover holes in understanding of the physics (like dark energy for example). Nevertheless, to some extent, the age quoted does assume we have the physics right.

At the moment, the age estimate is heavily dependent on measurements of features that formed when the universe was about 400,000 years old (the cosmic microwave background), combined with observations of supernovae in galaxies at a range of distances (and times in the past), that tell us precisely how the trajectory of the universe has changed with time.

The accuracy of the answer (as opposed to the precision, which is very high), can be verified by independent tests like estimating the ages of the oldest stars, looking at how much structure there is in the universe, both now and in the past, etc.

Basically, everything ties up reasonably well at the moment (in fact there are small discrepancies in the expansion rate measured now, compared with predictions from the ancient cosmic microwave background), so the age you quote is an age for the "concordance model", that uses an agreed (though not entirely understood) set of physics.

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