While we currently lack the knowledge that would enable us to ascertain a precise number, we can at least offer an estimate. As of 19 Feb 2023, astronomers have confirmed 5,250 exoplanet discoveries within 3,921 planetary systems. All of these exoplanets have been located within the Milky Way Galaxy* and almost all of them are gravitationally bound to stars.** The vast majority of these have been found in systems within 3,000 light years of our solar system:

[A graphic showing the distribution of exoplanets discovered within our galaxy. As of April 2022, the most distant yet found is K2-2016-BLG-0005Lb, located approximately 17,000 light years away. Most of the confirmed exoplanets are within 3,000 light years of the Sun. Image credit: NASA]

Based on these detections and their distance distributions, astronomers estimate that our Milky Way Galaxy could have between 1- 10 trillion gravitationally bound planets. The number of rogue planets could be 2 - 100 times greater. This value is quite uncertain due to the lack of confirmed rogue planet detections. This relative proportion is based largely on models which reveal that planet expulsions should be quite common during the star formation process.

We could then estimate that the Milky Way Galaxy could harbor between 3 trillion - 1.1 quadrillion planets. A very wide range, the bounds of which could very well change as new information becomes available.

Extrapolation is a somewhat tricky matter as not all galaxies are alike in terms of morphology or stellar population. Moreover, we still don’t know the precise number of galaxies or their size distribution percentages. However, we can estimate that the Universe contains about 10^22 stars. If we assume -perhaps incorrectly- that the planet star proportion within the galaxy is representative of that within the Universe 7.5: 1; ==> 2,750:1 the Universe could contain

7.5 x 10^23 to 6.05 x 10^26 planets

To put this value into perspective, the lower of these two cited numbers is about 440,000 times greater than the number of seconds that have elapsed since the Big Bang 13.8 billion years ago.

Again, these numbers are very rough estimates that might not only change, but which we cannot possibly confirm.

All the same, I do hope this response proves helpful.

*Astronomers have found a few possible extragalactic exoplanets, such as the one that might be located within the binary star system M51-ULS-1 within the Whirlpool Galaxy and PA-99-N2b within the Andromeda Galaxy. Neither of these nor the handful of other extragalactic planet candidates have yet to be confirmed.

**Approximately 70 - 170 rogue planets, those not attached to stars, have been detected within the Upper Scorpius young stellar association [cited publication: “A rich population of free-floating planets in the Upper Scorpius young stellar association” Nature Astronomy published 21 Dec 2021]