One would like to think that the age of the Earth times 3.14 times the speed of light would give the size of the Universe with time representing distance-if only it were that simple!
It has been speculated that in black holes at the singularity space may have an edge, or end. The vacuum of space is a field with implicit energy perhaps. Paremenides, the Ionian philosopher of the 5th century B.C. thought of mass-energy as a plenum and as space as not-existing. That which does not exist cannot have 'size'. What humans perceive as space is a protocol relation of mass-energy in a variegated event configuration. An empty 'space' may not exist.
The question of how the mass-energy is contained, of what it's in, may be a philosophical yet not a physical question. The Universe/plenum may be one of an infinity of plenums in existence that occur in variegated states of thermodynamical configuration of what is called 'space'-time. Delineating the protocols or relations of the pluralistic parts of each plenum is perhaps a project for multi-verse theory or theology. Let's return to more conventional approaches to the question of 'determining the size of space and if it ever ends'.
Space-time's 'size' is a function of the difficulty of traversing it in regard to human experience. If a hypothetical space-time ship could instantly cross to any other place-time immediately it could have no 'size' perhaps, but instead would have a 'place' in a deck of cards or position. What if it is possible to space-time travel every place, would it mean that one could space-time travel to places that do not yet exist because they are in a future that never yet happened, or before a space-time that first existed? If space-time is recurrent must it necessarily be finite, for is it possible for real infinity of space-time to end or recur?
A physicist named Freeman Dyson wrote a booked named 'Infinite in All Directions'. Beyond what Dyson wrote about there in, what can that mean-really? Mustn't everything really be infinite in all directions and therefore any defined regions of space-time be a contingent creation of God such as was described in the Bible book of Genesis as being created by The Word?
78 to 94 billion light years seem to be a basic theoretical size parameter for the universe in conventional cosmological terms...
A primary difference exists between the size of the observable universe from the Earth and the actual size of space-time/universe. Because general relativity treats space-time as a unified composition inferences about the size of the universe beyond the observable limits may be made by observing and considering the theoretical maximal intervals of travel starting at a given singular place-time such as near the big bang (a working concept).
All of the judgments about the size and age of space-time and the universe are made within a given frame of reference. That frame of reference is relative and part of the criterion of being-in-a-place-in-the-universe. Astrophysicists don't generally assume that the Earth and solar system is located in the center of the universe. There are perhaps 80 billion galaxies in the observable universe and the farther they are in space-time the younger they seem to be. Light from the most distant observable galaxies seems to be approx. 13 billion years old in all directions from the Earth. The only limit on the size and age of space beyond that associated distance would seem to be the stage of star and galactic formation. Recent studies have discovered remnants of star clusters formed shortly after the universe first admitted visible light into being. Yet this is all within a given frame of reference and in no way precludes any other hypothetical constructions of space-time from other more non-proximal locations beyond the observable universe in any direction.
Another interesting conjecture is about the smallest possible size of the universe. If extra-dimensions exist space-time may vary not only according to the principles of relativity in four-dimensions but in other relationships intrinsic to those extra-dimensions and their relationships with each other. Alterity (meaning programmatic change here), or assumptions regarding the points of view of the 'other', heterodox non-self aspect of existing may be associated with the context of being in given physical law coordinates. Very small extra dimensions may yield other values about spatial relations and distance. The size of this universe may be a relative term meaningful within the context of the yardstick of measurement used. Most remember the yardstick shrinking to fit the curvature of space-time given in examples of how special relativity works; there may be no absolute value for the size of space-time, and this universe one may or may not have a size that is a ratio given in relation to the size of the observable universe. Perhaps the most interesting physical question of cosmology, or at least one of the most interesting questions for philosophers is what emptiness, or what space-time was the space-time of the universe created in, or contained in. Physicists for mathematically reasons often say nothing exists outside of the space-time continuum. The size of that changes as it expands and/or contracts.