If the Mars polar caps were melted, how deep would the oceans be?

Question

If the Martian polar ice caps melted, given a surface temperature and pressure that allow for liquid water, how large would the oceans be? Would they match their ancient glory, or would they be smaller?

Answer 1

The oceans would be smaller because Mars has lost most of its water. From Wikipedia's article on the Martian polar ice caps:

Evidence that Mars once had enough water to create a global ocean at least 137 m deep has been obtained from measurement of the $HDO$ to $H_2O$ ratio over the north polar cap. In March 2015, a team of scientists published results showing that the polar cap ice is about eight times as enriched with deuterium, heavy hydrogen, as water in Earth's oceans. This means that Mars has lost a volume of water 6.5 times as large as that stored in today's polar caps.

The water for a time may have formed an ocean in the low-lying Vastitas Borealis and adjacent lowlands (Acidalia, Arcadia and Utopiaplanitiae). Had the water ever all been liquid and on the surface, it would have covered 20% of the planet and in places would have been almost a mile deep.

So if all the water melted (and the atmospheric pressure allowed liquid water) the ocean would cover roughly 6% of the planet, and be roughly half as deep as the original ocean. This crude estimate totally ignores the topography of the Martian surface. In the comments, David Hammen writes:

Given the marked unevenness of Mars's surface, if both of its ice cap melted completely the resulting water would cover a fraction of its northern hemisphere, plus a few depressions such as the Hellas Planitia (8 kilometers deep!), but to a depth much greater than 137 meters.

Heavy water is slightly heavier than normal water, so it evaporates slower and has a higher boiling point. So in a mixture of normal and heavy water the normal water evaporates at a slightly faster rate, which increases the relative concentration in the unevaporated water.

That same article mentions that the total volume of both Martian polar caps is around 3.2 million cubic kilometres. Most of that ice is water ice, but some of it is frozen carbon dioxide (aka "Dry ice"). The article doesn't state the proportions, but it says

During each year on Mars as much as a third of Mars' thin carbon dioxide ($CO_2$) atmosphere "freezes out" during the winter in the northern and southern hemispheres.
[...]
Analysis of data showed that if these deposits were all changed into gas, the atmospheric pressure on Mars would double.

Note that not all of Mars's water is in its polar caps, some may be frozen underground, especially near the poles, and some underground water may even be in a liquid state, due to a high salt concentration.

For further details, please see the linked article.