Having only one eye does not mean that you will have no depth perception, but you will have to re-learn to judge distances and depth during a range of new experiences.
85 of 125 patients questioned, stated that in their opinion loss of one eye had not changed their life in any permanent way… One of the first examples in change of depth perception is often experienced by patients soon after arriving home following surgery to remove the eye. Many patients have gone to make a cup of tea and missed the cup, pouring the water outside the rim.
Other things you may well experience during your “adaptation period” may be an affect on balance, and a decreased peripheral field of vision causing increased risk of bumping into objects. Both of these will improve over time and with rehabilitation.
In a survey carried out in 1988, 125 patients who had lost an eye were given a questionnaire on their life after having an eye removed. 85 of 125 patients questioned, stated that in their opinion loss of one eye had not changed their life in any permanent way.