Your phone is already your wallet, your bank, and your calendar. It might as well be your budget. Android users get the full menu of expense trackers with no compromises, so the question is not which apps exist. It is which one matches how your brain works.
YNAB is the grad school budget planner app for the planner personality. Every dollar assigned before it is spent. If you are the kind of person who makes spreadsheets for fun, and I say that with respect, start here.
EveryDollar's free tier is the obvious free grad school budget tracker app to try first. Categories, a monthly plan, done. It will not hold your hand, but it also will not charge you for the privilege of being organized. On a PhD stipend, free is not a nice-to-have. It is the requirement.
Rocket Money is the leak-finder. It watches for subscriptions and bill creep in the background, which is the kind of help a busy grad student actually needs. Nobody has time to audit their own bank statements during quals. Let the app do the boring part.
Monarch Money handles the modern reality that money is often shared. Splitting rent, groceries, and utilities with a partner or roommates gets messy fast, and this one was built for exactly that mess. Clean shared picture, fewer arguments.
Goodbudget is the digital envelope system. Old idea, new phone. You divide the month's money into envelopes and stop spending when one is empty. Brutally simple. Weirdly effective on a fixed income, because there is no room for creative accounting inside an envelope.
If all you want is a grad student expense tracker app without the full budgeting ceremony, that is a legitimate choice. But a note on honesty: no app tracks expenses you never enter or connect. The real feature is your own consistency. Pick the interface you will tolerate, give it a full semester, and let the habit do the work. And for the income side of the equation, the cost-of-living-adjusted offer reports at phdstipend.fyi show what your stipend actually buys in each city.