The bankroll you need depends on your ROI, which games you are playing, and your personal risk tolerance. A simple, consistent formula is

Bankroll = (comfort x SD^2)/(win rate)

*comfort* is something which depends on your risk tolerance and your ability to move down in stakes if you hit a bad streak. A comfort level of 2 is generally considered aggressive. A comfort level of 4 is conservative. You can use the same comfort level across many forms of advantage gambling. One other meaning of the comfort level is that your instantaneous risk of ruin, your chance to go broke if you stay in your current game, is about 1/7^comfort.

*SD = standard deviation* measures how spread out the results are of each tournament. For single table tournaments, this does not depend much on your playing style. In a 50-30-20 structure, your standard deviation is going to be about 145%-155% of a buy-in. In larger tournaments, the standard deviation is larger, and it becomes more sensitive to your playing style and how much you win. In a 45-player tournament, the standard deviation may be 280%-330% of a buy-in. In a 180 player tournament, the standard deviation may be 500%-800% of a buy-in.

Your *win rate* should be expressed in the same units as the standard deviation, say in buy-ins. You can include rakeback and bonuses. If you regularly take money out of your bankroll, then you should reduce your win rate by these withdrawals.

For example, if you use a target comfort level of 3, and you have an ROI of 5% in STTs, then you should have a bankroll of 3 x 1.55^2 / 0.05 = 144 buy-ins. With the same level of risk tolerance and in the same games, if your ROI is 10%, then you only need 72 buy-ins. If you have an ROI of 40% in 180 player tournaments with a standard deviation of 6 buy-ins, then you should have 3 x 6^2 / 0.40 = 270 buy-ins. MTT buy-ins are much easier to lose than STT buy-ins.

If your bankroll falls to below the target bankroll, that is ok, you don't have to move down immediately. However, if your bankroll falls to less than half of the target amount, then you should move down. Playing with less than half of the target bankroll means that playing should be viewed as an expense.

It is normal not to know exactly what your ROI is. You can make tentative calculations, and update them as you get more information. A rough 95% confidence interval for your ROI after n tournaments is your observed ROI +- 2 SD / Sqrt(n). You might want to play enough that this confidence interval does not include 0 before moving up. Be prepared to drop down again if you do not have good results at the higher level.