Suppose your assets worth $X appreciate on average by Y% every year in "real" terms (adjusted for monetary debasement) until you die.

The Safe Withdrawal Rate (SWR) is a term popularized in early retirement circles, and is defined as what sum you can safely skim off the top of your assets every year without eating into the principal. To retire forever, your expenses need to be less than the SWR.

The SWR is calculated as:

SWR = $X * Y% / 100%

For example: A Vanguard Life Strategy fund might return Y = 4% on average (inflation adjusted), and your living expenses in today's terms are $50k. So retire forever, you need a fund equal to X = $50k * 100% / 4% = $1.25M.

Bitcoin is a lot more interesting as it's highly volatile and nobody can predict how much it'll appreciate. But we can make some educated guesses. Let's assume it overtakes gold's market cap in the next 20 years, which is a 2000% increase from here or ~16% per year.

Using the same living expenses, the BTC stash needs to be X = $50k * 100%/16% = $313k = 12.2 BTC at today's prices of $25600 / BTC.

To be a bit more safe you could take BTC's price at the trough of the last bear market ($15k / BTC), meaning you'd need a stash of 20.8 BTC.

To put this all in a very easy formula:

This is all pulled completely out of my ass and will no doubt be invalidated in the near future, but it's fun to think about.