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This is a bug, and the explanation in the comments makes no sense.
At the bottom of the page, it clearly states "When your annual return on investments cover 100% of your expenses you are financially independent." The number of years until retirement should be the number of years until this point. This is not true when you change the withdrawal rate from anything other than 4% (or something very close). This is very clear with just a casual glance at the bottom chart.
With a 4% withdrawal rate, our "Percent Of Expenses Covered By ROI" approaches 100%, goes a little bit over, and stops. This is correct, and explained below: "The above table will likely show you need to work slightly longer because your withdrawal rate should be less than your return on investments."
If you double your withdrawal rate to 8%, the "Percent Of Expenses Covered By ROI" never actually reaches 100% before the number of years you can supposedly retire in. It stops at an arbitrary year before reaching 100%. (Also, many of the values in the table are mysteriously missing.)
Now, reduce withdrawal rate to 1% and check the chart again. 100% is reached relatively quickly, but the chart continues, again, to an arbitrary year, this time long after 100% of expenses are covered by ROI instead of too soon. In the final year, the dark line representing "Percent Of Expenses Covered By ROI" shoots way off the page.
kablamo, all the calculations you stated are correct, but they are unrelated to this problem. The problem is the calculation of the number of years until retirement. If I'm withdrawing 100%, it says I can retire instantly. If I withdraw 0.01%, it will take me over 100 years. You can see how this is obviously incorrect, right?
After thinking more about this, the solution is probably removing the ability to input "withdrawal rate" at all. If what you said is true, kablamo--that "the calculator assumes your current expenses are the same as your expenses after retirement"--then this withdrawal rate should be a calculated value, not something the user specifies.
If "current annual expenses" is $30,000 and "annual return on investment" is 7%, for example, withdrawal rate cannot be 50%. That would mean your total savings for retirement would NEED to be $60,000ish (because you are locked into withdrawing 30k, and you are ALSO locked into withdrawing 50%) and after slightly over 2 years, you'd be out of money.
Of the following 3 values:
-Current annual expenses
-Annual return on investment
-Withdrawal rate
... You need to specify 2 and calculate the third. By allowing all 3 to be specified, you can create scenarios where retirement is impossible.