Retirement
Years to financial independence
Income cancels out of this expression because savings rate determines both the contribution and the target. Assumes a 25x target and a constant real return.
The Formula
Years = ln(1 + 25 x r x (1 - s) / s) / ln(1 + r)
Income cancels out of this expression because savings rate determines both the contribution and the target. Assumes a 25x target and a constant real return.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| s | Savings rate as a share of take-home pay | decimal | Net of tax, since both contributions and eventually spending come from the same pool. |
| r | Real annual return before retirement | decimal | Nominal return minus inflation. Historically used values sit near five percent. |
| Y | Years of contributing until the target is met | years | Round up and add a buffer — the formula assumes a perfectly steady real return every year. |
What Each Symbol Means
sdecimal
Savings rate as a share of take-home pay
Net of tax, since both contributions and eventually spending come from the same pool.
rdecimal
Real annual return before retirement
Nominal return minus inflation. Historically used values sit near five percent.
Yyears
Years of contributing until the target is met
Round up and add a buffer — the formula assumes a perfectly steady real return every year.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate your fire number page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Your FIRE Number, filed under Finance. Every number the guide produces comes from substituting into this one line.