The math behind the savings-rate table
The calculator assumes your retirement spending equals what you spend now: take-home income minus savings. It sets the target as that spending divided by the withdrawal rate, then grows your current investments at the real return and adds a year of savings at the end of each year until the balance meets the target. Because everything is in today’s dollars, the income is assumed to rise only with inflation.
With no starting balance the number of years has a closed form: n = ln(1 + target × r ÷ annual savings) ÷ ln(1 + r), rounded up to whole years. Our unit tests check the calculator against that formula for several savings rates.
Why the savings rate matters more than income
Two households with different incomes but the same savings rate reach independence in the same number of years under these assumptions, because both the yearly savings and the target scale with income. That is why FIRE writers focus on the savings rate. Starting from zero with a 5% real return and a 4% withdrawal rate, the calculator gives these whole-year results:
| Savings rate | 3% real | 5% real | 7% real |
|---|---|---|---|
| 10% | 70 | 52 | 42 |
| 20% | 47 | 37 | 31 |
| 30% | 35 | 28 | 25 |
| 40% | 26 | 22 | 20 |
| 50% | 19 | 17 | 15 |
| 60% | 14 | 13 | 12 |
| 70% | 10 | 9 | 9 |
Notice that the return assumption matters most at low savings rates, where compounding has decades to work, and matters least at high savings rates, where contributions do most of the lifting.
Defining your savings rate
There is no official definition. This tool uses savings as a share of take-home pay, so pre-tax 401(k) contributions and any employer match should be added to both income and savings if you want them included. Be consistent: whatever you count as saved must not also be counted as spending. The savings-rate guide walks through an example.
Worked example
With $90,000 of take-home income, a 30% savings rate, $50,000 already invested, a 5% real return and a 4% withdrawal rate, spending is $63,000, the target is $1,575,000 and the calculator estimates about 27 years. Raise the savings rate to 40% and spending falls to $54,000, the target to $1,350,000, and the estimate drops to about 21 years — try it above.
Caveats
Real life is lumpier. Raises, children, housing changes and market falls all move the date. Spending in retirement may differ from today — commuting costs may disappear while health insurance appears. Treat the result as a direction of travel and update it with real numbers each year.