How FIRE numbers work

If you plan to withdraw 4 percent of a pile in the first year and then adjust that amount for inflation, the pile has to be $1 / 0.04 = 25$ times that first-year spending. $60,000 of spending wants $1,500,000. A 3 percent withdrawal wants $1 / 0.03 \approx 33.3$ times spending; a 5 percent withdrawal wants 20 times. The withdrawal rate and the multiple are the same fact written two ways.

$$F = \frac{S}{w}$$

$S$ is annual spending and $w$ the withdrawal rate as a decimal. The 4 percent figure is a research finding about a particular historical sample of US stock and bond returns, not a law of arithmetic. This calculator will apply whatever rate you type. It will not tell you that 4 percent is safe. Safe withdrawal rates is the page that treats the 4 percent rule as a claim about history rather than as a formula.

Sequence of returns sits beside this identity and is not inside it. Two piles of $1,500,000 that earn 7 percent on average can last very different lengths of time if the bad years arrive first. The sequence of returns guide is that picture, and the sequence of returns explorer is the interactive version.

The calculator above opens on $60,000, 4 percent, $50,000 saved and $25,000 a year at 7 percent, because those are the first worked example.

Once the target is known, the wait is a savings-goal question. Starting from a balance $B$, adding $C$ a year, at return $r$, the years $t$ to a target $F$ satisfy

$$(1+r)^t = \frac{F + C/r}{B + C/r}$$

From $50,000, adding $25,000 a year, at 7 percent a year, that closed form says 22.43 years to $1,500,000. The gap from what is saved now is $1,450,000.

At a 5 percent return, the same identity toward a $40,000-a-year lifestyle, a $1,000,000 pile at 4 percent, from $100,000 already saved plus $20,000 a year, takes 21.10 years. The gap is $900,000.

The compounding is annual, on purpose. A FIRE horizon is counted in years, and monthly precision on a 4 percent rule would be dressing. The return is constant, also on purpose, so two savings paths are comparable. A real path is a sequence, and an average return is not a compound return, which is the warning every compounding page on this site already makes.

The savings goal calculator is the same wait pointed at any target, not only at a spending multiple.

If the current pile already covers the spending at this withdrawal rate, years to FIRE is 0. $1,200,000 already covers $40,000 of spending at 4 percent, because the FIRE number is $1,000,000. The gap against the target is negative, which this page reports as already covered rather than as a number of years.

If the pile is shrinking in real terms and the saving cannot catch the target, there is no finite wait, and the calculator says so rather than printing a huge year count. A contribution of zero toward a target above the current pile, at a return of zero, is that case: the gap never closes.

Cut spending and two things happen at once: the target pile shrinks, and the annual saving, if the cut comes from current consumption, rises. That is why a savings-rate picture, like the savings rate explorer, is often a clearer FIRE tool than a pile-size tool. The pile is a consequence of the rate. The rate is the decision.

Raising the assumed return also cuts the wait, and it is the lever a reader does not control. Typing a high return because that is what a chart of the last decade shows is how a 22.43-year wait becomes a shorter wait on the screen and a 22.43-year wait in the world. This page will apply whatever return you type. It will not endorse it.

Treating 25 times spending as a law, then raising the assumed return until the wait looks short, is two mistakes stacked. 25 times is 4 percent. If you are not willing to withdraw at 4 percent, the multiple is not 25. And the wait is then being shortened on the screen by a return you do not control.

The wait on this page holds the return still. A working-life mix that gets safer as the date approaches is a different input. The allocation glide path is that mix over time, which is what a target-date fund is doing while this page is counting years to a pile.

Taxes, healthcare, housing that is or is not paid off, and a state pension or Social Security benefit all change the spending the pile has to cover. A $60,000 spending figure that already nets those out is a different input from a $60,000 figure that does not. The formula cannot tell which one you typed.

Inflation is inside a real return and inside a real spending figure, or it is inside neither. Mixing a 7 percent nominal return with $60,000 of today's spending, held flat in nominal terms, understates the pile you will need. The real return calculator is the conversion. The retirement withdrawal calculator is the other end of the same identity: a pile and a rate, looking at what comes out rather than at what has to go in.

Retirement spending is the input, not working-life spending. A working-life budget that includes commuting and a mortgage is not the same object as a retired budget. Using the working-life figure usually overstates the pile; using a wishful retired figure understates it.

A FIRE number sizes a portfolio you keep invested. Annuities explained is the other conversion: a lump exchanged for a payment that lasts as long as the holder does, with no portfolio left to sequence.

The FIRE number is a translation of a spending figure and a withdrawal rate into a pile, and then of a savings path into a wait. It is not a forecast of markets, not a tax calculation, and not a recommendation about when to stop working.

The figures throughout are a teaching path: $60,000 of spending at 4 percent from $50,000 plus $25,000 a year at 7 percent, a second path at $40,000 of spending, and a pile that is already there. They are there so every published number can be re-derived. This is educational material, not financial advice.