How this calculator works

1. Notation and conventions

All headline figures are expressed in today's money. Growth and inflation are annual effective rates, so a monthly rate is(1 + r)^(1/12) − 1, never r / 12 — the second form compounds a stated 7% up to an effective 7.23% and would let the projection out-earn the return that sized the target.

The real return, used everywhere a today's-money amount meets a nominal rate, is:

real = (1 + nominal) / (1 + inflation) − 1

Note the division. Subtraction is an approximation that always errs in the optimistic direction, and the gap grows with both the rates and the horizon.

2. The spending corpus

This is the core of the FIRE number, and it is not a multiple of expenses. It is the present value of drawing your inflation-adjusted annual spending every month from your retirement age to your life expectancy, discounted at your real post-retirement return:

horizon corpus = (E / 12) × (1 − (1 + m)^−n) / m

where E is annual spending in today's money, m is the monthly real post-retirement return, and n is the number of months between retirement age and life expectancy. Withdrawals are taken at the end of each month (the ordinary-annuity convention), matching the simulation in step 5 so that a fully-funded plan lands on its emergency buffer rather than drifting above or below it.

When the real return is effectively zero, the formula degenerates gracefully to(E / 12) × n — spending multiplied by months, with no help from compounding.

3. The withdrawal rate as a cap

Horizon math alone lands the portfolio on exactly zero at life expectancy, which leaves no margin for a poor sequence of early returns. So the safe withdrawal rate enters as a floor under conservatism rather than as the definition of the target:

swr corpus = E / (SWR / 100)

spending corpus = max(horizon corpus, swr corpus)

If the SWR corpus is larger, the cap is binding — your first-year draw would otherwise have exceeded your stated safe rate — and the results panel says so explicitly. The implied first-year withdrawal rate,E / spending corpus, is always reported, so the target is never a black box.

4. Emergency buffer and one-time goals

The buffer is sized off the lifestyle being funded:buffer = (E / 12) × emergency months.

One-time goals are entered in today's money at the age they occur. Goals falling strictly after retirement are discounted back to the retirement date at the real post-retirement return and added to the target:

goal PV = amount / (1 + real post return)^(goal age − retirement age)

Goals falling on or before the retirement age are excluded here, because the simulation has already deducted them from the projected balance — counting them in both places would charge you twice. Goals beyond life expectancy drop out entirely.

The headline is the sum:

FIRE number = spending corpus + emergency buffer + post-retirement goal PV

5. The trajectory simulation

The projection runs month by month from your current age to your life expectancy.

• Accumulation phase. The balance grows at the monthly equivalent of the pre-retirement return, and the monthly contribution is added. At the end of each year the contribution is multiplied by 1 + step-up.
• Retirement phase. The balance grows at the monthly equivalent of the post-retirement return, and one twelfth of your annual expenses — inflated to that month — is withdrawn.
• Goals are deducted at the end of the year they fall in, inflated from today's money to that age, in either phase.

The target line on the chart is the FIRE number inflated to each age, so the projection and the target are always compared in the same money. Mixing a future-money balance with a today's-money target is the most common error in hand-built models, and it flatters a twenty-year plan by roughly 1.8×.

6. Derived outputs

• FIRE age — the first age at which the projected balance meets the inflating target, on or before the chosen retirement age.
• Required monthly contribution — solved by binary search over the same simulation: the contribution that lands the balance exactly on the target at retirement. It is solved, not derived from a closed form, because the step-up and the goal deductions make the closed form wrong.
• Money lasts to — the age the balance first hits zero in the retirement phase, or nothing at all if it survives past life expectancy.
• Coast FIRE — the balance needed today that reaches the target at retirement with no further contributions:target at retirement / (1 + pre-retirement return)^years to retirement.
• Lean and Fat FIRE — the full requirement recomputed at 70% and 150% of your annual expenses, through the same three-part formula, so every figure on the page is built the same way rather than being scaled from the headline.

7. Defaults, and why

Every one of these is editable. They are starting points chosen to be defensible, not forecasts.

8. What the model does not do

Being explicit about the limits is more useful than a disclaimer, so here they are in full:

• No taxes. The model works in gross figures. Withdrawals from tax-deferred accounts are income in most jurisdictions, and a 4% gross draw can be a materially smaller net one. Model your spending as a post-tax requirement and add the expected tax drag yourself.
• No market volatility. Returns are applied smoothly. Real markets deliver an order, and the order matters enormously once you are withdrawing — seesequence of returns risk. A deterministic projection shows the central case, not the distribution.
• No Social Security, pension or annuity income. Later income sources reduce what the portfolio must fund; the model assumes the portfolio funds everything. If you expect a pension, your true requirement is lower than the headline.
• No spending curve. Real retirement spending often falls in the middle decades and rises again with healthcare late on. The model holds real spending constant, which is the standard simplifying assumption and is roughly conservative.
• No behaviour. It assumes you follow the plan through a 40% drawdown. History suggests this is the least reliable assumption in the whole model.

9. Privacy and computation

Every calculation on this site runs in your browser. No figure you enter is transmitted to a server, stored, or logged — there is no account, no database and no API call behind the numbers. See the privacy policy for the full detail on what the site does collect (analytics and advertising, both of which are unrelated to your inputs).