How Our FIRE Calculators Work

The math is the same on every calculator. What changes from page to page is the question each one asks, such as when you can stop saving or how long a balance lasts. Each statistic from outside the site links to the original on our sources page. Every other number on this page was computed by the calculator engine when the page was built, so the text cannot drift from the code.

How do we turn your return into today's dollars?

We convert your expected return, inflation and fees into one real return with the Fisher equation, and then do all the math in today's dollars. Spending, contributions, Social Security and pensions are all entered and shown in today's money, so they keep their buying power automatically.

With the default 7% return, 3% inflation and 0.1% fees, the real return is 3.79%. Simply subtracting would give 3.90%, which overstates growth by 0.11 percentage points a year. That sounds small, but it compounds over a 40-year plan. US inflation averaged 3% a year over 1928-2025 (our calculation from Damodaran's CPI series^[1]) and was 3.7% over the 12 months to September 2026^[2].

In the historical simulations, each year's real return comes from that year's actual inflation instead: (1 + nominal) ÷ (1 + inflation) − 1 for stocks and for bonds separately, the same method Damodaran uses. Fees are then subtracted from the portfolio's real return.

When are contributions and withdrawals counted?

The engine moves in whole years. Contributions go in at the end of each working year, so a new contribution earns nothing in the year it is made. Withdrawals come out at the start of each retirement year, before that year's growth. Both choices are slightly conservative.

• Ages are whole years. “Age 45” means the year that starts on your 45th birthday. Contributions stop at your retirement age, or earlier if a calculator lets you set a stop age (as the Coast FIRE calculator does).
• Income streams (Social Security, a pension, part-time work) count from their start age and stop at their end age, if any. If income is larger than spending, the surplus is reinvested.
• Contributions, spending and income stay flat in today's dollars. In nominal terms that means they rise with inflation every year.

How is the FIRE number calculated?

The basic FIRE number is annual spending divided by your safe withdrawal rate, which is 25 times spending at a 4% rate^[3]. The 4% figure comes from William Bengen's 1994 study, where a 4% inflation-adjusted first-year withdrawal lasted at least 33 years in every period he tested^[4], and from the Trinity study that followed^[5].

Most people will also have Social Security or a pension later, and some will have part-time income early on. A single 25x multiple ignores both. So the calculators value every year of retirement separately, using one rate that carries the same safety margin as your withdrawal rate.

1. Planning rate. Find the real rate at which withdrawing your withdrawal rate of the starting balance every year (raised with inflation) lasts exactly your retirement horizon, from retirement to your plan-until age. A 4% rate over 30 years implies about 1.31%; over 45 years, 3.06%.
2. Each year's need. Spending minus the income you receive that year (Social Security, pensions, part-time pay).
3. Required portfolio. The sum of every year's need, discounted to retirement at the planning rate.

With flat spending and no other income this gives exactly spending ÷ withdrawal rate, so the familiar 25x answer is unchanged. The difference shows up when income starts or stops: the expensive years before Social Security, or the cheap years of part-time work, are valued with the same caution you chose with your withdrawal rate rather than at the average market return. A year can have negative need (for example part-time pay above spending), which can fund later years; the running total never drops below zero, so a surplus late in life cannot pay for earlier shortfalls.

Worked example: retiring at 50 with Social Security at 67

Someone retires at 50, spends $60,000 a year, and expects $24,000 a year of Social Security from 67. The plan runs to 95 with a 4% withdrawal rate.

The plain 25x rule would say $1,500,000. Accounting for Social Security lowers the target by $275,933, even though the portfolio pays the full $60,000 for 17 years. You can run your own numbers in the FIRE number calculator.

A required portfolio is only as safe as the withdrawal rate behind it, and 4% is aggressive for a 45-year retirement. Replaying history with the calculators' default 80/20 stock/bond mix and 0.1% fees, exactly $1,224,067 lasted the full 45 years in 74% of the 54 start years (our calculation). Research on 50 to 60 year retirements points to 3.25%-3.5% instead^[6]. Every calculator runs these risk tests on your own plan.

How are the Coast FIRE number and FI age found?

Your Coast FIRE number is the required portfolio at your retirement age, discounted back to today at the real return. If you have that much invested now, you could stop contributing and, at the expected return, still reach your target on time.

Your financial independence (FI) age is found by stepping forward one year at a time. At each age, the engine compares your projected balance (contributions included) with the required portfolio if you retired at that age. Retiring later means fewer years before Social Security and a shorter horizon, so the target is recomputed for every age. The first age where the balance is enough is your FI age. If that never happens before your plan-until age, there is no FI age. Your Coast FIRE age is found the same way, against the Coast number at each age.

Same person as above, now at 35 with $150,000 invested and $30,000 a year going in. To retire at 60 they need $1,057,824, so their Coast number today is $1,057,824 ÷ 1.0379²⁵ = $417,736. If they keep investing, their FI age is 55, when the projected balance first covers the $1,150,014 needed to retire at that age.

How does the Monte Carlo simulation work?

The Monte Carlo test runs your whole plan, from today to your plan-until age, 2,000 times. Each simulated year borrows one real year from history, picked at random. The success rate is the share of those 2,000 lifetimes in which the money never ran out.

• Bootstrap of joint years. Each simulated year draws one of the 98 years from 1928-2025, with equal odds and with replacement. Stocks, bonds and inflation come from the same year, so the way they moved together is preserved. Draws are independent from year to year (an “iid” bootstrap).
• Portfolio. The return each year is your stock share times the real S&P 500 return plus the rest times the real 10-year Treasury return, minus fees. The weights reset every year, which is the same as rebalancing once a year.
• Whole plan. Contributions go in while you work and withdrawals come out in retirement, with the timing rules above. A run fails if, at the start of any retirement year before your plan-until age, the balance cannot cover that year's spending after other income. A failed run stays failed.
• Seeded, so it is repeatable. Random numbers come from a small seeded generator (mulberry32) instead of Math.random. The calculators use seed 2026, so the same inputs give the same answer on every visit, on every device and in the server-rendered page.
• Bands. The fan chart shows the 10th, 25th, 50th, 75th and 90th percentile balance at each age across all runs.

With 2,000 runs, sampling noise alone moves a success rate by at most about 1.1% (one standard error, our calculation). Treat a difference of a point or two between two plans as a tie.

What does “Match my return” do?

“Match my return” is an optional, more cautious risk model. It shifts every historical year by the same constant so that the long-run average (geometric mean) of the 98 years equals the real return you entered. The shift is found by bisection. Fees are assumed to be already included in your return, so they are not subtracted again.

The point is consistency. Your deterministic projection uses your return, and this mode makes the risk tests use it too. A plain replay of history assumes the past century's returns, which were high: an annually rebalanced 80/20 stock/bond mix earned 6.05% a year after inflation over 1928-2025 (our calculation). Matching that to the default 3.79% moves every year down by 2.24 percentage points. Only the level changes. The size of each year's swing, the joint stock, bond and inflation moves and, in the historical test, the order of years are all kept.

The default mode, “Raw history”, uses each year exactly as it happened, minus your fees. That is how the research we cite was done, from Bengen and the Trinity study to Early Retirement Now, so our success rates are directly comparable with theirs. Vanguard's current 10-year forecasts for US stocks (4.8%-6.8% nominal) sit well below the 10% history delivered^[8], so if you expect lower returns than the past century, switch to “Match my return”.

How does the historical backtest work?

The historical test starts a retirement in every year from 1928 that has a complete record for your whole retirement, and replays the actual returns and inflation in order. This is the approach behind Bengen's 4% rule^[4]. Unlike the Monte Carlo test, it keeps real bear markets and recoveries intact.

• Horizon. Your plan-until age minus your retirement age. Each cohort starts with your projected balance on the first day of retirement (on the FIRE number calculator, with the FIRE number itself).
• No wraparound. A cohort only counts if all its years exist. For a 30-year retirement that gives 69 cohorts (starting 1928-1996). For 45 years it gives 54 (1928-1981). We never loop back to 1928 after 2025.
• Success means the money lasted the full horizon. For failures, we report how many years the money lasted.

The first decade of retirement matters most. Kitces found that real returns in those years largely determine the safe withdrawal rate (a correlation of about 0.79)^[7], which is why both tests look at the order of returns and not just the average.

The 4% rule through both tests

To check the engine against published research, we ran the classic case: $1,000,000, $40,000 a year rising with inflation, 30 years, no fees, no other income.

Worst historical start years: 1929 for 100/0 (money lasted 21 years); 1966 for 75/25 (money lasted 26 years); 1966 for 50/50 (money lasted 24 years).

The Trinity study found 95%, 98% and 95% success for the same three mixes over 30 years using 1926-1995 data^[5]. Our historical figures are close but not identical, because the period (ours runs to 2025), the bond series and the timing conventions differ. The matched column is lower because a 3.79% real return is well below what history delivered. For 50 to 60 year retirements, research suggests 3.25%-3.5% held up in the worst historical periods^[6]. A 4% rule with a 50/50 portfolio drops to about 65% success over 60 years^[9]. Morningstar's 2025 estimate puts the safe starting rate for a 30-year retirement, at 90% success, at 3.9% a year^[10].

What market data do the simulations use?

Both risk tests use Aswath Damodaran's annual US return data from NYU Stern, 1928-2025, released January 5, 2026^[1]. Damodaran updates the file each January, and we refresh ours when he does.

• Stocks: S&P 500 total return including dividends. Before 1957, Damodaran back-fills with the large-company indexes that preceded it.
• Bonds: 10-year US Treasury bond total return, derived from constant-maturity yields (a par bond repriced at the year-end yield, plus its coupon).
• Inflation: CPI-U, December to December, not seasonally adjusted.

These summary figures are computed from that file every time this page is built. Our nominal S&P 500 figure of 10.02% a year matches the geometric average Damodaran publishes for the same period.

The gap between the simple and compound averages is volatility drag. It is also why “Match my return” targets the compound return. In the chart below, blue bars are years when stocks beat inflation and orange bars are years they lost to it. Orange shows direction only; it is not a warning color.

What does the model leave out?

The calculators are a planning aid, not a forecast. These are the simplifications we know about. Each one can move your answer, so leave yourself a margin.

• No tax rules. The engine does not model income tax brackets, capital gains or early-withdrawal penalties. Enter spending that already includes the taxes you expect to pay on withdrawals. The Fat FIRE calculator can add a flat effective tax rate for you, but that is a simple gross-up, not a tax calculation.
• US data only. The data covers US stocks and bonds and nothing else. If you invest elsewhere, or if the US does not repeat its own past, results can differ a lot.
• No crashes beyond history. The simulations can only replay or reshuffle the 98 years that happened, so apart from fees and the constant shift in “Match my return”, no simulated year is worse than the worst real one (for stocks, 1931 at -38.1% after inflation). There is no extra fat-tail modeling.
• Independent years in Monte Carlo. The iid bootstrap loses multi-year patterns such as momentum after crashes and mean reversion after booms. The historical test keeps them, but its cohorts overlap heavily, so 69 cohorts are far fewer than 69 independent experiments, and the most recent decades cannot yet appear as full long retirements.
• Fixed spending. Spending stays constant in real terms for life. Real retirees cut back after bad years, which flexible rules like guardrails formalize^[11]. We do not model that, which makes our results conservative for flexible spenders.
• Constant fees and returns. Fees are one flat percentage every year. The deterministic projection uses one constant real return, so its chart is a smooth line that real markets will not follow.
• Income streams are inflation-indexed. Social Security and pensions keep their real value for life. Social Security has an annual cost-of-living adjustment (3.6% for 2027^[12]), but many private pensions do not, so enter a non-indexed pension at a lower amount. Benefits are treated as certain.
• Two assets, annual steps. Only US stocks and 10-year Treasuries, rebalanced yearly. No cash, international stocks, real estate or annuities. Whole-year timing ignores when in the year things actually happen.
• Results stop at your plan-until age. We do not model longevity risk beyond the age you choose, so pick one you might plausibly reach.

What has changed in the methodology?

We log every change that can move a result here, with the date. Data refreshes (a new Damodaran year, new IRS limits) are also noted on the sources page.

This page explains our models. It is not financial advice. For decisions about your own money, consider a fee-only fiduciary adviser. See our terms and disclaimer.