Default assumptions.
Where a calculator needs a default, we use:
| Variable | Default | Basis |
|---|---|---|
| Nominal stock return | 7%/yr | Long-run S&P 500 total return, inflation-included |
| Real return (after inflation) | 4%/yr | ~3% long-run U.S. inflation removed |
| Inflation | 3%/yr | BLS CPI long-run average |
| Safe withdrawal rate | 4.0% | Bengen (1994) SAFEMAX; Trinity Study |
| Retirement horizon | 30 years | Trinity Study primary horizon |
| Bond return | 3%/yr nominal | Long-run intermediate Treasury yield |
These defaults are conservative for U.S. equities over multi-decade horizons and are clearly labelled in every tool. Users can override them on the page.
FIRE number (the 25× rule).
Used by: FIRE Calculator, Coast FIRE Calculator, Savings Rate Calculator.
= annual_expenses × 25 (when SWR = 4%)
The 4% safe withdrawal rate originates from William Bengen's 1994 paper “Determining Withdrawal Rates Using Historical Data” and was refined by the Trinity Study (Cooley, Hubbard & Walz, 1998). Both analysed historical U.S. market returns and concluded that a portfolio withdrawing 4% of its starting value, adjusted annually for inflation, had survived every rolling 30-year period in the historical record.
Limitations. The rule is U.S.-equity-heavy, assumes a 30-year horizon, and is sensitive to sequence-of-returns risk in the first decade. For early retirees with 40-50 year horizons, many practitioners use 3.0-3.5% instead. We surface this in the calculator.
Years to FIRE.
Years from a starting portfolio P, with annual contribution C, real return r, and FIRE target T:
Derived from the future-value-of-an-annuity-due formula. We use the real return (default 4%) so the FIRE target T is in today's dollars and no inflation adjustment is required.
Coast FIRE number.
Coast FIRE is the portfolio size at which compounding alone — with zero further contributions — reaches the FIRE number by traditional retirement age:
Where r is the real return (default 4%) and years_to_retirementis the time between today and the user's target retirement age. The result is the portfolio size today such that, even if you stopped contributing entirely, compounding alone reaches the FIRE number on schedule.
Savings rate & years-to-FIRE table.
Made famous by Mr. Money Mustache's 2012 article “The Shockingly Simple Math Behind Early Retirement.” Given a savings rate s (saved fraction of take-home), real return r (default 4%), and a 25× FIRE target, years to FIRE for someone starting from zero is:
Notable property: the result depends on the ratio of savings to expenses, not the absolute dollar amount of income. A 50% savings rate yields the same years-to-FIRE for a $40k earner and a $400k earner — the difference is only in lifestyle, not timeline.
Withdrawal simulator (Monte Carlo).
Used by: Withdrawal Simulator.
Runs 1,000 Monte Carlo trials per scenario. Each trial samples annual returns from a normal distribution with mean = expected return and standard deviation ≈ 16% (long-run S&P 500 volatility). The simulator is seeded with a deterministic PRNG so identical inputs always produce identical results (mulberry32, fixed seed) — meaning the “success rate” you see is reproducible.
Known caveats. A normal distribution understates fat-tail risk; real markets have more 3+ standard-deviation moves than a Gaussian predicts. Sequence-of-returns risk in the first decade of retirement matters more than the average return. We surface both caveats in the tool itself.
Debt payoff (avalanche vs. snowball).
Used by: Debt Payoff Calculator.
Two ordering strategies are simulated month-by-month:
- Avalanche. Highest interest rate first. Mathematically optimal — minimises total interest paid.
- Snowball. Smallest balance first. Slower mathematically; behaviorally validated by Kellogg School research (Gal & McShane, 2012) showing higher follow-through.
Each month: minimums are paid on every debt, the “extra payment” is applied to the targeted debt; once that debt clears, its minimum rolls into the extra payment for the next debt. We surface both strategies and the cost difference between them.
Primary sources we anchor on.
- Bengen, W. (1994).“Determining Withdrawal Rates Using Historical Data,” Journal of Financial Planning. Origin of the 4% rule.
- Cooley, Hubbard & Walz (1998).“Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable,” AAII Journal. The Trinity Study.
- Pfau, W. Multiple papers on safe-withdrawal-rate sensitivity to international data and longer horizons.
- IRS Publications 590-A & 590-B. Authoritative for IRA / Roth contribution limits, conversion rules, RMDs, and the 5-year rule.
- Bureau of Labor Statistics — CPI series. Inflation figures used in real-return defaults.
- Vanguard & Morningstar research desks. Long-run asset-class return assumptions and expense-ratio impact studies.
- Bogleheads wiki primary content. Practitioner consensus on tax-account priority order, three-fund portfolio mechanics.
Not personalized advice.
These calculators are educational projections, not predictions and not personalised financial advice. Markets do not deliver smooth 7% returns. Real outcomes depend on tax treatment, account location, portfolio composition, sequence of returns, and life events that no calculator can model. Treat the outputs as one input to a decision, not the decision itself. See the full financial disclaimer.