A plain-language reference for the assumptions, formulas, and limits behind every Fire-Calc tool. If you want to know exactly what a number means before you rely on it, this is the page to read.
Our overall approach
Three principles guide every calculator on the site. First, the math is deterministic: the same inputs always return the same outputs, and the core computation runs in your browser rather than on a server. Second, assumptions are transparent and adjustable; where a result depends on a return rate, an inflation rate, or a tax figure, we expose that input instead of burying it in a default you cannot see. Third, we lean conservative in the defaults we suggest, because a plan that survives a disappointing decade is more useful than one that only works if markets cooperate. None of the tools forecast the future or run Monte Carlo simulations that imply a false precision; they are structured what-if models that let you compare scenarios and see which assumptions actually move the answer.
FIRE, Coast FIRE, and Advanced drawdown
The retirement tools rest on the safe-withdrawal-rate idea: the share of a portfolio you can spend in the first year, then adjust for inflation, without running out over a long retirement. The familiar 4% figure traces back to William Bengen’s 1994 analysis of historical US market data and the 1998 Trinity study (Cooley, Hubbard, Walz), both of which tested 30-year retirements against past sequences of stock and bond returns. We treat 4% as a useful reference point, not a law: it was calibrated to a specific horizon and a specific history, and longer retirements or weaker future returns can make it too aggressive. Our FIRE calculator estimates the portfolio needed to support your spending at your chosen withdrawal rate; Coast FIRE finds the point where existing savings can compound to your goal without further contributions; and the Advanced calculator models drawdown across account types with tax-aware sequencing. Throughout, we distinguish real returns (after inflation, representing purchasing power) from nominal returns, because mixing the two is one of the most common ways a retirement projection goes wrong.
- Safe withdrawal rate: first-year spending as a percent of the portfolio, then inflation-adjusted; 4% is a starting reference, not a guarantee.
- Origin: Bengen (1994) and the Trinity study (Cooley, Hubbard, Walz, 1998), both based on historical 30-year US outcomes.
- Real vs nominal: we model returns and withdrawals in real (inflation-adjusted) terms so spending power stays comparable across years.
Compound interest and growth
The compound interest calculator isolates growth mechanics so you can see how principal, recurring contributions, time, and rate interact. It compounds on a regular schedule and applies contributions consistently across the horizon, which keeps the model easy to reason about and reproduce by hand. Because small changes in the assumed rate compound into large differences over decades, we encourage comparing at least one lower-return case rather than anchoring on a single optimistic path. The output is a clean accumulation baseline; it does not attempt to model taxes on interim gains or the drawdown behavior that the retirement tools handle separately.
Mortgage and rent-vs-buy
The mortgage calculator uses standard amortization: each scheduled payment is split between interest on the outstanding balance and principal, so early payments are interest-heavy and later ones retire principal faster. It can layer in property taxes, insurance, and extra principal to reflect true monthly cost rather than principal and interest alone. Rent-vs-buy compares long-term housing outcomes under your assumptions, including rent growth, ownership carrying costs, and the opportunity cost of a down payment. These tools deliberately do not try to predict home prices, and they cannot capture every local cost: PMI, HOA dues, special assessments, and maintenance vary widely by property and region, so we surface them as inputs or assumptions to stress-test rather than precise national figures. Break-even timing is highly sensitive to how long you actually stay, so we recommend running several stay-length scenarios.
- Amortization: payments split into interest on the balance and principal, following a standard schedule.
- Deliberately approximate: PMI, HOA dues, special assessments, and maintenance vary by property and are treated as adjustable inputs, not fixed truths.
- Break-even depends heavily on stay length and rent-growth assumptions, so compare multiple cases.
Paycheck estimates
The paycheck calculator converts gross pay into an estimate of take-home pay using bracket approximations for federal income tax alongside payroll taxes and the pre-tax deductions you enter. It is an estimate by design. Real withholding on your paycheck is governed by the details on your Form W-4, your employer’s payroll system, and IRS withholding methods (Publication 15-T), which can differ from a simplified bracket model. State and local taxes, credits, and mid-year changes add further variance. Use the result to sanity-check whether a budget target is realistic, then confirm against an actual pay stub before committing to new fixed expenses.
Debt payoff: avalanche, snowball, and rolled payments
The debt payoff calculator compares repayment strategies on the same set of balances. Both the avalanche and snowball methods require paying the minimum on every debt and directing any extra cash to one target debt at a time. Avalanche targets the highest interest rate first to minimize total interest paid; snowball targets the smallest balance first to create early wins and momentum. Critically, both strategies roll freed-up minimum payments forward: once a debt is cleared, the minimum payment it used to consume is added to the extra payment applied to the next target debt, so the amount going toward debt accelerates as balances disappear. This rolled-payment behavior is what makes a focused strategy meaningfully faster than paying minimums, and it is how the calculator models both methods. The tool also warns you when the payment you have entered is not enough to make progress against interest, meaning the debt would never be paid off at that rate.
- Avalanche: highest interest rate first, minimizing total interest cost.
- Snowball: smallest balance first, prioritizing motivation through early payoffs.
- Rolled payments: a cleared debt’s freed minimum is added to the next debt’s payment, so payoff speeds up over time.
- Never-payoff warning: if the entered payment cannot outpace interest, the calculator flags that the balance would not be retired.
Equity and job-offer comparisons
The equity and job-offer tools project grants such as RSUs, stock options, ESPP shares, and restricted stock along a single share-price path so competing packages can be compared on a consistent basis. They separate vested from unvested value and show after-tax alongside gross value. The tax treatment is simplified: ordinary income is applied when full-value grants vest, capital-gains rules are applied to later appreciation, and specialized rules such as ISO/AMT interaction, QSBS eligibility, ESPP discounts, and 83(b) elections are approximated rather than computed to the dollar. Vesting schedules and cliffs are modeled, but real outcomes also depend on liquidity events, dilution, and filing details that no calculator can know in advance. Treat the ranking as a defensible comparison under your stated assumptions, not a promise about any single exit.
What these tools deliberately do not model
Being explicit about the edges is part of being trustworthy. Our calculators do not predict markets, interest rates, home prices, or tax-law changes; they do not run probabilistic simulations; and they do not know your full personal situation. They generally do not model state and local tax nuance, one-off windfalls or shocks, health-care cost trajectories, Social Security claiming strategy, sequence-of-returns risk beyond the withdrawal-rate framing, or the behavioral reality that people adjust spending when markets move. When a factor is out of scope, we would rather say so than imply a precision the model does not have.
Testing, release checks, and updates
The engines are covered by a committed parity test suite that locks expected outputs across a range of scenarios and runs before releases, so an accidental change to a formula is caught rather than shipped. Our release process also runs a copy review, a type check and production build, and route checks that confirm each page and redirect behaves as intended. We have maintained the content and engines since early 2025 and record notable changes in a public changelog, which lets you tell whether a saved scenario predates a math change. When rules or figures that we cite move, or when we find a mistake, we update the affected tools and note material corrections. If you spot something wrong, report it through the /contact page with the inputs you used so we can reproduce and fix it.
Sources and citations
We prefer primary and government sources, and we cite the foundational research behind the withdrawal-rate tools by name so you can read it yourself.
- Bengen, W. (1994), "Determining Withdrawal Rates Using Historical Data," Journal of Financial Planning — origin of the 4% rule.
- Cooley, Hubbard, Walz (1998), the "Trinity study" on sustainable withdrawal rates over 30-year retirements.
- IRS — federal tax and withholding guidance, including Publication 15-T (irs.gov).
- Consumer Financial Protection Bureau — debt, budgeting, and mortgage education (consumerfinance.gov).
- U.S. Securities and Exchange Commission investor education — investing and compounding basics (investor.gov).